Miroslaw Truszczynski

Stable Models and an Alternative Logic Programming Paradigm

In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting, a program does not describe a single intended model, but a family of its stable models. These stable models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs.

Answer set programming at a glance

The motivation and key concepts behind answer set programming---a promising approach to declarative problem solving.

The computational complexity of dominance and consistency in CP-Nets

We investigate the computational complexity of testing dominance and consistency in CP-nets. Up until now, the complexity of dominance has been determined only for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. We show here that both dominance and consistency testing for general CP-nets are PSPACE-complete. The reductions used in the proofs are from STRIPS planning, and thus establish strong connections between both areas.

The Second Answer Set Programming Competition

This paper reports on the Second Answer Set Programming Competition . The competitions in areas of Satisfiability checking, Pseudo-Boolean constraint solving and Quantified Boolean Formula evaluation have proven to be a strong driving force for a community to develop better performing systems. Following this experience, the Answer Set Programming competition series was set up in 2007, and ran as part of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). This second competition, held in conjunction with LPNMR 2009, differed from the first one in two important ways. First, while the original competition was restricted to systems designed for the answer set programming language , the sequel was open to systems designed for other modeling languages, as well. Consequently, among the contestants of the second competition were a CLP(FD) team and three model generation systems for (extensions of) classical logic. Second, this latest competition covered not only satisfiability problems but also optimization ones. We present and discuss the set-up and the results of the competition.

Uniform semantic treatment of default and autoepistemic logics

We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For each logic, we introduce a monotone operator on the lattice of belief pairs. We then show that a whole family of semantics can be defined in a systematic and principled way in terms of fixpoints of this operator (or as fixpoints of certain closely related operators). Our approach elucidates fundamental constructive principles in which agents form their belief sets, and leads to approximation semantics for autoepistemic and default logics. It also allows us to establish a precise one-to-one correspondence between the family of semantics for default logic and the family of semantics for autoepistemic logic. The correspondence exploits the modal interpretation of a default proposed by Konolige. Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated. At the same time, they explain the source of the difficulty to formally relate the semantics of default extensions by Reiter and autoepistemic expansions by Moore. These two semantics occupy different locations in the corresponding families of semantics for default and autoepistemic logics.

The first answer set programming system competition

This paper gives a summary of the First Answer Set Programming System Competition that was held in conjunction with the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning. The aims of the competition were twofold: first, to collect challenging benchmark problems, and second, to provide a platform to assess a broad variety of Answer Set Programming systems. The competition was inspired by similar events in neighboring fields, where regular benchmarking has been a major factor behind improvements in the developed systems and their ability to address practical applications.

Revision programming

In this paper we introduce revision programming — a logic-based framework for describing constraints on databases and providing a computational mechanism to enforce them. Revision programming captures those constraints that can be stated in terms of the membership (presence or absence) of items (records) in a database. Each such constraint is represented by a revision rule α← α1, . . . , αk, where α and all αi are of the form in(a) and out(b). Collections of revision rules form revision programs. Similarly as logic programs, revision programs admit both declarative and imperative (procedural) interpretations. In our paper, we introduce a semantics that reflects both interpretations. Given a revision program, this semantics assigns to any database B a collection (possibly empty) of P -justified revisions of B. The paper contains a thorough study of revision programming. We exhibit several fundamental properties of revision programming. We study the relationship of revision programming to logic programming. We investigate complexity of reasoning with revision programs as well as algorithms to compute P -justified revisions. Most importantly from the practical database perspective, we identify two classes of revision programs, safe and stratified, with a desirable property that they determine for each initial database a unique revision.

Modal logic for default reasoning

In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agents initial assumptions and do not depend on their syntactic representation.Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion — weak iterative expansion — and we show that there is an important class of theories, that we call ℐ-programs, for which iterative and weak iterative expansions coincide. Thus, for ℐ-programs, iterative expansions can be equivalently defined by semantic means.

Modal nonmonotonic logics: ranges, characterization, computation

Many nonmonotonic formalism, including default logic, logic programming with stable models, and autoepistemic logic, can be represented faithfully by means of modal nonmonotonic logics in the family proposed by McDermott and Doyle. In this paper properties of logics in this family are thoroughly investigated. We present several results on characterization of expansions. These results are applicable to a wide class of nonmonotonic modal logics. Using these characterization results, algorithms for computing expansions for finite theories are developed. Perhaps the most important finding of this paper is that the structure of the family of modal nonmonotonic logics is much simpler than that of the family of underlying modal (monotonic) logics. Namely, it is often the case that different monotonic modal logics collapse to the same nonmonotonic system. We exhibit four families of logics whose nonmonotonic variants coincide: 5-KD45, TW5-SW5, N-WK, and W5-D4WB. These nonmonotonic logics naturally represent logics related to commonsense reasoning and knowledge representation such as autoepistemic logic, reflexive autoepistemic logic, default logic, and truth maintenance with negation.

Computing with default logic

Abstract Default logic was proposed by Reiter as a knowledge representation tool. In this paper, we present our work on the Default Reasoning System, DeReS, the first comprehensive and optimized implementation of default logic. While knowledge representation remains the main application area for default logic, as a source of large-scale problems needed for experimentation and as a source of intuitions needed for a systematic methodology of encoding problems as default theories we use here the domain of combinatorial problems. To experimentally study the performance of DeReS we developed a benchmarking system, the TheoryBase. The TheoryBase is designed to support experimental investigations of nonmonotonic reasoning systems based on the language of default logic or logic programming. It allows the user to create parameterized collections of default theories having similar properties and growing sizes and, consequently, to study the asymptotic performance of nonmonotonic systems under investigation. Each theory generated by the TheoryBase has a unique identifier, which allows for concise descriptions of test cases used in experiments and, thus, facilitates comparative studies. We describe the TheoryBase in this paper and report on our experimental studies of DeReS performance based on test cases generated by the TheoryBase.