Communicating answer set programs

Answer set programming i s a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules

Characterizing and Extending Answer Set Semantics using Possibility Theory

Answer Set Programming (ASP) is a popular framework for modeling combinatorial problems. However, ASP cannot easily be used for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, where this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP, in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been accepted for publication in Theory and Practice of Logic Programming, Copyright Cambridge University Pres

The DLV System for Knowledge Representation and Reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.Comment: 56 pages, 9 figures, 6 table

Possibilistic Nested Logic Programs

We introduce the class of possibilistic nested logic programs. These possibilistic logic programs allow us to use nested expressions in the bodies and the heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibilistic logic is defined. We show that this new semantics for possibilistic logic programs is computable by means of transforming possibilistic nested logic programs into possibilistic disjunctive logic programs. The expressiveness of the possibilistic nested logic programs is illustrated by scenarios from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded of vagueness and qualitative information

Disjunctive Logic Programs with Inheritance

The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP< is provided, which is shown to generalize the Answer Set Semantics of disjunctive logic programs. The knowledge modeling features of the language are illustrated by encoding classical nonmonotonic problems in DLP<. The complexity of DLP< is analyzed, proving that inheritance does not cause any computational overhead, as reasoning in DLP< has exactly the same complexity as reasoning in disjunctive logic programming. This is confirmed by the existence of an efficient translation from DLP< to plain disjunctive logic programming. Using this translation, an advanced KR system supporting the DLP< language has been implemented on top of the DLV system and has subsequently been integrated into DLV.Comment: 28 pages; will be published in Theory and Practice of Logic Programmin

Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering

Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness result does not rely on any built-in linear order on the database. To establish the expressive completeness, we introduce a novel semantic definition for OCQA ontologies. We also show that neither the class of disjunctive tuple-generating dependencies nor the class of embedded dependencies is expressively complete for recursively enumerable OCQA ontologies.Comment: 10 pages; the full version of a paper to appear in IJCAI 2016. Changes (regarding to v1): a new reference has been added, and some typos have been correcte