Related papers: Fages' Theorem and Answer Set Programming
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear…
Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…
FL$_\mathrm{ew}$-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability, between FL$_\mathrm{ew}$-terms and…
Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by so-called argumentation frameworks (AFs) and the reasoning…
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…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the…
Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
In answer set programming, two groups of rules are considered strongly equivalent if they have the same meaning in any context. Strong equivalence of two programs can be sometimes established by deriving rules of each program from rules of…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we…
Some normal logic programs under the answer set (stable model) semantics lack the appealing property of "cautious monotonicity." That is, augmenting a program with one of its consequences may cause it to lose another of its consequences.…
Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…