Related papers: Decidability of the Clark's Completion Semantics f…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
We prove the decidability for a class of languages which extend BST and NP-completeness for a subclass of them. The languages BST extended with unordered cartesian product, BST extended with ordered cartesian product and BST extended with…
This paper describes a generalization of Clark's completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to…
Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
In temporal logics, a central question is about the choice of modalities and their relative expressive power, in comparison to the complexity of decision problems such as satisfiability. In this tutorial, we will illustrate the study of…
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…
Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not…
We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible…
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…