Computing stable models by program transformation

In analogy to the Davis--Putnam procedure we develop a new procedure for computing stable models of propositional normal disjunctive logic programs, using case analysis and simplification. Our procedure enumerates all stable mofels without repetition and without the need for a minimality check. Since it is not necessary to store the set of stable models explicitly, the procedure runs in polynomial space. We allow clauses with empty heads, in order to represent truth or falsity of a proposition as a one--literal clause. In particular, a clause of form $\sim A \rightarrow$ expresses that $A$ is contrained to be true, without providing a justification for $A$. Adding this clause to a program restricts its stable models to those containing A, without introducing new stable models. Together with $A \rightarrow$ this provides the basis for case analysis. We present our procedure as a set of rules which transform a program into a set of solved forms, which resembles the standard method for presenting unification algorithms. Rules are sound in the sense that they preserve the set of stable models. $A$ subset of the rules is shown to be complete in the sense that for each stable model a solved form can be obtained. The method allows for concise presentation, flexible choice of a control strategy and simple correctness proofs

Set-Theoretic Completeness for Epistemic and Conditional Logic

The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the language (the semantics), a collection of axioms and rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness results. Here we consider an approach that is more common in the economics literature, which works purely at the semantic, set-theoretic level. We provide set-theoretic completeness results for a number of epistemic and conditional logics, and contrast the expressive power of the syntactic and set-theoretic approachesComment: This is an expanded version of a paper that appeared in AI and Mathematics, 199

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Representing First-Order Causal Theories by Logic Programs

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic.Comment: 29 pages. To appear in Theory and Practice of Logic Programming (TPLP); Theory and Practice of Logic Programming, May, 201

Structural Resolution with Co-inductive Loop Detection

A way to combine co-SLD style loop detection with structural resolution was found and is introduced in this work, to extend structural resolution with co-induction. In particular, we present the operational semantics, called co-inductive structural resolution, of this novel combination and prove its soundness with respect to the greatest complete Herbrand model.Comment: In Proceedings CoALP-Ty'16, arXiv:1709.0419