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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 395 (8 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.
Logic Programming with Ordered Disjunction
 In Proceedings of AAAI02
, 2002
"... Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows ..."
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Cited by 95 (8 self)
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Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A &times; B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs...
Equilibria in Heterogeneous Nonmonotonic MultiContext Systems
 In 22nd AAAI Conference on Artificial Intelligence (AAAI2007
, 2007
"... We propose a general framework for multicontext reasoning which allows us to combine arbitrary monotonic and nonmonotonic logics. Nonmonotonic bridge rules are used to specify the information flow among contexts. We investigate several notions of equilibrium representing acceptable belief states f ..."
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Cited by 77 (18 self)
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We propose a general framework for multicontext reasoning which allows us to combine arbitrary monotonic and nonmonotonic logics. Nonmonotonic bridge rules are used to specify the information flow among contexts. We investigate several notions of equilibrium representing acceptable belief states for our multicontext systems. The approach generalizes the heterogeneous monotonic multicontext systems developed by F. Giunchiglia and colleagues as well as the homogeneous nonmonotonic multicontext systems of Brewka, Serafini and Roelofsen. Background and Motivation Interest in formalizations of contextual information and intercontextual information flow has steadily increased over the last years. Based on seminal papers by McCarthy (1987)
Strong Equivalence Made Easy: Nested Expressions and Weight Constraints
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... Logic programs P and Q are strongly equivalent if, given any program R, programs P + R and Q + R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of logic programs: one can prove that a local change is correct without c ..."
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Cited by 69 (1 self)
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Logic programs P and Q are strongly equivalent if, given any program R, programs P + R and Q + R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of logic programs: one can prove that a local change is correct without considering the whole program. Lifschitz, Pearce and Valverde showed that Heyting's logic of hereandthere can be used to characterize strong equivalence for logic programs with nested expressions (which subsume the betterknown extended disjunctive programs). This note considers a simpler, more direct characterization of strong equivalence for such programs, and shows that it can also be applied without modication to the weight constraint programs of Niemel?a and Simons. Thus, this characterization of strong equivalence is convenient for the study of equivalent transformations of logic programs written in the input languages of answer set programming systems dlv and smodels. The note concludes with a brief discussion of results that can be used to automate reasoning about strong equivalence, including a novel encoding that reduces the problem of deciding the strong equivalence of a pair of weight constraint programs to that of deciding the inconsistency of a weight constraint program.
Representing Knowledge in AProlog
"... In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example ..."
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Cited by 65 (2 self)
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In this paper, we review some recent work on declarative logic programming languages based on stable models/answer sets semantics of logic programs. These languages, gathered together under the name of AProlog, can be used to represent various types of knowledge about the world. By way of example we demonstrate how the corresponding representations together with inference mechanisms associated with AProlog can be used to solve various programming tasks.
Bounded LTL model checking with stable models
 Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning
, 2003
"... In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1safe Petri nets, are used. It is shown how a 1safe Petri net and a req ..."
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Cited by 52 (6 self)
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In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1safe Petri nets, are used. It is shown how a 1safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.
Implementing Ordered Disjunction Using Answer Set Solvers for Normal Programs
"... Logic programs with ordered disjunction (LPODs) add a new connective to logic programming. This connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: AB intuitively means: if possible A, but if A is not possible, then at least B. The semantics ..."
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Cited by 34 (7 self)
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Logic programs with ordered disjunction (LPODs) add a new connective to logic programming. This connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: AB intuitively means: if possible A, but if A is not possible, then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. In this paper we show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not.
Representing Configuration Knowledge with Weight Constraint Rules
, 2001
"... The paper demonstrates that product configuration applications fit naturally the framework of answer set programming. It is shown that product configuration knowledge can be represented systematically and compactly using a logic program type rule language such that the answers of a configuration tas ..."
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Cited by 30 (4 self)
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The paper demonstrates that product configuration applications fit naturally the framework of answer set programming. It is shown that product configuration knowledge can be represented systematically and compactly using a logic program type rule language such that the answers of a configuration task, the con gurations, correspond to the models of the rule representation. The paper presents such a rulebased formalization of a unified configuration ontology using a weight constraint rule language. The language extends normal logic programs with cardinality and weight constraints which leads to a compact and simple formalization. The complexity of the configuration task de ned by the formalization is shown to be NPcomplete.
Predicatecalculus based logics for modeling and solving search problems
 ACM Transactions on Computational Logic
, 2006
"... search problems ..."