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Answer set programming with functions
 In Proc. KR’08
, 2008
"... To compute a function such as a mapping from vertices to colors in the graph coloring problem, current practice in Answer Set Programming is to represent the function as a relation. Among other things, this often makes the resulting program unnecessarily large when instantiated on a large domain. Th ..."
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Cited by 18 (1 self)
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To compute a function such as a mapping from vertices to colors in the graph coloring problem, current practice in Answer Set Programming is to represent the function as a relation. Among other things, this often makes the resulting program unnecessarily large when instantiated on a large domain. The extra constraints needed to enforce the relation as a function also make the logic program less transparent. In this paper, we consider adding functions directly to normal logic programs. We show that the answer set semantics can be generalized to these programs straightforwardly. We also show that the notions of loops and loop formulas can be extended, and that through program completion and loop formulas, a normal logic program with functions can be transformed to a Constraint Satisfaction problem.
Catching the Ouroboros: On Debugging Nonground AnswerSet Programs
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2010
"... An important issue towards a broader acceptance of answerset programming (ASP) is the deployment of tools which support the programmer during the coding phase. In particular, methods for debugging an answerset program are recognised as a crucial step in this regard. Initial work on debugging in AS ..."
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Cited by 11 (3 self)
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An important issue towards a broader acceptance of answerset programming (ASP) is the deployment of tools which support the programmer during the coding phase. In particular, methods for debugging an answerset program are recognised as a crucial step in this regard. Initial work on debugging in ASP mainly focused on propositional programs, yet practical debuggers need to handle programs with variables as well. In this paper, we discuss a debugging technique that is directly geared towards nonground programs. Following previous work, we address the central debugging question why some interpretation is not an answer set. The explanations provided by our method are computed by means of a metaprogramming technique, using a uniform encoding of a debugging request in terms of ASP itself. Our method also permits programs containing comparison predicates and integer arithmetics, thus covering a relevant language class commonly supported by all stateoftheart ASP solvers.
Computing Loops with at Most One External Support Rule for Disjunctive Logic Programs
"... Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constr ..."
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Abstract. We extend to disjunctive logic programs our previous work on computing loop formulas of loops with at most one external support. We show that for these logic programs, loop formulas of loops with no external support can be computed in polynomial time, and if the given program has no constraints, an iterative procedure based on these formulas, the program completion, and unit propagation computes the least fixed point of a simplification operator used by DLV. We also relate loops with no external supports to the unfounded sets and the wellfounded semantics of disjunctive logic programs by Wang and Zhou. However, the problem of computing loop formulas of loops with at most one external support rule is NPhard for disjunctive logic programs. We thus propose a polynomial algorithm for computing some of these loop formulas, and show experimentally that this polynomial approximation algorithm can be effective in practice. 1
Y.D.: Loop formulas for description logic programs
, 2010
"... Description Logic Programs (dlprograms) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to de ..."
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Cited by 5 (2 self)
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Description Logic Programs (dlprograms) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dlprogram can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dlprograms, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.
178 Stable Model Semantics and FirstOrder Loop Formulas
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2005
"... Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship betwe ..."
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Cited by 4 (1 self)
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Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship between the firstorder stable model semantics and firstorder loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a firstorder loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary firstorder theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving nonHerbrand stable models using firstorder reasoners. Such programs can be viewed as a special class of firstorder theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax. 1.
Tableau Calculi for Logic Programs under Answer Set Semantics
"... We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes finegrained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propag ..."
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Cited by 3 (1 self)
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We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes finegrained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SATbased and conflictdriven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the runtimes of bestcase computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.
A General FirstOrder Solution to the Ramification Problem
"... We present a combined solution to the frame and ramification problems that is independent of the underlying time structure. Indirect effects are expressed through ramification rules that are compiled into firstorder effect axioms. To cope with the notorious problem of selfjustifying cycles, we us ..."
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We present a combined solution to the frame and ramification problems that is independent of the underlying time structure. Indirect effects are expressed through ramification rules that are compiled into firstorder effect axioms. To cope with the notorious problem of selfjustifying cycles, we use techniques known from translations of normal logic programs to logical theories: cyclic fluent dependencies in the ramification rules are identified, and for each such loop, a loop formula is built into the effect axiom to guarantee proper treatment of circular causal dependencies.
Under consideration for publication in Theory and Practice of Logic Programming 1 On Elementary Loops of Logic Programs
, 2010
"... Part of the Computer Sciences Commons This Article is brought to you for free and open access by the Department of Computer Science at ..."
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Part of the Computer Sciences Commons This Article is brought to you for free and open access by the Department of Computer Science at
Proceedings, Eleventh International Conference on Principles of Knowledge Representation and Reasoning (2008) Computing Loops with at Most One External Support Rule
"... If a loop has no external support rules, then its loop formula is equivalent to a set of unit clauses; and if it has exactly one external support rule, then its loop formula is equivalent to a set of binary clauses. In this paper, we consider how to compute these loops and their loop formulas in a n ..."
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If a loop has no external support rules, then its loop formula is equivalent to a set of unit clauses; and if it has exactly one external support rule, then its loop formula is equivalent to a set of binary clauses. In this paper, we consider how to compute these loops and their loop formulas in a normal logic program, and use them to derive consequences of a logic program. We show that an iterative procedure based on unit propagation, the program completion and the loop formulas of loops with no external support rules can compute the same consequences as the “Expand ” operator in smodels, which is known to compute the wellfounded model when the given normal logic program has no constraints. We also show that using the loop formulas of loops with at most one external support rule, the same procedure can compute more consequences, and these extra consequences can help ASP solvers such as cmodels to find answer sets of certain logic programs.
On the progression semantics and boundedness of answer set programs
 In Proc. KR
, 2010
"... In this paper, we propose a progression semantics for firstorder answer set programs. Based on this new semantics, we are able to define the notion of boundedness for answer set programming. We prove that boundedness coincides with the notions of recursionfree and loopfree under program equivale ..."
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In this paper, we propose a progression semantics for firstorder answer set programs. Based on this new semantics, we are able to define the notion of boundedness for answer set programming. We prove that boundedness coincides with the notions of recursionfree and loopfree under program equivalence, and is also equivalent to firstorder definability of answer set programs on arbitrary structures.