The abstract interpretation of programs relates the exact semantics of a programming language to a finite approximation of those semantics. In this article, we describe an approach to abstract interpretation that is based in logic and logic programming. Our approach consists of faithfully representing a transition system within logic and then manipulating this initial specification to create a ...

There are two kinds of bisimulation, namely crisp and fuzzy, between fuzzy structures such as automata, labeled transition systems, Kripke models interpretations in description logics. Fuzzy bisimulations automata over a complete residuated lattice have been introduced by ?iri? et al. 2012. Logical characterizations (respectively, logics) the [0,1] with Gödel t-norm provided Fan 2015 Nguyen 202...

With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representat...

Prolog is originally rooted in logic with the elegant mapping: “programs = formulas, execution = proof search”. Constraint logic programming extends Prolog to program in a richer structure than mere Herbrand terms. The underlying constraint solving engine requires either to be built-in or to add coroutines mechanisms that are not in the scope of logical reading. Implementations add other non-lo...

All promiment examples of first-order predicate fuzzy logics are undecidable. This leads to the problem of the arithmetical complexity of their sets of tautologies and satisfiable sentences. This paper is a contribution to the general study of this problem. We propose the classes of first-order core and ∆-core fuzzy logics as a good framework to address these arithmetical complexity issues. We ...

Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning withvague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whetheran ontology representing a knowledge domain is consistent. Surprisingly, not much is known about thecomplexity of this problem for semantics based on complete De Morgan lattices. T...

Sieber has described a model of PCF consisting of continuous functions that are invariant under certain ((nitary) logical relations, and shown that it is fully abstract for closed terms of up to third-order types. We show that one may achieve full abstraction at all types using a form of \Kripke logical relations" introduced by Jung and Tiuryn to characterize-deenability.