Results 1  10
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29
S.: Modularity aspects of disjunctive stable models
 LPNMR 2007. LNCS (LNAI
, 2007
"... Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answerset programming where fully declarative and nonmonotonic languages are applied. In ..."
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Cited by 27 (9 self)
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Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answerset programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stablemodel semantics. We define the notion of a DLPfunction, where a welldefined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stablemodel semantics for DLPfunctions. The module theorem extends the wellknown splittingset theorem and enables the decomposition of DLPfunctions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLPfunctions using a generalization of a translationbased verification method. 1.
Facts do not Cease to Exist Because They are Ignored: Relativised Uniform Equivalence with AnswerSet Projection
 In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI 2007
, 2007
"... Recent research in answerset programming (ASP) focuses on different notions of equivalence between programs which are relevant for program optimisation and modular programming. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joine ..."
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Cited by 14 (11 self)
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Recent research in answerset programming (ASP) focuses on different notions of equivalence between programs which are relevant for program optimisation and modular programming. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joined with an arbitrary set of facts. In this paper, we study a family of more finegrained versions of uniform equivalence, where the alphabet of the added facts as well as the projection of answer sets is taken into account. The latter feature, in particular, allows the removal of auxiliary atoms in computation, which is important for practical programming aspects. We introduce novel semantic characterisations for the equivalence problems under consideration and analyse the computational complexity for checking these problems. We furthermore provide efficient reductions to quantified propositional logic, yielding a rapidprototyping system for equivalence checking.
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
"... ..."
A common view on strong, uniform, and other notions of equivalence in answerset programming. Theory and Practice of Logic Programming
"... Logic programming under the answerset semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, i ..."
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Cited by 8 (6 self)
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Logic programming under the answerset semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are different concepts. The former holds, given programs P and Q, iff P can be faithfully replaced by Q within any context R, while the latter holds iff P and Q provide the same output, that is, they have the same answer sets. Notions in between strong and ordinary equivalence have been introduced as theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programs R or by bounding the set A of atoms allowed to occur in R (relativized equivalence). For the latter approach, different A yield properly different equivalence notions, in general. For the former approach, however, it turned out that any “reasonable ” syntactic restriction to R coincides with either ordinary, strong, or uniform equivalence (for uniform equivalence, the context ranges over arbitrary sets of facts, rather than program rules). In this paper, we propose a parameterization for equivalence notions which takes care of both such kinds of restrictions simultaneously by bounding, on the one hand, the atoms which are allowed to occur in the rule heads of the context and, on the other hand, the atoms which are allowed to occur in the rule bodies of the context. We introduce a general semantical characterization which includes known ones as SEmodels (for strong equivalence) or UEmodels (for uniform equivalence) as special cases. Moreover, we provide complexity bounds for the problem in question and sketch a possible implementation method making use of dedicated systems for checking ordinary equivalence. KEYWORDS: Answerset programming, strong equivalence, relativized equivalence.
Hyperequivalence of logic programs with respect to supported models
 PROCEEDINGS OF AAAI 2008
, 2008
"... Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. ..."
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Cited by 7 (6 self)
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Recent research in nonmonotonic logic programming has focused on certain types of program equivalence, which we refer to here as hyperequivalence, that are relevant for program optimization and modular programming. So far, most results concern hyperequivalence relative to the stablemodel semantics. However, other semantics for logic programs are also of interest, especially the semantics of supported models which, when properly generalized, is closely related to the autoepistemic logic of Moore. In this paper, we consider a family of hyperequivalence relations for programs based on the semantics of supported and supported minimal models. We characterize these relations in modeltheoretic terms. We use the characterizations to derive complexity results concerning testing whether two programs are hyperequivalent relative to supported and supported minimal models.
Logic Programming for Knowledge Representation
, 2007
"... This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation. ..."
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Cited by 7 (0 self)
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This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.
A Solver for QBFs in Negation Normal Form
"... Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers ..."
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Cited by 6 (1 self)
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Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver, qpro, which is able to handle arbitrary formulas. To this end, we extend algorithms for QBFs to the nonnormal form case and compare qpro with the leading normal form provers on several problems from the area of artificial intelligence. We prove properties of the algorithms generalized to nonclausal form by using a novel approach based on a sequentstyle formulation of the calculus. 1.
S.: Belief revision of logic programs under answer set semantics
 In: KR’08, AAAI
, 2008
"... We address the problem of belief revision in (nonmonotonic) logic programming under answer set semantics: given logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P ∗ Q. Unlike previous approaches in logic programming, our formal techniqu ..."
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Cited by 6 (2 self)
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We address the problem of belief revision in (nonmonotonic) logic programming under answer set semantics: given logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P ∗ Q. Unlike previous approaches in logic programming, our formal techniques are analogous to those of distancebased belief revision in propositional logic. In developing our results, we build upon the model theory of logic programs furnished by SE models. Since SE models provide a formal, monotonic chacterisation of logic programs, we can adapt wellknown techniques from the area of belief revision to revision in logic programs. We investigate two specific operators: (logic program) expansion and a revision operator based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical AGMstyle belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy the majority of the AGM postulates for revision. A complexity analysis reveals that our revision operators do not increase the complexity of the base formalism. As a consequence, we present an encoding for computing the revision of a logic program by another, within the same logic programming framework.
Relativized Hyperequivalence of Logic Programs for Modular Programming
"... Abstract. A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, indep ..."
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Cited by 3 (2 self)
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Abstract. A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence wrt the three other types of context programs. 1
Merging Logic Programs under Answer Set Semantics
"... This paper considers a semantic approach for merging logic programs under answer set semantics. Given logic programs P1,..., Pn, the goal is to provide characterisations of the merging of these programs. Our formal techniques are based on notions of relative distance between the underlying SE models ..."
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Cited by 3 (1 self)
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This paper considers a semantic approach for merging logic programs under answer set semantics. Given logic programs P1,..., Pn, the goal is to provide characterisations of the merging of these programs. Our formal techniques are based on notions of relative distance between the underlying SE models of the logic programs. Two approaches are examined. The first informally selects those models of the programs that vary the least from the models of the other programs. The second approach informally selects those models of a program P0 that are closest to the models of programs P1,..., Pn. P0 can be thought of as analogous to a set of database integrity constraints. We examine formal properties of these operators. Moreover, we give encodings for computing the mergings of a multiset of logic programs, within the same logic programming framework. As a byproduct, we provide a complexity analysis revealing that our operators do not increase the complexity of the base formalism.