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61
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 312 (5 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 us t ..."
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Cited by 75 (7 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 × B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs...
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 63 (1 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.
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 62 (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.
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 45 (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.
Equilibria in Heterogeneous Nonmonotonic MultiContext Systems
"... 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 fo ..."
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Cited by 42 (11 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)
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 32 (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.
Propositional Satisfiability in AnswerSet Programming
 In Proceedings of Joint German/Austrian Conference on Artificial Intelligence, KI'2001
, 2001
"... We show that propositional logic and its extensions can support answerset programming in the same way stable logic programming and disjunctive logic programming do. To this end, we introduce a logic based on the logic of propositional schemata and on a version of the Closed World Assumption. We ..."
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Cited by 22 (7 self)
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We show that propositional logic and its extensions can support answerset programming in the same way stable logic programming and disjunctive logic programming do. To this end, we introduce a logic based on the logic of propositional schemata and on a version of the Closed World Assumption. We call it the extended logic of propositional schemata with CWA (PS , in symbols). An important feature of the logic is that it supports explicit modeling of constraints on cardinalities of sets. In the paper, we characterize the class of problems that can be solved by finite PS theories. We implement a programming system based on the logic PS and design and implement a solver for processing theories in PS . We present encouraging performance results for our approach  we show it to be competitive with smodels, a stateoftheart answerset programming system based on stable logic programming.
Answer set based design of knowledge systems
 ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE
, 2006
"... The aim of this paper is to demonstrate that AProlog is a powerful language for the construction of reasoning systems. In fact, AProlog allows to specify the initial situation, the domain model, the control knowledge, and the reasoning modules. Moreover, it is efficient enough to be used for pra ..."
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Cited by 22 (12 self)
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The aim of this paper is to demonstrate that AProlog is a powerful language for the construction of reasoning systems. In fact, AProlog allows to specify the initial situation, the domain model, the control knowledge, and the reasoning modules. Moreover, it is efficient enough to be used for practical tasks and can be nicely integrated with programming languages such as Java. An extension of AProlog (CRProlog) allows to further improve the quality of reasoning by specifying requirements that the solutions should satisfy if at all possible. The features of AProlog and CRProlog are demonstrated by describing in detail the design of USAAdvisor, an AProlog based decision support system for the Space Shuttle flight controllers.