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49
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 390 (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.
Smodels  an Implementation of the Stable Model and WellFounded Semantics for Normal Logic Programs
, 1997
"... The Smodels system is a C++ implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs. The system includes two modules: (i) smodels which implements the two semantics for ground programs and (ii) parse which computes a grounded version of a range ..."
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Cited by 291 (9 self)
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The Smodels system is a C++ implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs. The system includes two modules: (i) smodels which implements the two semantics for ground programs and (ii) parse which computes a grounded version of a rangerestricted functionfree normal program. The latter module does not produce the whole set of ground instances of the program but a subset that is sufficient in the sense that no stable models are lost. The implementation of the stable model semantics for ground programs is based on bottomup backtracking search where a powerful pruning method is employed. The pruning method exploits an approximation technique for stable models which is closely related to the wellfounded semantics. One of the advantages of this novel technique is that it can be implemented to work in linear space. This makes it possible to apply the stable model semantics also in areas where resulting programs are highly n...
ProbView: A Flexible Probabilistic Database System
 ACM TRANSACTIONS ON DATABASE SYSTEMS
, 1997
"... ... In this article, we characterize, using postulates, whole classes of strategies for conjunction, disjunction, and negation, meaningful from the viewpoint of probability theory. (1) We propose a probabilistic relational data model and a generic probabilistic relational algebra that neatly capture ..."
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Cited by 201 (14 self)
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... In this article, we characterize, using postulates, whole classes of strategies for conjunction, disjunction, and negation, meaningful from the viewpoint of probability theory. (1) We propose a probabilistic relational data model and a generic probabilistic relational algebra that neatly captures various strategies satisfying the postulates, within a single unified framework. (2) We show that as long as the chosen strategies can be computed in polynomial time, queries in the positive fragment of the probabilistic relational algebra have essentially the same data complexity as classical relational algebra. (3) We establish various containments and equivalences between algebraic expressions, similar in spirit to those in classical algebra. (4) We develop algorithms for maintaining materialized probabilistic views. (5) Based on these ideas, we have developed
Efficient Implementation of the Wellfounded and Stable Model Semantics
 Proceedings of the Joint International Conference and Symposium on Logic Programming
, 1996
"... An implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs is presented. It includes two modules: an algorithm for implementing the two semantics for ground programs and an algorithm for computing a grounded version of a rangerestricted funct ..."
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Cited by 141 (15 self)
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An implementation of the wellfounded and stable model semantics for rangerestricted functionfree normal programs is presented. It includes two modules: an algorithm for implementing the two semantics for ground programs and an algorithm for computing a grounded version of a rangerestricted functionfree normal program. The latter algorithm does not produce the whole set of ground instances of the program but a subset which is sufficient in the sense that no stable models are lost. The implementation of the stable model semantics for ground programs is based on bottomup backtracking search. It works in linear space and employs a powerful pruning method based on an approximation technique for stable models which is closely related to the wellfounded semantics. The implementation includes an efficient algorithm for computing the wellfounded model of a ground program. The implementation has been tested extensively and compared with a state of the art implementation of the stable mode...
Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation
 Information and Computation
, 1997
"... Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunct ..."
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Cited by 88 (20 self)
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Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfoundedfree models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the wellfounded WP operator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of functionfree programs. The algor...
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.