Commonsense Knowledge, Ontology and Ordinary Language

Int. J. Reasonin g-based Intelli gent Systems, Vol. n, N o. m, 2008 43 Copyright © 200 8 Inderscience Enterprises Ltd. Commonsen se Knowledge, Ontology and Ordinary Language Walid S. Saba American Institute s for Resear ch, 1000 Thomas J efferson Street, NW, Was hington, D C 20007 USA E-mail: wsaba@air .org Abstract: Over two d ecades ago a “quite r evolution” overwhelmingly replaced knowledge- based approaches in natural language processing (NLP) by quantitative (e.g., statistical, corpus-based, machine lear ning) methods. Al though i t is our firm belief that purely quanti- tative approaches cannot be the only paradigm for NLP, dissatisfaction wi th purely engi- neering ap proaches to the constructi on of lar ge knowledge bases for NLP are somewhat justified. In this paper we hope to demonstrate that both trends are partly misguided and that the time has come to enrich logical s emantics with an ontological s tructure that reflects our commonsense view of the wor ld a nd the way we talk a bout in or dinary language. In this paper it will be demonstrated tha t a ssuming such an ontological structure a number of challenges in the semantics of natural language ( e.g., metonymy, int ensionality, copredica- tion, nominal compounds, etc.) can be properly and uniformly address ed. Keywords: Ontology, compositional semantics, commonsense knowledge, reasoning. Reference to this paper should be made a s follows: Saba, W. S. (2008) ‘Commonsense Knowledge, Ontology a nd Ordinary La nguage’, Int. Journal of Reasoning-based Intelligent Systems , Vol. n, No. n, pp.43–60. Biographical notes: W. Saba received his PhD i n Co mputer Science fr om Ca rleton Uni- versity in 1 999. He is c urrently a Pr incipal Software Engineer at the American Institutes for Research in Washington, DC. Prior to this he was in academia where he taught c omputer science at the Universi ty of Windsor and the A merican Univers ity of B eirut (AUB). For over 9 y ears he was also a c onsulting software engineer where worked at s uch places as AT&T Bell Labs, MetLife and Cognos, Inc. His r esearch interests ar e in n atural l anguage processing, ontology, t he repr esentation of and r easoning with c ommonsense k nowledge, and intelligent e-commerce agents. 1 INTRODUCTION Over two decades a go a “quite re volution”, as Charniak (1995) once calle d it, overw helmingl y re placed knowled ge- based appr oaches in natural l anguage proces sing (N LP) b y quantitative (e.g., statist ical, corpus-base d, machine learn- ing) methods. In recent years, however, the ter ms ontology , semantic web and sema ntic c omputing have been in vogue, and re gardless of how these t erms are being used ( or mis- used) we belie ve that this ‘semantic c ounter re volution’ is a positive trend since c orpus-based approache s t o NLP, while useful in some language processing tasks – see (N g a nd Zelle, 1997) f or a good re view – cannot ac count for c ompo- sitionality and productivit y in nat ural l anguage, n ot to men- tion the complex inferential patterns t hat occur in ordinary language use. The inferences we have in m ind here can be illustrated b y the following ex ample: (1) Pass that car will you. a. He is really annoy ing me. b. They are really annoying m e. Clearly, speakers of ordinar y language can easil y infer that ‘he’ in (1a) refer s to the person driving [ that] car, wh ile ‘they’ in (1b) is a reference to the pe ople ridin g [ that] car. Such infere nces, we belie ve, cannot the oretically be lear ned (how m an y such exa mples w ill be needed? ), and are thus beyond the ca pabilities of an y qua ntitative a pproach. On the other hand, and although it is our f irm belief that purel y quantitative appr oaches cannot be the onl y para digm for NLP, dissatisfacti on with purel y engineering appr oaches to the constructi on of large k nowledge bases f or NLP (e.g. , Lenat and G hua, 1990) are somewhat justified. While lan- guage ‘understa nding’ i s f or the most part a commonse nse ‘reasoning’ process at t he pr agmatic le vel, a s e xample ( 1) illustrates, the knowledge structure s that a n NLP s ystem must utilize should have sou nd linguistic and ontol ogical underpinnings and must be f o r malized if we ever hope to build scalable systems (or as John Mc Carthy once said, if we e v er hope t o buil d system s that we can ac tuall y u nder- stand!). Thus, a nd a s we h ave ar gued elsewhe re (S aba, 2007), we believe that bot h trends are partl y mis guided and that the time has come to enr ich logical se mantic s with a n 44 W . S . SABA ontological structure t hat re flects our c ommonsense view of the world and the wa y we talk about i n ordinar y lan guage. Specificall y , we ar gue that very little progre ss within l ogical semantics have been made i n the past several y ears due to the fa ct that these s ystems ar e, for the most part, mere s y m- bol manipulati on systems that are devoid of an y c ontent. In particular, in such s ystems where there is hardly a ny l ink between sema ntics a nd our commonsense view of the world, i t is quite difficult to envision how one can “un- cover” the considerable amount of content that i s clearl y implicit, but almost neve r ex plicitly stated in our e veryda y discourse. Fo r exa mple, consider the following: (2) a. Sim on is a rock. b. The ham sandwich w ants a beer . c. Sheba is articul ate . d. Jon bought a brick house . e. Carlos likes to play bridge . f. Jon enjoyed the book . g. Jon visited a house on every street . Although the y tend to use the least nu mber of words t o con- vey a particular thought (per haps for computationa l eff ec- tiveness, as G ivon ( 1984) once suggested), s peakers of ordi- nar y language clearl y understand the sente nces in (2) as follows: (3) a. Simon is [as s olid as] a rock . b. The [person eati ng the] ham sandwich wants a beer . c. Sheba is [an] articulate [person]. d. Jon bought a brick [ -made] house . e. Carlos likes to play [the game] bridge . f. Jon enjoyed [re ading/writing] the book . g. Jon visited a [ different] house on every street. Clearl y , an y compositi onal semantics must somehow ac- count for this [missing text], a s such sentences are quite common and are not at all ex otic, far fetched, or contrived . Linguists and semantici sts have usuall y dea lt with such se n- tences by i nvestigatin g various phenomena such as meta- phor (3a); metonymy (3 b); textual entailment (3c); nomina l compounds (3d); lexic al am biguity (3e ), c o-predication (3f); and q uantifier sco pe am biguity ( 3g), t o na me a few. H ow- ever, and alt hough they see m to have a comm on denomina- tor, it is somewhat surprisin g that in lookin g at the literature one finds that these phenome na have been stu died quite independently; to the point where there is ver y little, if a ny, that seems to be common between t he various proposa ls that are o ften su ggested. In our opinion this state of affairs is ver y problema tic, as the prospect of a distinct paradigm f or every single phen omenon in natural l anguage cannot be realistically c ontemplate d. M o re over, and as we hope t o demonstrate in this paper, w e believe that there is in deed a common s ymptom underlying these (and other) challenging problems in the sem antics of na tural language. Before we make our case, let us at thi s ver y earl y junc- ture sugge st this i nformal expla nation f or the missing text in (2): SOLID i s (one of) the most salient feature s of a Rock (2a); people, and not a sandwich, have ‘wa nts’ a nd EAT i s the most salient relati on that holds betwee n a H uman and a Sandwich (2b) 1 ; Human is t he t y pe of object of w hich AR- TICULATE is the m ost salient propert y (2c); ma de-of is the most salient r elation between an Ar tifact (and conse- quently a Ho use ) and a substance ( Brick ) ( 2d); PLAY is t he most salient relation that holds betwee n a Human and a Game , and not some struct ure (and, bridge is a game); a nd, finally, in the (poss ible) worl d that we live in, a Ho use can- not be locate d on more than one Stre et . The point of this informal explanati on is to suggest t hat the proble m underl y- ing most challen ges in t he semanti cs o f natural la nguage seems to lie in semantic formalism s t hat em ploy logics that are mere abstract s ymbol m anipulation systems; systems that are devoi d of an y ontological c ontent. What we suggest, instead, i s a compositional semantics that is grounded in commonsense metaph ysics, a semantics that views “l ogic as a language”; that is, a l ogic t hat has conte nt, an d ont ological content, in particular , as has been re cently and quite c on- vincingly advocated b y Cocchiarella ( 2001). In the r est of t he pa per we wi ll first propose a semantics that i s grounded in a str ongly -t yped ontolo gy that reflects our c ommonsense view of real ity a nd the w ay we t alk about it in ordinar y language; subse quently, we w ill formalize the notion of ‘salient pr operty’ and ‘salie nt relation’ a nd suggest how a str ongly-typed c ompositional system can p ossibl y utilize such information to explai n s ome complex phenom- ena in natural langua ge. 2 A TYPE SYSTEM FOR ORDINARY LANGUAGE The utility of enrichi ng t he ont ology of l ogic by introducin g variables and quantificati on is well-known. For example, q r p ) ( ∧ ⊃ is not e ven a valid state ment in propositional logic, when p = a ll humans are mortal , q = S ocrates is a huma n and r = Socrates i s m ortal . In first-order lo gic, however, this inference is easily produced, by exploiting one important aspect of v aria bles, namely, their sco pe . However, and as will s hortly be demonstrated, copredica- tion, metonymy and various other problems that are rele- gated t o inte nsionalit y in natural language are due the fa ct that another important aspect of a variable, namely its t y pe, has not been exploited. In particular, muc h like scope con- nects various predicates within a f ormula, when a variable has more t han one t ype in a si ngle sc ope, type unification is the pr ocess by w hich one ca n discover implicit relati onships that ar e not e xplicitl y stated, but are in fact implicit in t he type hierarchy. To be gin wit h, theref ore, we shall first intro- duce a type s y ste m that is assumed in the r est of the paper. 2.1 T he Tree of Language In Type s and O ntology Fred Sommers (1963) su ggested several years ago that there is a strongly t yped ont ology t hat seems to be implici t in all t hat we sa y in ordinary spoken 1 In addition to EAT , a Human can of course also BUY , SELL , MAKE , P RE- PARE , WATCH , or HOLD , et c. a Sand wich . Why EAT mi ght b e a more salient relation b etween a Pe rson and a Sandwich is a question w e sha ll p ay con- siderable attention to below. COMMONSEN SE KNOWLED GE , ONTOLOGY A ND ORIDNA RY LANGUAGE 45 language, w here tw o objects x an d y are consi dered t o be of the sa me type iff the set of monadic predicates that are sig- nificantly ( that is, truly or fal sel y but n ot a bsurdl y ) predica- ble of x i s equivale nt t o t he set of pre dicates t hat are si gnifi- cantly pre dicable of y . T hus, while t hey make a ref erences to four distinct classes (sets of object s), f or an ontologist interested in t he relati onship between ontology and natural language, t he noun phrases in (4) are ulti mately referring to two types onl y, na mely Cat and Number : (4) a. an old cat b. a black cat c. an even number d. a prime num ber In other words, whether we make a ref erence to an old cat or t o a black cat , in both insta nces we are ulti matel y speak- ing of objects tha t are of the same t ype; and thi s, according to Sommers, is a reflection o f t he fact that the set of m o- nadic predicates in our natu ral language that are signif i- cantly predicable of old cat s is exactl y the same set that is significantly predicable of blac k cats. Let u s say sp ( t , s ) i s true if s is the set of predicate s t hat a re significantl y predi- cable of som e t ype t , a nd let T re present the set of all t ypes in our ontolog y , the n (5) a. φ ≡ ∃ ≠ ( )[ ( , ) ( )] ∈ ∧ s sp s s t t T b. sp 1 2 1 2 1 2 ≡ ∃ , [ ( ) ( , ) ( , ) ( )]  s ∧ ∧ ⊆ ⊆ ⊆ ⊆ s t t s s sp s s s s c. sp 1 2 1 2 1 2 = = ≡ ∃ , [ ( ) ( , ) ( , ) ( )] s ∧ ∧ s t t s s sp s s s s That is, to be a t y pe ( in the ontology) is t o have a n on-empt y set of pre dicates that are significantl y pre dicable (5a) 2 ; and a type s is a subtype of t iff the set of predicates that a re significantly predica ble of s is a subset of the set of predi- cates that are significantly predicable o f t (5b); c onse- quently, t he identit y of a c oncept (and t hus c oncept similar- ity) is well-defined as given by (5c). N ote here that accord- ing t o (5a), abstrac t objects such as e vents , states , proper- ties , activities , proces ses , etc. are also pa rt of our ontolog y since the set of predicat es tha t is signific antly predicabl e of any suc h object is not empty. For example, one can always speak of an imm inent event, or an event t hat was c ancelled , etc., that is sp etc. { } Event IMM INENT CANCELLED ( , , , ). In addition t o e vents, abstract objects such as states and proc- esses, etc. can al so be predicated; for exa mple, one ca n al- ways sa y idle o f a some state, and one always s peak o f starting and terminating a process, etc. In our r epresentation, t herefore, c onc epts belong to tw o quite distinct cate gories: ( i ) ontological concepts, such as Animal , Substance , Entity , Artefact , Ev ent , State , etc., which are a ssumed to ex ist i n a subsumpti on hierarch y , and where the fact that an object o f t ype Human is (ultimatel y ) an ob- ject of type Entity is expres sed as  Hum a n Ent ity ; an d ( ii ) logical concepts, which are the pr operties (that ca n be said) of and the relations (that can h old) bet ween ont ological con- cepts. To illustrat e the difference (and the relation) between the two, consider the following: 2 Interestingly , (5a) seems to be related to what Fodor (1 998) meant by “to be a concept is to be locked to a p roperty”; in that it seems that a genuine concept (or a Sommers’ type) is one that `owns’ at least one word/predica te in the language. (6) 1 : ( :: ) old Entity r x 2 : ( :: ) heavy Physical r x 3 : ( :: ) hu ngry Living r x 4 : ( :: ) articulate Hum an r x 5 : ( :: , :: ) Hum an Artifact r x y make 6 : ( :: , :: ) manufacture Hum an Instrum ent r x y 7 : ( :: , :: ) ride Hum an Veh icle r x y 8 : ( :: , :: ) drive Hum an Car r x y The pre dicates in ( 6) are su pposed to re flect the fa ct t hat in ordinary sp oken we langua ge we can sa y O LD of any Entit y ; that we sa y HEAVY of objects that are of t ype Physic al ; that HUNGR Y is said of objec ts that ar e of t ype Livin g ; tha t AR- TICULATE is said of objects that must be of type Human ; that make is a relation t hat c an hold bet ween a Hum an and an Art efact ; t hat manufac ture is a relation t hat can hold between a H uman a nd a n Instrum ent , etc. Note t hat the type assignments in (6) i mplicitly define a t ype hierarch y as t hat shown in fi gure 1 below. Co nsequently, an d a lthough not explicitly stated in (6), in ordi nar y spoken language one ca n always attri bute the propert y HEAVY t o an object of type Car since     Car Vehicle Physical . Figure 1 The type hierarchy implied by (6) In addition to logical and ontological concepts, there a re also pr oper nouns, w hich are the names o f objects; objects that could be o f an y t ype. A pr oper noun, such as sheba , is interpreted as (7)   sheba 1 P P [( )( ( :: , ‘ ’) ( :: ))] ∃ ⇒ ∧ λ x x sheba x noo T hing t where x s Thing noo ( :: , ) is true o f s ome individual object x (which could be any T hing ), and s if (the la bel) s i s the nam e of x , a nd t is presuma bly the type of objects t hat P applies t o (to simplif y n otation, howe ver, we will often wr ite ( 7) as 1 P P ∃   [( :: )( ( :: ))] ⇒ Thing t sheba sheba sheba λ ). Consider 46 W . S . SABA now the foll owing, where ( :: ) x Huma n teache r , th at is, where TEACHER is a ssumed to be a propert y that is ordinar- ily said of objects that must be of type H uman , and where x y ( , ) BE is true when x and y are the same objects 3 : (8)   sheba is a t eacher x 1 ( :: )( ) ∃ ∃ Thing ⇒ sheba ( ( :: ) ( , )) BE x sheba x Human ∧ TEACHER This s tates t hat t here is a unique object named sheba (w hich is an object that c ould be an y Thing ), and some x such that x is a TEACHE R (and t hus must be an object of t ype H uman ), and such that sheba is that x . Since ( , ) BE sheba x , we can replace y by the constant sheba obtaining the following: (9)   sheba is a t eacher x 1 ( :: )( ) ∃ ∃ Thing ⇒ sheba ( ( :: ) ( , )) BE x sheba x Human ∧ TEACHER 1 ( :: ) ( ( :: )) ∃ ⇒ sheba sheba Thing Human TEACHER Note now that sheba is a ssociated w ith more than one t ype in a single scope. In t hese situati ons a type unification must occur, where a t ype u nification • ( ) s t between two t ypes s and t and where Q ∃ ∀ , , ∈ { } is defined (f or now) as f ollows (10) Q P Q P if Q P if Q Q P i f msr otherwise ( :: ( ))( ( )) ( :: )( ( ) ), ( ) ( :: ) ( ( )), ( ) ( :: )( :: )( ( , ) ( )), ( )( ( , )) , •    ≡  ∧ ∃ =   ⊥  R R R s t s s t t t s s t s t x x x x x x x y x y y   where R i s s ome salient rela tion that m ight exi st be tween objects of type s and objects of t y pe t . That is, i n situati ons where there is no subsumption relation between s a nd t the t y pe unification res ults in k eeping the variables of both t y pes a nd in i ntroducing some salie nt r elation betwee n t hem (we shall discuss the se situations bel ow). Going to back t o (9), the t y pe unific ation in this case i s actually quite sim ple, since Human T hing ( )  : (11)   sheba is a t eacher x 1 ( :: ) ( )( ( :: )) ∃ ∃ ⇒ sheba sheba Thing Human TEACHER 1 ( :: ( ))( ( ) ) • ∃ ⇒ sheba sheba Thing Human TEACHER 1 ( :: )( ( )) ∃ ⇒ sheba sheba Human TEACHER In t he fi nal a nal y s is, theref ore, sheba is a teacher is inter- preted as f ollows: t here is a unique object named sheba , a n object that must be o f type H uman , s uch that sheba is a TEACHER . N ote here t he clear distincti on betw een ontologi- cal concepts (such as Human ), which C occhiarella (2 001) calls first-intensi on c oncepts, and l ogical (or sec ond- intension) concepts, such as TEACHER ( x ). That is, w hat onto- logically e xist are objects of t ype Human , not t eachers, and 3 We are using the fact that, when a is a constant and P is a predicate, Pa x Px x a [ ( )] ≡ ∃ = ∧ (see Gaskin, 1995). TEACHER is a mere propert y that we ha ve come to use t o talk of obj ects of t y p e Human 4 . In other words, while t he property of bei ng a TEACHER that x ma y exhibit is acc idental (as well as tempora l, cultural-depende nt, etc.), the fact t hat some x is a n object of type Human (and t hus an Animal , etc.) is not. Moreover, a logical concept suc h as T EACHER is as- sumed to be defined by virtue of some logical expre ssion such as ( :: )( ( ) ), ϕ ∀ ≡ x x Human df TEACHER where the e x- act nature of ϕ might very well be susceptible to temporal, cultural, and other contextual f actors, dependin g on what, a t a certain point in time, a certain communit y considers a TEACHER t o be. S pecificall y, the l ogical c oncept TEACHER must be defined by some expression such as ( :: )( ( ) ∀ x x Human TEACHER ( :: )( ( ) ( ))) ≡ ∃ ∧ a a a, x Activity df teaching agen t That is, any x , w hich must be an object of t ype Human , is a TEACHER iff x is the a gent of s ome Acti vity a , where a is a TEACHING a ctivity. I t is certa inly not f or convenience, ele- gance or mere ontol ogical i ndulgence that a l ogical concept such as T EACHER must be defi ned in term s of more basic ontological ca tegories ( such as an Activity ) as c an be illus- trated by the f ollowing example: (12)   sheba is a superb teache r 1 ( :: )( ( :: ) ∃ ⇒ sheba sheba Thing Human superb ( :: )) ∧ sheba Human teacher Note that in (12), i t is sheba , and not her teachin g that is erroneousl y considered t o be superb . This is problematic o n two grounds: fir st, while SUPERB is a property t hat could apply t o objects of t ype H uman (such a s sheba ), the logica l form in (1 2) must have a reference to an object of t ype Ac- tivity , as S UPERB is a pr operty that could als o be said o f sheba ’s teaching activit y . T his poi nt i s more ac utely made when superb is r eplaced by adjecti ves such a s certified , lousy , etc., where the corresponding properties do not even apply to she ba , but are c learly modif ying sheba ’s tea ching activity (that it is C ERTIFIED , or L OUSY , et c.) We shall dis- cuss this i ssue in some detail below. Before we proceed, however, we need t o e xtend the notion of type unification slightly. 2.2 Mor e on Type Unification It sh ould be c lear by now that our ontolog y, as defined thus far, assumes a Platonic universe which admi ts the e xistence of a nything that can be ta lked about in o rdinar y language. Thus, and as also argued by Cocchiarella (1996), besides abstract obj ects, refer ence in ordinar y langua ge can be made to objects that might have or could ha ve existed, as well as to objects that might exi st sometime i n the f uture. In gen- eral, theref ore, a reference to an object ca n be 5 4 N ot rec ognizing the d ifference between logical (e.g., TEACHER ) a nd onto- logical concepts (e.g., Human ) is p erhaps the re ason why ontologies in most AI systems are rampant with multi ple inheritance. 5 We can use ◊ a to state that an object is possibly a bstract, instead of ¬  c , which is intended to s tate t hat the object is not necessarily con crete (or that it does not necessarily actually exist). COMMONSENSE KNOWLEDGE , ONTOLOGY AND ORIDNARY LANGUAG E 4 7 • a reference to a t ype (in the ont ology ) : X P X ( :: )( ( )) ∃ t ; • a refer ence to an ob ject of a certa in t y pe, an object that must have a c oncrete existence: X P X ( :: )( ( )) ∃  c t ; or • a refer ence to an ob ject of a certa in t y pe, an object that need not actuall y exist: X P X ( :: )( ( )) ¬ ∃  c t . Accordingly, and as su ggested by H obbs (1985), the above necessitates t hat a distinction be made in our logical form between mere being and c oncrete (or actual) existence. To do this we introduce a predicate ( ) Exist x which is true when s ome object x ha s a concret e (or ac tual) e xistence, a nd where a reference to an object of s ome t y pe i s initiall y as- sumed to be i mply mere being, w hile a ctual (or concrete) existence i s onl y i nferred fr om the c ontext. T he relations hip between mere being and concrete existence can be defined as follows: (13) a. X P X ∃ ( :: )( ( )) t b. c X P X ∃ ( :: )( ( ))  t X X P ( :: )( )( ( , ) ( ) ( )) ≡ ∃ ∃ x Inst x Ex ist x x ∧ ∧ t c. X P X ( :: )( ( )) ¬ ∃  c t X X P ( :: )( )( ( , ) ( ) ( )) ≡ ∃ ∀ x Inst x Ex ist x x ⊃ ∧ t In ( 13a) we ar e simpl y stating that some pr operty P is tru e of some objec t X of t ype t . Thus, while, ontologica lly, there are objects of type t that we can speak about, nothing i n (13a) entails the actual (or co ncrete) e xistence of any suc h objects. In (13b) we are statin g that the pr opert y P is tr ue of an object X of t yp e t , an object that m ust have a c oncrete ( or actual) existence (and i n particular at le ast t he instance x ); which is equivalent to saying that there is some obj ect x which is a n instance of some abstract object X , where x ac- tually exists, and where P is true of x . Finally, (1 3c) states that w henever some x , which is an instance of some abs tract object X of t ype t exists, then the pr opert y P is t rue of x . Thus, w hile ( 13a) makes a re ferenc e to a kind ( or a type in the ontology), (13b) and ( 13c) make a ref erence to s ome instance of a specific t ype, an instance that ma y or ma y not actually exi st. To simplif y not ation, theref ore, we can write (13b) and (13c) as follows, respective ly: X P X ( :: )( ( )) ∃  c t P X X X ≡ ∃ ∃ ( :: ) ( ( )) ( ) ( , ) ( ) t ∧ ∧ x Inst x Exist x P ≡ ∃ :: ( ( )) ( ) ( ) t ∧ x Exist x x X P X ( :: )( ( )) ¬ ∃  c t P X X ≡ ∃ ∀ ( :: ) ( ( )) ( ) ( , ) ( ) ⊃ t x Inst x Exist x x ∧ P ≡ ∀ :: ( ( )) ( ) ( ) ⊃ t x Exist x x Furthermore, i t shoul d be note d that x in (1 3b) is a ssumed to have actual/c oncrete existence assuming that t he pr op- ert y /relation P is act ually true of x . If the truth of P ( X ) is just a possibilit y , then so is the concrete existence o f s ome i n- stance x of X . Formall y, we have the foll owing: X P X X P X ¬ ∃ ≡ ∃ ( :: )( ( ( ))) ( :: )( ( ))   can can c c t t Finally, and since different relati ons and properties have different existence assum ptions, t he existence assum ptions implied b y a c ompound ex pression is determine d b y t ype unification, whic h is de fined a s f ollows, and w here the basic type unification ( ) • s t is that defined in (10): ( :: ( )) ( : : ( ) ) • • =   x x c c s t s t ( :: ( )) ( :: ( ) ) ¬ ¬ • • =   x x c c s t s t ( :: ( )) ( :: ( ) ) ¬ • • =    x x c c c s t s t As a f irst exa mple c onsider t he foll owing (w here te mporal and modal a uxiliaries are re presented as s uperscripts on the predicates): (14)   jon needs a computer X ∃ ∃ 1 ( : : )( :: ) ⇒ Human Compu ter jon NEED ( ( , :: )) does Thing jon X In (1 4) we are stating that some unique object name d j on , which i s of type Human d oes NEED something we call C om- puter . On the other hand, con sider now the interpretation of ‘ jon fixed a computer ’: (15)   jon fixed a com puter X 1 ( :: ) ( :: ) ∃ ∃ jon ⇒ Human Com puter ( ( , :: )) did  jon X c Th ing FIX X 1 ( :: )( :: ( )) • ∃ ∃  jon ⇒ c Hum an Com pu ter T hin g ( ( , )) did jon X FIX X 1 ( :: )( :: ) ∃ ∃  jon ⇒ c Hum an C om put er ( ( , )) did jon X FIX X 1 ( :: ) ( :: ) ∃ ∃ jon ⇒ Hum an C om put er X ( )( ( , )) ( , ) ( ) ∃ did x x x jo n X Inst Ex ist ∧ ∧ FIX ∃ ∃ 1 ( :: )( :: ) ⇒ jon x Hum an Com pu ter FIX ( ( , )) ( ) did Exist x jon x ∧ That is, ‘ jon fixed a computer ’ is interprete d as follows: there is a unique object named jon , w hich is an object of type Human , and some x of type Comput er (an x that actu- ally exi sts) such that jon did FIX x . However, consider now the following: (16)   jon can fix a comput er X 1 ( :: ) ( :: ) ∃ ∃ jon ⇒ Hum an C om put er ( ( , :: )) ¬ c an  jon X c Th ing FIX X 1 ( :: )( :: ( )) ¬ • ∃ ∃  jon ⇒ c Hum an Com p uter T hin g ( ( , ) ) can jon X FIX X 1 ( :: )( :: ) ¬ ∃ ∃  jon ⇒ c Hum an Co m put er ( ( , ) ) can jon X FIX X 1 ( :: ) ( :: ) ∃ ∃ jon ⇒ Hum an C om put er X ( ( , )) ( ) ( , ) ( ) ∀ can x x x jon X Inst Exist ⊃ ∧ FIX ∃ ∃ 1 ( :: )( :: ) ⇒ jon x Hum an Co mp ut er FI X ∀ ( ( , )) ( ) ( ) ⊃ can x Exist x jon x Essentially, ther efore, ‘ jon ca n fix a computer ’ is stat ing that whenever an obje ct x of t ype Computer exists, then j on c an fix x ; or, equivalentl y, that ‘ jon can fix any computer ’. Finally, consider the f o llowing, where i t is assumed that our ontology reflect s the comm onsense fact that we c an always speak of an A nimal cli mbing some Phys ical object:   a snake can climb a tree 48 W . S . SAB A X Y ( :: )( :: ) ∃ ∃ ⇒ Sna ke Tree X ( ( :: , : : )) ¬ ¬ can   Y c c Anim al Physical CLIMB X Y ( : : ( ))( : : ( )) ¬ ¬ • • ∃ ∃   ⇒ c c Snake An imal Tree Physical X ( ( , )) can Y CLIMB X X Y ( : : )( :: )( ( , )) ¬ ¬ ∃ ∃ can   Y ⇒ c c Snake Tree CLIMB X Y ( : : )( :: ) ∃ ∃ ⇒ Snake Tree X Y ( )( )( ( , ) ( ) ( , ) ∀ ∀ x x y x y Inst Exist Inst ∧ ∧ ( , )) ( ) can y x y Exist ⊃ ∧ CLIMB ( :: )( : : ) ∀ ∀ x y ⇒ Snake Tree ( , )) ( ( ) ( ) can x y x y Exist Exist ⊃ ∧ CLIMB That is, ‘ a s nake can climb a tree ’ i s e ssentiall y i nterpreted as any snake (if it exists) can c limb an y tree (if it exists). With this bac kground, we no w proceed t o ta ckle some interesting pr oblems in the semantics of natural langua ge. 3 SEMANTICS WITH ONTOLOGICAL CONTENT In t his sect ion we di scuss several problems in the semantic of na tural lan guage and dem onstrate the utilit y of a seman- tics e mbedded in a s trongly-typed ontology that reflects our commonsense view of rea lity and t he way we ta ke ab out i t in ordinar y language. 3.1 T ypes, Polymorphism and Nominal Modification We fi rst demonstrate t he role t y pe unification and pol ymor- phism pla ys i n nominal modificati on. C onsider t he sente nce in (1) which c ould be uttered by some one who belie ves that: ( i ) Olga is a dancer and a bea utiful person; or ( ii ) Olga is beautiful as a dancer (i.e., Olga is a dancer and she dance s beautifully). (17) Olg a is a beautiful dancer As suggested by Larson (1998), t here are two possible routes to e xplain this ambiguity: one c ould assu me t hat a noun such a s ‘dancer’ is a simple one place predicate of t y pe , e t   and ‘ blame’ this a mbiguit y on t he a djective; al- ternativel y, one could assume that the adjective is a simple one p lace predicate and blame the a mbiguit y on some sort of complexit y in the structure of the head noun ( Larson calls these alternatives A - analysis and N -anal ysis, respecti vely). In an A -analysis, an a pproach advocated b y Sie gel (1976), adjectives are assumed to belong to two classes, termed predicative and attributive, w here predica tive a djec- tives (e .g., red , small , etc.) are ta ken to be simple f unctions from entities to tr uth-values, and are t hus extensional and intersective: =       Adj Noun Adj Noun ∩ . Attributive adjectives (e. g., former , p revious , rightful , etc.), on the other hand, are f unctions from c ommon noun d enotati ons to common noun denotati ons – i.e., t hey are predicate modifi- ers of t ype , , , e t e t     , and are thus intensiona l and non- intersective ( but s ubsective:     Adj Noun Noun ⊆ ). On this view, the a mbiguit y in (17) is e xplained by posti ng two distinct l exemes ( beautiful 1 and beautiful 2 ) f or the a djec- tive beautiful , one of which is an at tributive w hile the other is a predicative adjective. In ke eping with Mont ague’s (1970) edict that similar s y nta ctic categories must have the same semantic t ype, f or this pr oposal t o work, all adjecti ves are initially assigne d the t ype , , , e t e t     where intersec- tive a djectives are considered to be subt ypes obtained b y triggering an a ppropriate meanin g postulate. Fo r exa mple, assuming t he lexeme beautiful 1 is mar ked (f o r example b y a lexical fe ature such as + INT ERSECTIVE ), then the meaning postulate P Q x Q x P x Q x ∃ ∀ ∀ [ ( )( ) ( ) ( )] ↔ beautiful ∧ does yield an intersective meaning when P is beautiful 1 ; and where a phrase s uch as `a beautiful da ncer' is inter preted as follows 6 : 1   a beautiful dancer P x x x P x ∃ [( )( ( ) ( ) ( ))] ⇒ λ dancer beautif ul ∧ ∧ 2   a beautiful dan cer P x x P x ∃ [( )( (ˆ ( )) ( ))] ⇒ λ beautiful dancer ∧ While i t does explain the a mbiguity i n ( 17), several reser va- tions have been rai sed regarding this pr oposal. As L arson (1995; 1998) notes, this a pproach e ntails c onsiderable du- plication i n the lexicon a s t his means t hat ther e are ‘dou- blets’ for all adjectives that can be ambi guous between an intersective and a non-intersecti ve meaning. An other objec- tion, raised b y McNa lly a nd Boleda (20 04), i s t hat in an A - analysis t here ar e no obvious wa y s of deter mining the c on- text in which a c ertain adjecti ve can be considere d intersec- tive. For example, t hey suggest that t he m ost natural r eading of ( 18) is t he one whe re be autiful i s de scribing O lga’s da nc- ing, although it does not modif y any n oun and is thus wrongly considere d intersective b y modifying Olga. (18) Look at Olga dance. She is beautiful. While valid in other c ontexts, in our opinion this obser va- tion does not nece ssarily h old in this specific exa mple since the res o lution of `she' must ult imately c onsider all entities in the discourse, includin g, presumabl y , the dancing act ivity that would be intr oduced by a Da v ids onian representati on of ‘Look at Olga da nce’ (this issue is disc ussed further bel ow). A more promising al ternati ve to the A -anal ysis of the ambiguity in ( 17) has been proposed by Larson ( 1995, 1998), who su ggests that beautiful i n (17) is a simple i nter- sective ad jective of t ype 〈 e , t 〉 and that the source of the a m- biguity is due to a complexit y in t he structure of the head noun. Specificall y , Lar son suggests that a deverbal nou n such a s dancer should have the Davidsonian representation ∀ = ∃ x x e e e x ∧ df DANCER DANCING AGENT ( )( ( ) ( )( ( ) ( , ))) i.e., any x is a dancer iff x is the a gent o f some dancing ac tivit y (Larson’s notati on i s slightl y different). In t his anal ysis, the ambiguity i n (1) i s attri buted to a n ambigui ty i n w hat beau- tiful is modif ying, in t hat it could be sai d of Ol ga or her dancing Activi ty . That is, (17) i s to be interpreted a s follows:   Olga is a beautiful dancer ∃ e e e olga ⇒ ∧ ( )( ( ) ( , ) dancing agent e olga ∧ ∨ ( ( ) ( ))) beautif ul beautif ul 6 Note that as an alternat ive to meanin g postulates that s pecialize inte rsec- tive adjectives to , e t   , one can perform a type-lifting operation from , e t   to , , , e t e t     (see Partee, 200 7). COMMON SENSE KNOW LEDGE , ONTOLOGY A ND ORIDNAR Y LANGU AGE 49 In our opinion, L ars on’s pr oposal is plausible on several grounds. First, i n Larson’s N -analysis there is no need f o r impromptu introducti on of a conside rable a mount of lexical ambiguity. Second, and for rea sons that are beyond the am- biguity of beautiful i n (17), and as a rgued in the interpreta- tion of example (1 2) above, there is ample e vidence that th e structure of a deverbal n oun such as dancer must admit a reference t o an abstract object, namely a danci ng Activi ty ; as, for example, in the res olution of ‘that’ in ( 19). (19) Olga is an old dan cer. She has been doing that for 30 years. Furthermore, and in addit ion t o a plausible explanati on of the ambigui t y i n ( 17), Larson’ s pr oposal see ms t o provide a plausible expla nation f or w hy ‘old’ in (4a) seem s t o be am- biguous while t he same is not true of ‘elde rly’ in ( 4b): ` old’ could be sai d of Olga or her te aching; whi le elderly is n ot an adjective t hat is ordi narily sai d of objects that are of t ype activity: (20) a. Olga is an old dancer. b. Olga is an elderly teacher. With all its apparent appeal, however, Larson’ s proposal is still la cking. For one thin g, and it presupp oses t hat some sort of type matching is what ultimate ly res ults in re jecting the subsective meaning of el derly in (20b), the details of such processes are mo re inv olved than L arson’s p roposal seems to impl y . F or example, w hile it e xplains the a mbigu- ity of beautiful in ( 17), it is not quite clear how an N - Analysis can explain w hy beautiful does n ot seem to ad mit a subsective meaning in (21). (21) Olga is a beautiful young street danc er. In fact, beautiful i n ( 21) seems t o be m odifying O lga for the same r eason the sentence i n (22a) seems to be more natura l than that in (22 b). (22) a. Maria is a clever young girl . b. Maria is a young clever girl . The se ntences in (22) exem plify what is known i n the litera- ture as adje ctive ordering restrictions (A ORs). However, despite numerous studi es of AORs (e .g., see Wul ff, 2003 ; Teodorescu, 2006), th e sl ightl y d iffering AORs t hat have been sugge sted in t he literat ure have never been formall y justified. What we hope to demonstrate below however i s that the ap parent a mbiguity of some adjecti ves and adjec - tive-ordering restrictions are both related to the nature of the ontological cate gories t hat these adjectives a pply t o i n ordi- nar y spoken la nguage. Thus, and while the general a ssump- tions in Lar son’s ( 1995; 1998) N-Analysis see m to be valid, it will be dem onstrated here that nomina l modi fication seem to be m ore in volved than has been suggested t hus far. In particular, it seems that atta ining a pr oper semantic s for nominal modificati on requires a mu ch richer type system than currentl y e mployed in formal sema ntics. First le t us begin b y showin g that the apparent ambiguit y of an ad jective such as beautiful is e ssentiall y due to t he fact that beautif ul applies to a very ge neric type t hat subsumes many others. C onsider the fol lowing, where we as- sume ( :: ) x Entity beautiful ; that is t hat BEAU TIFUL ca n be said of any E ntity :   Olga is a beautiful danc er 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an Activ ity a a Olga Hu ma n ∧ ∧ DANCING AGENT ( ( ) ( , : : ) :: :: ( ( ) ( )) a Olga Entity Entity ∨ BEAUTIFUL BEAUTIFU L Note now that, in a single sc ope, a is considere d t o be an object of t y pe Activity as wel l as an object of type E ntity , while Olga is c onsidered t o be a H uman and an En tity . This, as di scussed above, requires a pair of type unifications, ( )  Hum an Entity and ( )  Activ ity Ent ity . In t his ca se b oth type unifications succeed, resultin g in Hum an and Activi ty , respectively:   Olga is a beautiful danc er 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an Activ ity a a Olga ∧ DANCING AGENT ( ( ) ( , ) ( ( ) ( ))) a Olga ∧ ∨ BEAUTIFUL BEAUTIFUL In the final anal y sis, t herefore, ‘O lga is a beautiful dancer’ is inter preted as : Ol ga is the a gent of some dancin g Ac tivity , and either Olga is BEAUT IFUL or her DA NCING (or, of course, both). Howe ver, c onsider now the following, where ELD- ERLY is assu med to be a prope rt y that a pplies t o objects that must be of t ype Human :   Olga is an elderly teacher 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an Activ ity a a Olga Hu ma n ∧ ∧ TEACHING AGENT ( ( ) ( , :: ) :: :: ( ( ) ( ))) a Olga Hum an Hum an ∨ ELDERLY ELDERLY Note now that the t ype unification concernin g Olga i s triv- ial, while t he t ype unification concerning a w ill fail since ( Acti vity • Human ) = ⊥ , thus r esulting in the f ollowing:   Olga is an elderly teacher 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an Activ ity a a Olga Hum an ∧ TEACHING AGENT ( ( ) ( , :: ) :: ( ( ( )) • a Hum an Activ ity ∧ ELDERLY :: ( )) Olga Hum an ∨ ELDERLY 1 ( :: )( :: ) ( ( ) ∃ ∃ Olga a a ⇒ Hum an Activ ity TEACHING ⊥ a Olga Olga ∧ ∧ ∨ AGENT ELDERLY ( , ) ( ( )) 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an Activ ity a a Olga Olga ∧ ∧ TEACHING AGENT ELDERLY ( ( ) ( , ) ( )) Thus, in t he fi nal anal ysis, ‘ Olga is an el derly teacher ’ is interpreted as f ollows: there is a unique object na med Olga , an object t hat must be of t ype Huma n , and an obj ect a of type Act ivity , such t hat a is a teaching ac tivit y , O lga is th e agent of the acti vity , and such that elderly is true of Ol ga . 3.2 Adjective Ord ering Restrictions Assuming ( :: ) x Entity BEAUTIFUL - i.e., that beautiful is a property that can be sa id of objects of type Entity , then it is a 50 W . S . SAB A Figure 2. Adjectives as polymorphic functions propert y that can be s aid of a Cat , a P ers on , a City , a M ovie , a Dance , an Island , etc. Therefore, BEAUTIFUL can be thought of as a p olymorphic funct ion tha t applies to objects at several le vels a nd where the semantics o f this f unction depend on the t ype of t he object, as il lustrated in figure 2 below 7 . Thus, and alt hough BE AUTIFUL applies to objects of t y pe Entity , in saying ‘a beautiful car’, for example, the meaning of beautiful that is a ccessed is that defi ned in the t y pe P hysic al ( which could in principal be inherited f rom a supert y pe). M oreover, and a s is well known in the the o r y of programming language s, one can alwa ys perform t ype cast- ing upwar ds, but not downwards (e. g., one c an alwa ys view a Car as just a n Entity , but the converse is not true ) 8 . Thus, and assuming also t hat ( :: ) x Physical RED ; that is, assuming that RED can be sai d of Physical obj ects, the n, f or example, the t ype casting that will be require d in (23a) i s valid, while that in ( 23b) is not. (23) a. ( ( :: ) :: ) x Physical Enti ty BEAUTIFUL RED b. ( ( :: ) :: ) x Entity Physical RED B EAUTIFUL This, in fact, is precisel y w hy ‘ Jon owns a be autiful red car ’, for example, is more natural than ‘ Jon ow ns a red beautiful car ’. In general, a sequence ( ( :: ) :: ) x s t 1 2 a a is a valid sequence iff ( )  s t . Note that this is different fro m t y pe unification, in t hat t he unificati on does succe ed in both cases in ( 11). H owever, bef ore we perform t ype u nification 7 It is p erhaps worth inves tigating the relat ionship be tween the nu mber of meanings of a certain adjective (say in a res ource s uch as WordNet), and the numbe r of differe nt funct ions that one would expect to d efine for the correspond ing adject ive. 8 Techn ically, th e reason we c an alwa ys c ast up is tha t we c an a lways i g- nore additiona l in formation. Casting down, which entails adding informa- tion, is h oweve r undecidable. the directi on of the t y p e castin g must be valid. For exa mple, consider the f ollowing:   Olga is a beautiful young dancer 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an A ctivity a a Olga ∧ ∧ DANCING AGE NT ( ( ) ( , ) ) ( ( ( ) ) a Activ ity Physical Entity BEAUTIFUL YOUNG :: :: :: :: ( ( ) Olga Hum an ∨ BEAUTIFUL YOUN G :: :: )) ) Physical Entity Note now t hat t he t ype casting re quired (and thus the order of adjectives) is valid si nce ( )  Physical Entity . This means that we c an now perform the required type u nifications whi ch would proceed as f ollows: 1 ( :: )( :: ) ∃ ∃ Olga a ⇒ Hum an A ctivity a a Olga ∧ ∧ DANCING AGE NT ( ( ) ( , ) ) ( ( ( ) ) a Activ ity Physical Entity BEAUTIFUL YOUNG :: :: :: :: ( ( ) Olga Hum an ∨ BEAUTIFUL YOUN G :: :: )) ) Physical Entity Note n ow that the t ype casting re quired (and thus the order of ad jectives) is valid since ( )  Physical Entity . T his means that we can n ow perform the required t y pe unifications which would proceed a s follows:   Olga is a beautiful young dancer 1 ( :: )( :: ) , ( ) ∃ ∃ Olga a a Olga ⇒ Hum an Activity ∧ AGENT :: ( ( ( ( )) • a Activity Physical ∧ BEAUTIF UL YOUNG :: ( ( ( )) • Olga Huma n Physical ∨ BEAUTIFUL YOUN G Since ( ) • =⊥ Activity Physical , the ter m inv olving this type unification is reduced t o ⊥ , and ( ) β ⊥ ∨ to β , hence: COMMON SENSE KNOW LEDGE , ONTOLOGY A ND ORIDNAR Y LANGU AGE 51   Olga is a beautiful young dancer 1 ( :: )( :: ) , ( ) ∃ ∃ Olga a a Olga ⇒ Hum an Activity ∧ AGENT ( ( ( ))) Olga ∧ BEAUTIF UL YOUNG Note here that since BEAU TIFUL was prece ded b y YOUNG , it could ha ve not been applica ble to an abstract object of t ype Activity , but was instead re duced t o that defined at the l evel of Phy sical , and subsequently to that define d at the type Human . A valid question tha t comes t o min d here is how then do we e xpress the t hought ‘Ol ga is a young dancer a nd she dances beautifully’. The answer is that we usually make a statement such a s this: (24) Olg a is a young and beautiful dancer . Note that i n t his c ase we are e ssentially overridin g the se- quential processin g of the a djectives, and thus the ad jective- ordering restrictions ( or, e quivalently, t he t ype-casting rules!) are no more ap plicable. That is, (24) is essentiall y equivalent to tw o sentences that are processed in parallel:   Olga is a yong and beautifu l dancer ≡   Olg a is a y oun g dancer   Olg a i s a beaut iful dan cer ∧ Note now that ‘beaut iful’ w ould a gain have an intersec tive and a subsective m eaning, alt hough ‘ young’ will onl y appl y to Olga due to t ype constraints. 3.3 Int ensional Verbs and Coordination Consider the f ollowing sentences a nd their corresp onding translation into standard first-order l ogic: (25) a.   jon fo und a u nicorn ( )( ( ) ( , )) ∃ x x j on x ⇒ ∧ UNICORN FIND b.   jon sought a unicorn ( )( ( ) ( , )) ∃ x x jon x ⇒ ∧ UNICORN SEEK Note that ( )( ( )) ∃ x x UNICORN can be infe rred in both cases, although it is clear that ‘ jon sought a unicorn’ shoul d not entail the existence of a u nicorn. In a ddressing this problem, Montague (1960) suggested t reating seek as an intensional verb that more or less has t he meaning of ‘tr ies to find’; i.e. a verb of t ype 〈 〈 〈 〉 〉 〈 〉 〉 e t t e t , , , , , using the tools of a higher- order intensional logic. To handle contexts w here there are intensional as well a s extens ional verbs, mechani sms s uch as the ‘t ype li fting’ operation o f Part ee and Rooth (198 3) were also introduced. The type lifting operation essent ially coerces the t y p es i nto the l owest t ype, the as sumption being that if ‘ jon s ought a nd f ound’ a unicorn, then a unicorn t hat was initiall y s ought, but subseque ntly found, must hav e concrete existence. In add ition to unnecessary complicati on o f the logical form, we believe t he same i ntuition be hind the ‘ type lifti ng’ operation, whic h, as also note d b y (Kehler et. al. , 1995) a nd Winter (2007), fails in mixed contexts c ontaining more tha n tow verbs, can be ca ptured without the a priori separation of verbs int o intensional and e xtensional one s, and in particular since most ver bs seem to function i ntensionall y and extensionall y depending on the context. To illustrate this point further consi der the foll owing, where it is assumed that ( :: , :: ) paint x y Hum an Physical ; that is, it is assumed that the object of paint does not necessaril y (although it might) exist: (26)   jon pa inted a dog 1 ( :: )( :: ) ∃ ∃ jon D ⇒ Hum a n Dog ( ( : : , :: )) did pain t jon D Human P hysical 1 ( :: ) ( :: ( )) • ∃ ∃ ⇒ jon D Hum a n Dog P hysica l ( ( , )) did pain t jon D 1 ( : : )( :: ) ( ( , )) ∃ ∃ did ⇒ jon D j on D Hum a n D og paint Thus, ‘ Jon painted a dog ’ s impl y states that some unique object na med jon , which is an object of t ype H uman painted something w e ca ll a Do g . H owever, let u s n ow a ssume ( : , :: )  own x y c Human Entity ; that is, if som e Human owns some y then y must act ually exist. Conside r now all the ste ps in the interpretation of ‘ j on painted his dog ’: (27)   jon p ainted his dog 1 ( :: )( :: ) ∃ ∃ j on D ⇒ Hu m a n Do g ( ( :: , :: )  own jon D c Human Physical ( :: , :: )) jon D Hum an En tity ∧ paint 1 ( :: )( :: ) ∃ ∃ j on D ⇒ Hu m a n Do g ( ( , :: ( ) ) ( , )) •  own paint ∧ jon D jon D c Physical Enti ty 1 ( :: )( :: ) ∃ ∃ j on D ⇒ Hu m a n Do g ( ( , :: ) ( , ))  own pai nt jon D jon D c Phy sical ∧ 1 ( :: )( :: ( )) • ∃ ∃  ⇒ jon D c Hu m a n D og Ph ysic al ( ( , ) ( , ) ) jon D j on D ∧ own paint 1 ( :: )( : : ) ∃ ∃  ⇒ jon D c Hu m an D og ( ( , ) ( , )) jon D jon D ∧ own paint Thus, that while painting something does not e ntail its e xis- tence, owning something does, an d the t ype unification of the conjunction y ie lds the desired result. As given by the rules concerning e xistence a ssumptions given in ( 13) above, the final interpretation sh ould now be pr oceed as f ollows:   jon p ainted his dog 1 ( :: ) ( :: ) ∃ ∃ ⇒ jon D Hum an Dog ( )( ( ) ( ) ∃ d Inst d, D Exist d ∧ ( , ) ( , )) ∧ ∧ own paint jon d jon d 1 ( :: ) ( :: ) ∃ ∃ ⇒ jon d Hum an Do g ( ( ) ( , ) ( , ) ) Exist d jon d jon d ∧ ∧ o wn p a int That i s, ‘ jon painted his dog ’ is interprete d as follows: t here is a unique object name d jon , which is an obj ect of t ype Human , some object d which of t ype Dog , such that d act u- ally exists, jo n does OWN d , and jon di d PAINT d . The point of t he above exa mple was to illustrate that the notion of intensional verbs ca n be capt ured i n t his si mple f ormalism without the t ype liftin g operati on, particula rl y si nce an ex- tensional inter pretation might a t times be implied even if an ‘intensional’ verb does not c oexist w ith an extensiona l verb in the same context. As a n illustrati ve example, let us as- 52 W . S . SAB A sume x y ( : : , :: ) Hum an Even t plan ; that is, that it always makes se nse t o sa y that some Human i s planni ng (or did plan) som ething we call an Event . Consi der now the f ollow- ing: (28)   jon p lanned a trip jon e 1 ( :: )( :: ) ∃ ∃ ⇒ Entity Trip jon e ( ( : : , :: )) Hum an Eve nt plan jon e jon e 1 ( :: )( :: ( ))( ( , )) • ∃ ∃ plan ⇒ Entity Trip Event jon e jon e 1 ( :: )( :: )( ( , )) ∃ ∃ ⇒ Entity Trip plan That is, ‘ j on planned a trip ’ simply states t hat a s pecific object that must be a Huma n has plan ned somethi ng w e call a Tr ip ( a trip that mi ght not ha ve ac tuall y h appened 9 ). Assuming e ( :: )  c Even t lengthy , however, i.e ., that LENGTHY is a property t hat is ordi narily sa id of an (e xisting) Event , then the inter pretation of ‘john planned the le ngthy trip’ should proce ed as follows:   jon planne d a lengthy tri p jon e 1 ( :: )( :: ) ∃ ∃ ⇒ Hu m an Tr ip jon e e ( ( , :: )) ( :: ))  plan lengthy c Eve nt Ev ent ∧ Since ( ( )) ( ) • • = • =    c c c Trip Ev ent Event T rip Ev ent Trip w e finally get the f ollowing: (29)   jon p lanned a lengthy trip jon e 1 ( :: )( :: ) ∃ ∃  ⇒ c Entity Trip jon e e ( ( , ) ( ) ) ∧ pl an l e ngth y jon e 1 ( :: )( :: ) ∃ ∃ ⇒ Ent ity Trip jon ( ( , ) ( ) ( )) e e e Exist ∧ ∧ pl an len gthy That is, there is a specific Hum an na med jon that ha s planned a Tr ip , a trip that actuall y e xists, a nd a trip t hat was LENGTHY . Finally, i t shoul d be noted here tha t the trip in (29) wa s f inall y consi dered to be a n existing Event due to other i nformation c ontained in the same se ntence. In gen- eral, however, this inf ormation can be c ontained in a larger discourse. For exam ple, in interpreting ‘ John planned a trip. It was lengthy ’ the resolut ion of ‘it’ w ould f orce a retracti on of t he t ypes inferred i n proces sing ‘ J ohn planned a trip ’, as the information that follows w ill ‘bring down’ the af ore- mentioned Tr ip f rom ab stract to a ctual e xistence ( or, f rom mere being t o c oncrete existence). Th is discourse leve l analysis is cle arly be yond t he scope of this paper , but rea d- ers interested in t he c omputational details of s uch processes are referr ed to (van Deemter & Peter s, 1996). 3.4 Met onymy a nd Copr edication In addition to so-called intensiona l verbs, our proposal seems to als o appropriately h andle other situa tions that, on the s urface, seem t o be addre ssing a different issue. F or e x- ample, consider the f ollowing: 9 Note th at it is the Tri p (even t) th at did n ot necessa rily happen , not the plannin g ( Activity ) for i t. (30) Jon read the boo k and then he burn e d it. In Asher and Pustejovsk y (2005) it is ar gued that t his is an example of what the y t erm copredicat ion; whic h is t he pos- sibility of incomp atible pre dicates to be applie d t o the same type of object. It is ar gued tha t in (30), for example, ‘b ook’ must ha ve what is called a dot type, which is a complex structure t hat i n a sense carrie s the ‘inf ormational c ontent’ sense (which is ref erenced when it is being r ead) as well as the ‘physical object’ sense (w hich is referenced when it is being burned). Ela borate m achiner y is then intr oduced to ‘pick out’ the ri ght sense in the ri ght c ontext, and a ll in a well-typed c ompositional lo gic. But t his appr oach presu p- poses that one can e numerate, a priori, all possible uses of the w ord ‘book’ in ordinar y la nguage 10 . Moreover, c opredi - cation seems to be a special case of me tonymy, where the possible relati ons that could be i mplied are i n fact much more c onstrained. An approac h t hat can e xplain both no- tions, a nd hope fully w ithout introducing much c omplexity into the logical f orm, should then be m ore desirable. Let us first suggest t he following: (31) a. x y ( :: , :: ) Hum an C onte nt read b. x y ( :: , :: ) Huma n Physical burn That is, w e a re assu ming her e that s peakers of ordi nary la n- guage u nderstand ‘read’ and ‘burn’ as follows: it always makes sense to speak of a Human tha t read some C ontent , and of a Human that burned s ome Physical object. Consider now the following: (32)   jon read a book and then h e burned it jon b 1 ∃ ∃ ⇒ Entity Boo k ( :: )( :: ) jon b Huma n Conten t ( ( :: , :: )) read jon b Huma n P hysical ∧ ( :: , :: )) burn The t y pe unification of jon i s straightforward, as t he agent of BUR N and R EAD are of t he same type. Concerning b , a pair of t ype unificati ons • • Book Physical Con te nt (( ) ) must occur, resulting in t he following: (33)   jon read a book and th en h e burned it jon b 1 ∃ ∃ • ⇒ Entity Book Con tent ( :: )( :: ( )) jon b jon b ( ( , ) ( , ))) read burn ∧ Since no su bsumption rela tion exists between B ook an d Content , t he two variables are k e pt and a salient relatio n between them is introduce d, resulting i n the following: (34)   jon read a book and th en h e burned it jon b c 1 ∃ ∃ ∃ ⇒ Entity Bo ok Content ( :: )( :: )( :: ) b c jon c jon b ( ( , ) ( , ) ( , )) R read burn ∧ ∧ That is, there i s s ome unique object of type Human ( named jon ), s ome Book b , some c ontent c , such that c is the Con- tent of b , and such that j on read c and burned b . 10 Simi lar presupp ositions are also made in a h ybrid (connecti on- ist/symboli c) ‘sen se modulation ’ approac h des cribed in (Rais-Ghas em & Corrivea u, 1998). COMMON SENSE KNOW LEDGE , ONTOLOGY A ND ORIDNAR Y LANGU AGE 53 As in the case of c opredication, t ype unifications intr o- ducing a n a dditional variable and a salient relation occurs also in sit uations where we have what we refer to a s meton- ymy. To illustrate, c onsider th e following example: (35)   the ham sadnwich wa nts a bee r x y 1 ( :: )( :: ) ∃ ∃ ⇒ Ham Sa ndw ich Beer x y ( ( :: , :: )) Huma n T hing want x y 1 ( :: )( :: ( )) ∃ ∃ • ⇒ Ham San dwich B eer Thing x y ( ( :: , )) Hum an want x y 1 ( :: )( :: ) ∃ ∃ ⇒ Ham Sa ndw ich Beer x y ( ( :: , )) Hum an want While the t y pe unification between Beer and Thing is t rivial, since ( )  Bee r T hing , the t y pe u nification involving the vari- able x fails since there i s no subsu mption re lationshi p be tween Human a nd HamS andwich . As argued a bove, in these situati ons both t ypes ar e kept and a salie nt r elation be tween them is intro- duced, as follows:   the ham sadnwich wa nts a bee r x z y 1 1 ( :: )( : : )( :: ) ∃ ∃ ∃ ⇒ Ham Sa ndw ich Hum an Bee r x z z y ( ( , ) ( , )) R ∧ want where msr = R Hum an S an dwich ( , ) , i.e., where R is as- sumed to be some salie nt rel ation ( e.g., EAT , OR DER , etc.) that e xists betwee n an object of type Hu man , a nd a n object of type Sandwic h (more on this below). 3.5 T ypes and Salient Relations Thus far we have assumed the existe nce of a functi on msr s t ( , ) that ret urns, if it e xists, the most salient relati on R between two ty pes s and t . Before w e discuss what thi s function m ight l ook like, we need to extend the notion of assigning ontological types to pr operties and relations slightly. Let us first reconsider (1), which is repeate d below: (36) Pass that car, will you. a. He is real ly annoying me. b. Th ey are really annoying me. As disc ussed a bove w e ar gue that ‘he’ in ( 36a) refers to ‘ the person dri ving [ that] c ar’ while ‘ they’ in (36b) refers to ‘ the people riding in [that] car’. The que stion here is this: al- though t here are many possible relati ons betwee n a Person and a Car (e.g., DR IVE , R IDE , M ANUFACTUR E , D ESIGN , MAKE , etc.) how is it that DRIVE i s the one that mos t s peak- ers assume i n ( 36a), w hile R IDE is t he one most speakers would assu me in (36b)? Here’s a pla usible answer: • DRIVE i s more salie nt than RIDE , MANUFACTU RE , DE - SIGN , MAK E , etc. since the other r elations a ppl y higher- up in the hierarch y; that is, the fact that we MAKE a Car , for exa mple, is not due to Car , but to the fact that M AKE can be said of an y Artif act and  Car Artif act ( ) . • While DRIVE is a more salient relation between a Hu- man and a Car t han R IDE , most spe akers of ordinary English understand the DR IVE r elation to hold between one Hum an and one Car (at a spec ific p oint in time), while R IDE is a relati on t hat holds between ma ny ( sev- eral, or few! ) people and one car. Thus, ‘the y’ in ( 36b) fails to unif y with DR IVE , a nd the next most salient rela- tion must be pic ked up, which in thi s case is R IDE . In other w ords, the t ype assignments of DRIVE and R IDE are understood b y speake rs of ordinar y language as follows: x y Huma n Car ( :: , :: ) 1 1 drive x y Hum an Car ( :: , :: ) 1+ 1 ride With thi s bac kground, let us now suggest how t he function msr ( , ) s t that picks out the most salient relation R bet ween two types s and t is c omputed. We say ( , ) pap t p when t he propert y P applies to objects of type t , and ( , , ) rap s t r w hen the relation r holds be- tween objects of t ype s and objects of type t . We define a list ( ) lpap t of all properties that ap ply to objects of t y pe t , and ( , ) lrap s t of a ll relations that hold be tween objects of type s and objects of t ype t , as f ollows: (37) = ( ) [ ( , )] lpa p t pa p t p p | m n m n = 〈 〉 ( , ) [ , , ( , , )] lrap s t rap s t r r | The li sts (of lists) * ( ) lpap t and * ( , ) lrap s t c an now be inductively define d as follows: (38) * ( ) [ ] = lpap Thing = * * ( ) ( ) : ( ( )) lpap t lpap t lpap sup t * ( , ) [ ] = lrap s Thing = * * ( , ) ( , ) : ( , ( )) lrap s t lrap s t lrap s sup t where e s ( : ) is a list t hat re sults f rom attac hing the object e to the fr ont of the (ordered) list s , and where ( ) sup t returns the imme diate ( and si ngle!) parent of t . Finall y, we now define t he fu nction m n ( , ) 〈 〉 msr s t which returns most the salient relati on betwee n objects of type s and t , with c on- straints m and n , respective ly, as follows: m n ( , ) ( [ ]) ( ) 〈 〉 = ≠ ⊥ msr s t if s then h ead s else where a b a m b n = 〈 〉 ≥ ≥ ∈ | ∧ ∧ * [ , , ( , ) ( ) ( )] s lrap s t r r Assuming now the ont ological a nd logical concepts sh own in figure 1, for exa mple, then * ( ) l pa p Hum an [[ , .. .], [ , .. .], [ , . ..], ,[ , ...], ...] = articulate hungry heavy old * ( , ) lra p Human Car [[ , 1 , 1 , ...],[ , 1 , 1 , ...], , . ..] + = 〈 〉 〈 〉 drive ride Since these lists a re ordere d, the degree to w hich a propert y or a rela tion i s salient is in versel y relate d to the posit ion of the proper ty or the relation in the list. Thus, for example, while a Human ma y drive , ride , make , buy , sell , build , etc. a Car , drive is a more sal ient relation bet ween 54 W . S . SAB A a Human a nd a Car than ride , whic h, i n turn, is more sali- ent tha n manufacture , make , etc. M oreover, assuming the above sets we have 1 1 〈 〉 = Hum an Car ( , ) msr drive 1 1 + 〈 〉 = Huma n Car ( , ) msr ride which essentiall y says drive is the most salie nt r elation in a c ontext where we are spea king of a si ngle H uman and a single Car , and ri de i s the most salient r elation betwee n a number of pe ople a nd a Car . Note now tha t ‘they ’ in (36b) can be interpreted as f ollows:   They are annoying m e they me ( :: ( ))( :: ) ∃ • ∃ Hum a n Car Hum a n ⇒ 1+ 1 they me ( ( , )) annoying they c m e ∃ ∃ ∃ Hum a n Car Hum an ⇒ ( :: )( :: )( :: ) 1+ 1 they c they me ∧ ( ( , ) ( , )) riding annoying It should be clear fr om the ab ove t hat type unificati on and computing the most salient rel ation be tween two ( ontologi- cal) t y pe s i s w hat dete rmines that Jon enjoyed ‘reading’ the book in (39a), and e njoyed ‘watchin g’ the movie in (39b). (39) a. Jon enjoyed th e book. b. Jon enjoyed the movi e. Note howeve r that i n additi on to READ , an object o f t ype Human ma y also WR ITE , BUY , S ELL , etc a Book . Similarly, in addition to WA TCH , an object of t y pe Hum an may als o CRITI- CIZE , D IRECT , PROD UCE , etc. a M ovie . Although this issue is beyond the scope of the current paper we simpl y note that picking out the most salient r elation is stil l deci dable d ue to tow differences betwee n READ / WRI TE and WATCH / D IRECT (or WATCH / PR ODUCE ): ( i) the number o f people that u sually read a book (watch a movie) is much greater tha n the num- ber of people t hat usually wr ite a book (direct/ produce) a movie, an d salie ncy is i nversel y proportional to t hese num- bers; and (ii) our ontol ogy typically has a specific name f or those who write a b ook (author), and those who direct (di- rector) or pr oduce (producer) a movie. 4 ONTOLOGICAL TYPES AND THE COPULAR Consider the following sente nces involving two differe nt uses of the copular ‘ is’: (40) a. Willia m H. Bonney is Billy the Kid. b. Liz is famous. The copular ‘is’ in (40a) is usuall y referred to as the ‘is o f identity’ while that in (40b) as the ‘ is of predication’ a nd the standard first- order logic translation of t he sente nces in (4 0) is usually gi ven by (41a) and (41b), r espectively (usin g w hb for William H. Bonney and btk for Bill the Kid ): (41) a. whb btk = b. Famous L iz ( ) However, we argue that ‘is’ is not a mbiguous but, like any other r elation, it can oc cur in c ontexts in w hich an addi- tional sa lient relation is i mplied, depending on the types of the objects invol ved. Thus, we ha v e the f ollowing: (42)   whb is btk 1 1 ∃ ∃ BE ( :: )( :: )( ( , )) whb btk w hb btk ⇒ Hum an Huma n 1 1 ( :: )( :: )( ( , )) ∃ ∃ ⇒ Huma n Hu m an EQ whb btk whb btk Note that si nce both objects ar e of the same t ype, BE in (42) is triviall y translate d into an equalit y. However, consider now the following: (43)   liz is f amous 1 ∃ ∃ ( :: )( :: ) liz p ⇒ Hum an Prope rty BE ( ( ) ( :: , :: ) ) fame ∧ p liz p Hum an Prop erty As we have done thus far, since no su bsumption relation exists between Hum an and P roperty , some salient relation must be intr oduced, where the most salie nt relation bet ween an object x and a propert y y is HAS ( x , y ), mea ning that x has the property y :   liz is f amous 1 ∃ ( :: ) ⇒ liz Hum an ∃ HAS ( :: )( ( ) ( , )) fame p p liz p Propert y ∧ Thus, sa ying that ‘ Liz is famous ’ is sa ying that there is some unique object named Liz , an object o f t y pe H uman , and some Propert y p , such that Liz ha s that propert y. A similar analysis yields the f ollowing interpretations: (44) a.   aging is in evitabl e 1 1 ∃ ∃ ( :: )( :: ) x y ⇒ Process Prope rty HAS ( ( ) ( ) ( , ) ) aging inevitabili ty x y x y ∧ ∧ b.   fame is desirable 1 1 ∃ ∃ ( :: )( :: ) x y ⇒ Propert y Prop erty HAS ( ( ) ( ) ( , )) fame des irabil ity x y x y ∧ ∧ c.   sheba is dead 1 1 ∃ ∃ IN ( :: )( :: )( ( ) ( , )) death x y y x y ⇒ ∧ Hum an St ate d.   jon is aging 1 1 ∃ ∃ ( :: )( :: ) jon y ⇒ Hum an P rocess GT ( ( ) ( , )) aging y x y ∧ That is, t he Pr ocess of AGING has the P roper ty of being in- evitable (4 4a); the Propert y FA ME has t he ( other) Pr operty of being DESRIBA LE ( 44b); sheba is in a ( physical) State cal led DEATH (4 4c); and, fi nally, j on is going through ( GT ) a Pr oc- ess called AG ING (44d). Finall y, c onsider the f ollowing well-known example (due , we believe, t o Barbara Pa rtee): (45) a. The temp erature is 90. b. The temperature is rising. c. 90 is rising. It has been argued that such s entences re quire a n inte nsional treatment since a p urely extensiona l treatment w ould mak e COMMON SENSE KNOW LEDGE , ONTOLOGY A ND ORIDNAR Y LANGU AGE 55 (54a) and (45b) err oneousl y entail ( 45c). H owever, we be- lieve that the embed ding of ontological t ypes i nto the pr op- erties and relations yi elds th e correct entailments wi thout the nee d f or complex higher-order intensi onal f ormalisms. Consider the f ollowing: 90   the temperature is 1 1 ∃ ∃ ( :: )( :: ) Te mp eratu re Measu re x y ⇒ 90 ( ( , ) value y ( :: , :: )) ∧ BE x y Te mp eratu re M easu re Since no subsumption relati on exits between an object of t y pe T emperatur e a nd an obj ect of t ype Me asure , the t ype unification in BE ( x , y ) shoul d result in a salient relati on between the two t ypes, as foll ows; (46) 90   the temperature is 1 1 ∃ ∃ ( :: )( :: ) x y ⇒ Te mp eratu re Measu re 90 x y HAS ( ( , ) ( , )) value y ∧ On the other hand, c onsider now the following: (47)   the temperature is rising 1 1 x y ∃ ∃ BE ( :: )( :: )( ( , )) x y ⇒ Te m pera ture P rocess Again, as no subsumption rela tion exist s betwe en an object of t ype Temp erature and an object of t ype Pr ocess , some salient relation between the t wo is introduce d. However, in this case the salient relation is qu ite diff erent; in partic ular, the relation is that of x -going-thr ough the State y : (48)   the temperature is rising 1 1 ∃ ∃ ( :: )( :: ) x y ⇒ Te m pera ture Pro cess GT ( ( ) ( , )) rising y x y ∧ Note now t hat (46) a nd ( 48) yield the following, which es- sentiall y sa ys that ‘the temperatur e is 90 and it is r ising’: 1 1 ∃ ∃ ∃ ( :: )( :: )( :: ) Te mp eratu re Meas ure Proce ss x y z 90 ( ( ) ( , ) risin g value z y ∧ ( , ) ( , ))) ∧ ∧ GT HAS x y x z Finally, note t hat uncoverin g the ont ological commit ments implied b y the se ntences in (4 5a) and (54b) will not result in the erroneous entail ment of (45c). Contrar y to the sit uation in (45 ), however, uncovering the ont ological commitments implied b y some sentences should some times a dmit s ome valid entail ments. For e xam- ple, consider the f ollowing: (49) a . exercising is wis e. b. jon is exercising. c. jon is wise. Clearl y , ( 49a) an d (49b) should entail (4 9c), al though one can hardly think of attrib uting the property W ISE t o an Ac tiv- ity ( EXERC ISING ). Let us see how we mi ght explain this ar- gument. We start with the si mplest: (50)   jon is exercising jon act 1 1 ( :: )( :: ) ∃ ∃ ⇒ Hum an A ctivi ty act act jo n ( ( ) ( , )) ∧ exer cising agent Let us now consi der the following: (51)   exercising is wise a a ( :: )( ( ) ∀ ⇒ Activ ity exe rc ising p p 1 ( :: ) ( ( ) ∃ ⊃ Propert y wisdom a p ( :: , )) HAS Hum an ∧ That is, an y exer cising Act ivity has a pr operty, namel y wi s- dom , which is a pr opert y that ordinaril y an object of t y pe Human ha s. N ote, however, that a t ype unificati on for the variable a must now occur: (52)   jon is exercising a a ( :: ( ))( ( ) • ∀ ⇒ Activ ity Hu ma n exercising p ∃ 1 ( :: ) ⊃ Propert y p a p ( ( ) ( , )) HAS wisdom ∧ The most salient relation betw een a Huma n and an Ac tivity is that of age ncy – t hat is, a human is t ypicall y the a gent of an activity: (53)   jon is exercising a x a ( :: )( :: )( ( ) ∀ ∀ ⇒ Activ ity Hum a n exercising a x p 1 ( , ) ( : : ) ∃ ⊃ Propert y ∧ agent p a p ( ( ) ( , )) HAS ∧ wisdom Essentially, t herefore, we get the f ollowing: an y h uman x has the pr operty of being wise whenever x is the a gent of an exercising acti vity. Note now that (5 0), (53) and modes ponens results in the following, which is the meaning of ‘ jon is wise ’: jon 1 ( :: ) ∃ Hum an p p x p 1 ( :: )( ( ) ( , )) ∃ HAS wisdom ∧ Prope rty Finally, note that the inferen ce i n (49) was proven valid only afte r uncove ring the mis sing text, since ‘ exercising is wise ’ was e ssentiall y inter preted as ‘ [an y huma n t hat per- forms the activit y of] exercising is wise ’. 5 CONCLUDING REMARKS If the main busi ness of semanti cs is to explai n how linguistic constructs relate t o the world, then semantic analysis of natural la nguage text is, indi rectl y , an at tempt a t uncovering the se miotic ontol ogy of comm onsense knowledge, and part icularly t he bac kground knowledge that seems to be implicit in all that we say in our ever yday discourse. While thi s i ntimate relations hip betwee n language and the w orld is g ener ally accepted, sema ntics (i n all its paradigms) ha s traditionall y proceede d i n one direction: by first sti pulating an assume d set of ontol ogical 56 W . S . SAB A commitments f o llowed b y some machiner y t hat i s supp osed to, somehow, model m eanings in terms of that stipulated structure of realit y. With the gross mismatch bet ween the trivial ontological commitments of our se mantic formalisms a nd the r eality of the world these formalisms p urport to represent, it is not surprising therefore that challenges i n the semantics of natu- ral language are rampant. However, as correctl y observed by H obbs ( 1985), se mantics could becom e nearl y tri vial if it was grounded in an ontologic al structure that i s “is omorphic to the wa y we talk a bout t he world”. The obvious question however is ‘how does one arrive a t this ontological structure that implicitly unde rlies all that we s a y in everyda y dis- course?’ One plausible ans wer is the (see mingly circular) suggestion that the semantic an alysis of natural language should itself be used to unc over this struct ure. In this re gard we strongl y agree with Dumme tt (1991) who states: We must not tr y t o resolve the metaphysical questions first, and t hen c onstruct a meaning- theory in light of t he answers . We should investi- gate how our language actually f unctions, and how we can construct a workable s ystematic de- scription of how it func tions; the answers t o those questions will then determine the answers to the metaphysical ones. What t his suggests, and c o rre ctl y so, in our opinion, is t hat in our effort to understan d the complex and i ntimate relationship betwee n ordina ry language an d ever yday commonsense knowledge, one could, as als o su ggested in (Bateman, 1995), “use langua ge as a tool for uncoverin g the semiotic ontolog y of c ommonsense” since ordinary language is the best k nown theory we have of ever yday knowledge. To avoid this seeming c ircularit y (in wa nting this ont ological struc ture t hat w ould trivialize semantics; while at the same t ime suggesting that semantic a nalysis should itself be used as a guide to uncoveri ng thi s ontological structure), w e su ggested here performin g semantic analysis from the ground up, assuming a minimal (almost a trivial a nd ba sic) ontology, in t he hope of b uilding up t he ontology as we go guided by the result s of the semantic ana lysis. The advanta ges of th is approach are: ( i ) the ontology thus constructe d as a result of this proces s would not be invented, as is the case i n most appr oaches to ontology (e. g . , Lenat, & G uha (1990); G uarino ( 1995); a nd Sowa ( 1995)), but w ould instead be di scovered fr om what is in fact implicitly a ssumed in our use of lan guage in everyda y discourse; ( ii ) the semantics of several natural language phe nomena s hould a s a result be come tri vial, since the semantic anal ysis was itse lf the source of the unde rlying knowledge str uctures (in a se nse, t he semantics w ould have been done bef ore we even started!) Throughout this paper we have tried to demonstrate t hat a number of challen ges in the semantics of na tural lan guage can be easily tac kled if semantics i s grounde d in a strongl y- t y ped ont ology t hat reflects our commonsen se view of the world and the wa y w e tal k a bout it in ord inar y lan guage. 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