We discuss the use of model building for temporal representations. We chose Polish to illustrate our discussion because it has an interesting aspectual system, but the points we wish to make are not language specific. Rather, our goal is to develop theoretical and computational tools for temporal model building tasks in computational semantics. To this end, we present a first-order theory of time and events which is rich enough to capture interesting semantic distinctions, and an algorithm which takes minimal models for first-order theories and systematically attempts to ``perturb'' their temporal component to provide non-minimal, but semantically significant, models.
In this paper we discuss the use of model building for temporal representations. We chose Polish to illustrate the main points because (in common with other Slavic languages) it has an interesting aspectual system, but the main ideas are not language specific. Rather, our goal is to provide theoretical and computational tools for temporal model building tasks. To this end, we present a first-order theory of time and events which is rich enough to capture interesting semantic distinctions, and an algorithm which takes minimal models for first-order theories and systematically attempts to "perturb" their temporal component to provide nonminimal, but semantically significant, models.
The work has been implemented in a modified version of the Curt architecture. This architecture was developed by Blackburn and Bos [2] to illustrate the interplay of logical techniques useful in computational semantics. Roughly speaking, the Curt architecture consists of a representation component (which implements key ideas of Montague semantics [10]) and an inference component. In this paper we have used a modified version of the representation component (based on an external tool called Nessie written by Sébastien Hinderer) which enables us to specify temporal representations using a higher-order logic called T Y 4 . However, although we shall briefly discuss how we build our temporal representations, the main focus of the paper is on the other half of the Curt architecture, namely the inference component.
Inference is often though of simply as theorem proving. However one of the main points made in [2] is that a wider perspective is needed: theorem proving should be systematically coupled with model building and the Curt architecture does this. Model building takes a logical representation of a sentence and attempts to build a model for it; to put it informally, it attempts to return a simple picture of the world in which that formula is true. This has a number of uses. For example, as is emphasized in [2], model building provides a useful positive test for consistency; if a model for a sentence can be built, then that sentence is consistent (this can be useful to know, as it enables us to prevent a theorem prover fruitlessly searching for a proof of inconsistency). Moreover, in subsequent papers, Johan Bos and his co-workers have demonstrated that model building can be a practical tool in various applications (see for example [6,5,4]).
The work described here attempts to develop a Curt style architecture rich enough to handle natural language temporal phenomena. So far we have concentrated on the semantic problems raised by tense and aspect. We have developed a first-order theory of time and events, which draws on ideas from both [9] and [3]. Although these theories were developed for English, we believe the underlying ideas are more general, and to lend support to this claim we shall work here with Polish.
As we shall see, however, more than a theory of time and events is required. Model builders typically build the smallest models possible, but such models may not be suitable for all tense and aspectual combinations, which often underspecify the temporal profile of the situations of interest. We thus provide an algorithm which takes as input a first-order theory, a first-order formula, and a model for the theory and formula, and systematically attempts to “perturb” the temporal part of the model to find non-minimal but semantically relevant models.
In this section, we shall discuss the logical modeling of tense and aspect, drawing on some simple examples from Polish, and informally introduce a temporal ontology of time and events which will let us express temporal and aspectual distinctions in a precise way. The formal definition of a theory over this temporal ontology (which draws on ideas from [3] and [9]) will be given in Section 4.
Consider the following four Polish sentences:
- Piotr pospaceruje 2. Piotr pokochal Aline
The first sentence refers to a walking event and adopts a perfective point of view: it insists on the fact that the mentioned action will be terminated at some point in the future. The second sentence mentions an eventuality of loving and also adopts a perfective point of view. However, the reading of this sentence differs from the previous one. The first sentence insisted on the termination of the event, whereas the second one insists on its beginning. In other words, the second sentence has an inchoative reading. This is because the verb “kocha” from which “pokochac” is derived is a state verb, and perfective state verbs have inchoative readings in Polish. So the second sentence means that at some point in the past Piotr started to love Alina.
The last two sentences, which are also perfective, both refer to the termination of a writing event which is located in the past. The difference between these two sentences concerns the way the writing event terminated. In the “napisac” variant, an idea
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