Tight Logic Programs

This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets. Francois Fages showed that if a logic program satisfies a certain syntactic condition, which is now called ``tightness,'' then its stable models can be characterized as the models of its completion. We extend the definition of tightness and Fages' theorem to programs with nested expressions in the bodies of rules, and study tight logic programs containing the definition of the transitive closure of a predicate.Comment: To appear in Special Issue of the Theory and Practice of Logic Programming Journal on Answer Set Programming, 200

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

Intelligent Instantiation and Supersafe Rules

In the input languages of most answer set solvers, a rule with variables has, conceptually, infinitely many instances. The primary role of the process of intelligent instillation is to identify a finite set of ground instances of rules of the given program that are "essential" for generating its stable models. This process can be launched only when all rules of the program are safe. If a program contains arithmetic operations or comparisons then its rules are expected to satisfy conditions that are even stronger than safety. This paper is an attempt to make the idea of an essential instance and the need for "supersafety" in the process of intelligent instantiation mathematically precise

Temporal Phylogenetic Networks and Logic Programming

The concept of a temporal phylogenetic network is a mathematical model of evolution of a family of natural languages. It takes into account the fact that languages can trade their characteristics with each other when linguistic communities are in contact, and also that a contact is only possible when the languages are spoken at the same time. We show how computational methods of answer set programming and constraint logic programming can be used to generate plausible conjectures about contacts between prehistoric linguistic communities, and illustrate our approach by applying it to the evolutionary history of Indo-European languages. To appear in Theory and Practice of Logic Programming (TPLP)

On the Semantics of Gringo

Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be easily explained in terms of stable models in the sense of the original definition of this concept and its straightforward generalizations. Manuals written by designers of answer set solvers usually explain such constructs using examples and informal comments that appeal to the user's intuition, without references to any precise semantics. We propose to approach the problem of defining the semantics of gringo programs by translating them into the language of infinitary propositional formulas. This semantics allows us to study equivalent transformations of gringo programs using natural deduction in infinitary propositional logic.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke

On Equivalence of Infinitary Formulas under the Stable Model Semantics

Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same stable models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming. To appear in Theory and Practice of Logic Programming (TPLP)

Fages' Theorem and Answer Set Programming

We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as smodels and dlv is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelae is discussed as an example

On Program Completion, with an Application to the Sum and Product Puzzle

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 completion of a program then we may be able to find standard models of these axioms by running an answer set solver. As an example, we apply this "reverse completion" procedure to the Sum and Product Puzzle.Comment: Submitted to the 2023 International Conference on Logic Programmin