Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Answer Sets for Consistent Query Answering in Inconsistent Databases

A relational database is inconsistent if it does not satisfy a given set of integrity constraints. Nevertheless, it is likely that most of the data in it is consistent with the constraints. In this paper we apply logic programming based on answer sets to the problem of retrieving consistent information from a possibly inconsistent database. Since consistent information persists from the original database to every of its minimal repairs, the approach is based on a specification of database repairs using disjunctive logic programs with exceptions, whose answer set semantics can be represented and computed by systems that implement stable model semantics. These programs allow us to declare persistence by defaults and repairing changes by exceptions. We concentrate mainly on logic programs for binary integrity constraints, among which we find most of the integrity constraints found in practice.Comment: 34 page

A Program-Level Approach to Revising Logic Programs under the Answer Set Semantics

An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that A is in K * A. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs

Minish HAT: A Tool for the Minimization of Here-and-There Logic Programs and Theories in Answer Set Programming

[Abstract] When it comes to the writing of a new logic program or theory, it is of great importance to obtain a concise and minimal representation, for simplicity and ease of interpretation reasons. There are already a few methods and many tools, such as Karnaugh Maps or the Quine-McCluskey method, as well as their numerous software implementations, that solve this minimization problem in Boolean logic. This is not the case for Here-and-There logic, also called three-valued logic. Even though there are theoretical minimization methods for logic theories and programs, there aren’t any published tools that are able to obtain a minimal equivalent logic program. In this paper we present the first version of a tool called that is able to efficiently obtain minimal and equivalent representations for any logic program in Here-and-There. The described tool uses an hybrid method both leveraging a modified version of the Quine-McCluskey algorithm and Answer Set Programming techniques to minimize fairly complex logic programs in a reduced time

Symmetries in logic programs

We investigate the structures and above all, the applications of a class of symmetric groups induced by logic programs. After establishing the relationships between minimal models of logic programs and their simplified forms, and models of their completions, we show that in general when deriving negative information, we can apply the CWA, the GCWA, and the completion procedure directly from some simplified forms of the original logic programs. The least models and the results of SLD-resolution stay invariant for definite logic programs and their simplified forms. The results of SLDNF-resolution, the standard or perfect models stay invariant for hierarchical, stratified logic programs and some of their simplified forms, respectively. We introduce a new proposal to derive negative information termed OCWA, as well as the new concepts of quasi-definite, quasi-hierarchical and quasi-stratified logic programs. We also propose semantics for them