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A MetaProgramming Technique for Debugging AnswerSet Programs ∗
"... Answerset programming (ASP) is widely recognised as a viable tool for declarative problem solving. However, there is currently a lack of tools for developing answerset programs. In particular, providing tools for debugging answerset programs has recently been identified as a crucial prerequisite ..."
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Answerset programming (ASP) is widely recognised as a viable tool for declarative problem solving. However, there is currently a lack of tools for developing answerset programs. In particular, providing tools for debugging answerset programs has recently been identified as a crucial prerequisite for a wider acceptance of ASP. In this paper, we introduce a metaprogramming technique for debugging in ASP. The basic question we address is why interpretations expected to be answer sets are not answer sets of the program to debug. We thus deal with finding semantical errors of programs. The explanations provided by our method are based on an intuitive scheme of errors that relies on a recent characterisation of the answerset semantics. Furthermore, as we are using a metaprogramming technique, debugging queries are expressed in terms of answerset programs themselves, which has several benefits: For one, we can directly use ASP solvers for processing debugging queries. Indeed, our technique can easily be implemented, and we devised a corresponding prototype debugging system. Also, our approach respects the declarative nature of ASP, and the capabilities of the system can easily be extended to incorporate differing debugging features.
Approaching the core of unfounded sets
 Proceedings of the International Workshop on Nonmonotonic Reasoning
, 2006
"... We elaborate upon techniques for unfounded set computations by building upon the concept of loops. This is driven by the desire to minimize redundant computations in solvers for Answer Set Programming. We begin by investigating the relationship between unfounded sets and loops in the context of part ..."
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We elaborate upon techniques for unfounded set computations by building upon the concept of loops. This is driven by the desire to minimize redundant computations in solvers for Answer Set Programming. We begin by investigating the relationship between unfounded sets and loops in the context of partial assignments. In particular, we show that subsetminimal unfounded sets correspond to active elementary loops. Consequentially, we provide a new looporiented approach along with an algorithm for computing unfounded sets. Unlike traditional techniques that compute greatest unfounded sets, we aim at computing small unfounded sets and rather let propagation (and iteration) handle greatest unfounded sets. This approach reflects the computation of unfounded sets employed in the nomore++ system. Beyond that, we provide an algorithm for identifying active elementary loops within unfounded sets. This can be used by SATbased solvers, like assat, cmodels, or pbmodels, for optimizing the elimination of invalid candidate models.
On loop formulas with variables
 In Proceedings of the International Conference on Knowledge Representation and Reasoning (KR
, 2008
"... Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop f ..."
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Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary firstorder sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in firstorder logic, providing a way to apply firstorder theorem provers to reasoning about nonHerbrand stable models.
Headelementarysetfree logic programs
 Proceedings of the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’07
, 2007
"... Abstract. The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose th ..."
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Abstract. The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose the notion of headelementarysetfree (HEF) programs, a more general class of disjunctive programs than headcyclefree (HCF) programs proposed by BenEliyahu and Dechter, that can still be turned into nondisjunctive programs in polynomial time and space by ”shifting ” the head atoms into the body. We show several properties of HEF programs that generalize earlier results on HCF programs. Given an HEF program, we provide an algorithm for finding an elementary set whose loop formula is not satisfied, which has a potential for improving stable model computation by answer set solvers. 1
Alternative Characterizations for Program Equivalence under AnswerSet Semantics based on Unfounded Sets
, 2007
"... Logic programs under answerset semantics constitute an important tool for declarative problem solving. In recent years, two research issues received growing attention. On the one hand, concepts like loops and elementary sets have been proposed in order to extend Clark’s completion for computing a ..."
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Logic programs under answerset semantics constitute an important tool for declarative problem solving. In recent years, two research issues received growing attention. On the one hand, concepts like loops and elementary sets have been proposed in order to extend Clark’s completion for computing answer sets of logic programs by means of propositional logic. On the other hand, different concepts of program equivalence, like strong and uniform equivalence, have been studied in the context of program optimization and modular programming. In this paper, we bring these two lines of research together and provide alternative characterizations for different conceptions of equivalence in terms of unfounded sets, along with the related concepts of loops and elementary sets. Our results yield new insights into the model theory of equivalence checking. We further exploit these characterizations to develop novel encodings of program equivalence in terms of standard and quantified propositional logic, respectively.
Characterising equilibrium logic and nested logic programs: Reductions and complexity
, 2009
"... Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kind ..."
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Cited by 6 (2 self)
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Equilibrium logic is an approach to nonmonotonic reasoning that extends the stablemodel and answerset semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present polynomial reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of secondorder logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical concepts of equilibrium logic and nested logic programs. In particular, our encodings map a given decision problem into some QBF such that the latter is valid precisely in case the former holds. The basic tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions
Characterizing ASP inferences by unit propagation
 IN: LASH ICLP WORKSHOP
, 2006
"... Computational approaches to Satisfiability Checking (SAT) and Answer Set Programming (ASP) have many aspects in common. In fact, the basic algorithms of ASP solvers are very similar to the DavisLogemannLoveland procedure (DLL) for SAT. The major difference lies in the inference rules, which are m ..."
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Computational approaches to Satisfiability Checking (SAT) and Answer Set Programming (ASP) have many aspects in common. In fact, the basic algorithms of ASP solvers are very similar to the DavisLogemannLoveland procedure (DLL) for SAT. The major difference lies in the inference rules, which are more complex in ASP. In this paper, we provide a generic framework, based on concepts from Constraint Processing (CSP), which allows us to view ASP inferences as forms of unit propagation. We develop declarative characterizations of ASP solvers nomore++ and smodels in terms of constraints. By putting ASP solving into a common context with SAT and CSP, we shed new light on ASP solving techniques and their relationships to neighboring fields.
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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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.
On the complexity of identifying Head Elementary Set Free programs ∗
, 2009
"... Headelementarysetfree programs were proposed in (Gebser et al. 2007) and shown to generalize over headcyclefree programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying headelementarysetfree programs. Thi ..."
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Headelementarysetfree programs were proposed in (Gebser et al. 2007) and shown to generalize over headcyclefree programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying headelementarysetfree programs. This note solves the open problem, by showing that the problem is complete for coNP.
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