Related papers: A Well-Founded Semantics for FOL-Programs

Computability logic (CoL) is a formal theory of interactive computation. It understands computational problems as games played by two players: a machine and its environment, uses logical formalism to describe valid principles of…

In this note we consider the problem of introducing variables in temporal logic programs under the formalism of "Temporal Equilibrium Logic" (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators.…

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with…

Program semantics can often be expressed as a (many-sorted) first-order theory S, and program properties as sentences $\varphi$ which are intended to hold in the canonical model of such a theory, which is often incomputable. Recently, we…

Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic…

Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…

We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…

Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…

Formal Semantics and Distributional Semantics are two important semantic frameworks in Natural Language Processing (NLP). Cognitive Semantics belongs to the movement of Cognitive Linguistics, which is based on contemporary cognitive…

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…

We show how definite extended logic programs can be used for defining and reasoning with rough sets. Moreover, a rough-set-specific query language is presented and an answering algorithm is outlined. Thus, we not only show a possible…

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…

The Curry-Howard correspondence is about a relationship between types and programs on the one hand and propositions and proofs on the other. The implications for programming language design and program verification is an active field of…

In this paper we adapt the definitions and results from Apt and Vermeulen on `First order logic as a constraint programming language' (in: Proceedings of LPAR2001, Baaz and Voronkov (eds.), Springer LNAI 2514) to include important ideas…

We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…

We propose a new method for mining frequent patterns in a language that combines both Semantic Web ontologies and rules. In particular we consider the setting of using a language that combines description logics with DL-safe rules. This…