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Extending and Implementing the Stable Model Semantics
, 2002
"... A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities ..."
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Cited by 396 (9 self)
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A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a frontend and a kernel language implementation. The frontend allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.
Stable models and an alternative logic programming paradigm
 In The Logic Programming Paradigm: a 25Year Perspective
, 1999
"... 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 ..."
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Cited by 310 (19 self)
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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 wellfounded semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting programs do not describe a single intended model, but a family of 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 wellattuned to problems in the class NP, has a welldefined 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. 1
Default Reasoning System DeReS
, 1996
"... In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one ..."
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Cited by 71 (6 self)
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In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, finding one or all extensions (if at least one exists) and querying if a formula belongs to one or all extensions. If an input theory is a logic program, DeReS computes stable models of this program and supports queries on membership of an atom in some or all stable models. The paper contains an account of our preliminary experiments with DeReS and a discussion of the results. We show that a choice of a propositional prover is critical for the efficiency of DeReS. We also present a general technique that eliminates the need for some global consistency checks and results in substantial speedups. We experimentally demonstrate the potential of the concept of relaxed stratification for making automated reasoning systems practical.
Computing With Default Logic
, 1999
"... 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 l ..."
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Cited by 38 (6 self)
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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 largescale 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 i...
Towards Constraint Satisfaction through Logic Programs and the Stable Model Semantics
, 1997
"... Logic programs with the stable model semantics can be thought of as a new paradigm for constraint satisfaction, where the rules of a program are seen as constraints on the stable models. In this work the paradigm is realized by developing an efficient procedure for computing the stable models of gro ..."
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Cited by 30 (1 self)
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Logic programs with the stable model semantics can be thought of as a new paradigm for constraint satisfaction, where the rules of a program are seen as constraints on the stable models. In this work the paradigm is realized by developing an efficient procedure for computing the stable models of ground logic programs. A strong pruning technique based on two deductive closures is introduced. The technique is further strengthened by the introduction of backjumping, which is an improvement over chronological backtracking, and lookahead, a new pruning method. Moreover, a strong heuristic is derived. The two deductive closures are given lineartime implementations that provide a linearspace implementation method for the decision procedure. A high lower bound on the least upper bound on the complexity of the procedure is found. In order to generalize the procedure such that it can handle programs with variables, an algorithm for grounding a functionfree range restricted logic program that...
Fixpoint 3valued semantics for autoepistemic logic
 IN PROCEEDINGS OF THE 15TH NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE. MIT PRESS / AAAIPRESS
, 1998
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A RuleBased Formal Model For Software Configuration
, 1999
"... In this work we examine the software configuration management problem. We give a short introduction to the current state of the art and present a declarative rulebased formal language for representation of configuration knowledge. As a novel feature, the rule language allows finite existential quan ..."
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Cited by 13 (3 self)
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In this work we examine the software configuration management problem. We give a short introduction to the current state of the art and present a declarative rulebased formal language for representation of configuration knowledge. As a novel feature, the rule language allows finite existential quantification over the configuration components. We show a translation from the rule language to normal logic programs with stable model semantics. As a case study we examine the configuration management problem for the Debian GNU/Linux system which consists of over 2000 distinct software packages. We examine the current practice to identify the main components of the problem and present a way to formalize them using the rule language. We construct two formal models: one for finding valid configurations and one for diagnosing unsatisfiable user requirements. We show that the decision problem for the configuration model is NPcomplete. We present a translator that reads a highlevel description of the Debian configuration system and produces the corresponding set of rules. We evaluate the configuration model by using actual data from Debian version 2.1 and a set of randomly generated user requirements. The evaluation shows that the model is computationally feasible.
Extremal Problems in Logic Programming and Stable Model Computation
"... We study the following problem: given a class of (disjunctive) logic programs C, determine the maximum number of stable models (answer sets) of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at mo ..."
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Cited by 10 (1 self)
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We study the following problem: given a class of (disjunctive) logic programs C, determine the maximum number of stable models (answer sets) of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of all logic programs of size at most n. We also characterize the programs for which the maxima are attained. We obtain similar results for the class of all disjunctive logic programs with at most n clauses, each of length at most m, and for the class of all disjunctive logic programs of size at most n. Our results on logic programs have direct implication for the design of algorithms to compute stable models. Several such algorithms, similar in spirit to the DavisPutnam procedure, are described in the paper. 1 Introduction In this paper we study extremal problems appearing in the context of finite propositional logic programs. Specifically, we consider the following problem: given a class of logic programs C, determine th...
Towards Programming in Default Logic
"... In this paper we describe a fragment of default logic suitable for encoding problems from other domains. We investigate a subclass of first order open default theories, which we call extensional default theories. This class of default theories allows easy and compact encodings of problems for expe ..."
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Cited by 1 (0 self)
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In this paper we describe a fragment of default logic suitable for encoding problems from other domains. We investigate a subclass of first order open default theories, which we call extensional default theories. This class of default theories allows easy and compact encodings of problems for experimenting with default reasoning systems. Because most existing systems for default reasoning assume that all input defaults are closed or propositional we show how to transform an extensional default theory to a closed first order default theory or a propositional default theory with same extensions. Finally, we present several encodings of known graph problems in the language of extensional default theories. These encodings can be regarded as benchmark problems for experimenting with nonmonotonic reasoning systems. 1 Introduction In this paper we develop a simple first order nonmonotonic reasoning formalism for describing combinatorial problems Our framework is based on default log...
Minimal Number of Permutations Sufficient to Compute All Extensions a Finite Default Theory
"... In this paper we analyze an algorithm for generating extensions of a default theory. This algorithm considers all permutations (orderings) of defaults. For each permutation, it constructs a tentative extension incrementally, in each step firing the first applicable default, where the applicabilit ..."
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Cited by 1 (0 self)
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In this paper we analyze an algorithm for generating extensions of a default theory. This algorithm considers all permutations (orderings) of defaults. For each permutation, it constructs a tentative extension incrementally, in each step firing the first applicable default, where the applicability of a default is defined with respect to the part of a tentative extension constructed so far. When no more defaults can be fired, an a posteriori consistency check is performed to test whether all defaults that were fired remain applicable with respect to the final theory. If so, this theory is returned as an extension. Otherwise, the next ordering is tried. Straightforward worst case analysis implies that this algorithm may have to inspect all n! permutations in order to be complete (here n is the number of defaults in an input default theory). In this paper we show that this number can be significantly reduced. Namely, we exhibit a set of \Gamma n bn=2c \Delta 0:8 \Theta 2...