All posts under category "Computer Science / Logic"
For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank-1 logics enjoy a sh
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time an
We define two transformations from term rewriting systems (TRSs) to context-sensitive TRSs in such a way that termination of the target system implies outermost termination of the original system. In the transformation based on 'context extension', each outermost rewrite step is modeled by exactly o
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs allow one to describe classical data-structures (possibly with
Term unification plays an important role in many areas of computer science, especially in those related to logic. The universal mechanism of grammar-based compression for terms, in particular the so-called Singleton Tree Grammars (STG), have recently drawn considerable attention. Using STGs, terms o
We propose a logic for true concurrency whose formulae predicate about events in computations and their causal dependencies. The induced logical equivalence is hereditary history preserving bisimilarity, and fragments of the logic can be identified which correspond to other true concurrent behaviour
Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general class of monads called monads with arities, so that not onl
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof for most modal logics below first order is still too ambiti
This paper presents a novel technique for state space reduction of probabilistic specifications, based on a newly developed notion of confluence for probabilistic automata. We prove that this reduction preserves branching probabilistic bisimulation and can be applied on-the-fly. To support the techn
Cyber-Physical Systems (CPS) are systems composed by a physical component that is controlled or monitored by a cyber-component, a computer-based algorithm. Advances in CPS technologies and science are enabling capability, adaptability, scalability, resiliency, safety, security, and usability that wi
Fixed point combinators (and their generalization: looping combinators) are classic notions belonging to the heart of lambda-calculus and logic. We start with an exploration of the structure of fixed point combinators (fpc's), vastly generalizing the well-known fact that if Y is an fpc, Y(SI) is aga
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a general non-deterministic Kripke-style semantics is provided
In earlier work, we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern [1988] by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is n
The Plan Execution Interchange Language (PLEXIL) is a synchronous language developed by NASA to support autonomous spacecraft operations. In this paper, we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance logical engine. The rewriting logic semantics is by itself a formal i
The theme of the paper is the use of commutative Frobenius algebras in braided strict monoidal categories in the study of varieties of circuits and communicating systems which occur in Computer Science, including circuits in which the wires are tangled. We indicate also some possible novel geometric
Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full abstraction is a highly desirable property, indicating a pe
We study the international standard XACML 3.0 for describing security access control policy in a compositional way. Our main contribution is to derive a logic that precisely captures the idea behind the standard and to formally define the semantics of the policy combining algorithms of XACML. To gua
In this paper, we present a model based on relations for bigraphical reactive systems [Milner09]. Its defining characteristics are that validity and reaction relations are captured as traces in a multi-set rewriting system. The relational model is derived from Milner's graphical definition and direc
We formally specified a program logic for higher-order procedural variables and non-local jumps with Ott and Twelf. Moreover, the dependent type systems and the translation are both executable specifications thanks to Twelf's logic programming engine. In particular, relying on Filinski's encoding of
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new frameworks. The approach we present here is different: We show how
Most available tools propose simulation frameworks to study models of biological systems, but simulation only explores a few of the most probable behaviours of the system. On the contrary, techniques such as model checking, coming from IT-systems analysis, explore all the possible behaviours of the
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms is computed from the solution to the corresponding system of
A choreography describes a transaction in which several principals interact. Since choreographies frequently describe business processes affecting substantial assets, we need a security infrastructure in order to implement them safely. As part of a line of work devoted to generating cryptoprotocols
In this paper we extend PALPS, a process calculus proposed for the spatially-explicit individual-based modeling of ecological systems, with the notion of a policy. A policy is an entity for specifying orderings between the different activities within a system. It is defined externally to a PALPS mod
We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's trace encoding which is universally defined for any function
In a functional calculus, the so called Omega-rule states that if two terms P and Q applied to any closed term <i>N</i> return the same value (i.e. PN = QN), then they are equal (i.e. P = Q holds). As it is well known, in the lambdabeta-calculus the Omega-rule does not hold, even when the eta-rule (
We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead presented as a rewriting system. We discuss how our method allow
We construct an example of proof within the main formal system from arXiv:1010.4760v3, which is intended to capture the bisimulation equivalence for non-deterministic first-order grammars, and show that its conclusion is semantically false. We then locate and analyze the flawed argument in the sound
We give the first elementary construction of equivalent formulas in Hanf normal form. The triply exponential upper bound is complemented by a matching lower bound.
The paper starts from the observation on the complexity of the manipulation of fuzzy processes that increases very rapidly with the extents of the processes representation. Therefore, a productive approach is to divide the problem into smaller parts, treated separately and then the results combined.
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of parameters in a standard way. The free right algebra F(L, C) o
The BioAmbients calculus is a process algebra suitable for representing compartmentalization, molecular localization and movements between compartments. In this paper we enrich this calculus with a static type system classifying each ambient with group types specifying the kind of compartments in wh
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results, expressiveness and proof systems.
We develop an incremental-tableau-based decision procedure for the multi-agent epistemic logic MAEL(CD) (aka S5_n (CD)), whose language contains operators of individual knowledge for a finite set Ag of agents, as well as operators of distributed and common knowledge among all agents in Ag. Our table
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