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

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Backdoors to Normality for Disjunctive Logic Programs

Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be utilized for the efficient solution of problems that are harder than NP or co-NP. In particular, we consider the fundamental reasoning problems in propositional disjunctive answer set programming (ASP), Brave Reasoning and Skeptical Reasoning, which ask whether a given atom is contained in at least one or in all answer sets, respectively. Both problems are located at the second level of the Polynomial Hierarchy and thus assumed to be harder than NP or co-NP. One cannot transform these two reasoning problems into SAT in polynomial time, unless the Polynomial Hierarchy collapses. We show that certain structural aspects of disjunctive logic programs can be utilized to break through this complexity barrier, using new techniques from Parameterized Complexity. In particular, we exhibit transformations from Brave and Skeptical Reasoning to SAT that run in time O(2^k n^2) where k is a structural parameter of the instance and n the input size. In other words, the reduction is fixed-parameter tractable for parameter k. As the parameter k we take the size of a smallest backdoor with respect to the class of normal (i.e., disjunction-free) programs. Such a backdoor is a set of atoms that when deleted makes the program normal. In consequence, the combinatorial explosion, which is expected when transforming a problem from the second level of the Polynomial Hierarchy to the first level, can now be confined to the parameter k, while the running time of the reduction is polynomial in the input size n, where the order of the polynomial is independent of k.Comment: A short version will appear in the Proceedings of the Proceedings of the 27th AAAI Conference on Artificial Intelligence (AAAI'13). A preliminary version of the paper was presented on the workshop Answer Set Programming and Other Computing Paradigms (ASPOCP 2012), 5th International Workshop, September 4, 2012, Budapest, Hungar

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

Linear-Logic Based Analysis of Constraint Handling Rules with Disjunction

Constraint Handling Rules (CHR) is a declarative committed-choice programming language with a strong relationship to linear logic. Its generalization CHR with Disjunction (CHRv) is a multi-paradigm declarative programming language that allows the embedding of horn programs. We analyse the assets and the limitations of the classical declarative semantics of CHR before we motivate and develop a linear-logic declarative semantics for CHR and CHRv. We show how to apply the linear-logic semantics to decide program properties and to prove operational equivalence of CHRv programs across the boundaries of language paradigms