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29
Uniform Equivalence of Logic Programs under the Stable Model Semantics
, 2003
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to sta ..."
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Cited by 49 (13 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R = ;), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is wellknown, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for inputbased problem solving.
On Solution Correspondences in Answer Set Programming
 In Proc. of 19th International Joint Conference on Artificial Intelligence, 97–102
, 2005
"... We introduce a general framework for specifying program correspondence under the answerset semantics. The framework allows to define different kinds of equivalence notions, including previously defined notions like strong and uniform equivalence, in which programs are extended with rules from a giv ..."
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Cited by 31 (20 self)
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We introduce a general framework for specifying program correspondence under the answerset semantics. The framework allows to define different kinds of equivalence notions, including previously defined notions like strong and uniform equivalence, in which programs are extended with rules from a given context, and correspondence is determined by means of a binary relation. In particular, refined equivalence notions based on projected answer sets can be defined within this framework, where not all parts of an answer set are of relevance. We study general characterizations of inclusion and equivalence problems, introducing novel semantical structures. Furthermore, we deal with the issue of determining counterexamples for a given correspondence problem, and we analyze the computational complexity of correspondence checking. 1
Semantical Characterizations and Complexity of Equivalences in Answer Set Programming
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2007
"... In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answe ..."
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Cited by 27 (11 self)
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In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R =∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is wellknown in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong
Engineering an Incremental ASP Solver
"... Abstract. Many realworld applications, like planning or model checking, comprise a parameter reflecting the size of a solution. In a propositional formalism like Answer Set Programming (ASP), such problems can only be dealt with in a bounded way, considering one problem instance after another by gr ..."
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Cited by 27 (15 self)
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Abstract. Many realworld applications, like planning or model checking, comprise a parameter reflecting the size of a solution. In a propositional formalism like Answer Set Programming (ASP), such problems can only be dealt with in a bounded way, considering one problem instance after another by gradually increasing the bound on the solution size. We thus propose an incremental approach to both grounding and solving in ASP. Our goal is to avoid redundancy by gradually processing the extensions to a problem rather than repeatedly reprocessing the entire (extended) problem. We start by furnishing a formal framework capturing our incremental approach in terms of module theory. In turn, we take advantage of this framework for guiding the successive treatment of program slices during grounding and solving. Finally, we describe the first integrated incremental ASP system, iclingo, and provide an experimental evaluation. 1
Modularity Aspects of Disjunctive Stable Models
, 2007
"... Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general ..."
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Cited by 26 (8 self)
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Practically all programming languages used in software engineering allow to split a program into several modules. For fully declarative and nonmonotonic logic programming languages, however, the modular structure of programs is hard to realise, since the output of an entire program cannot in general be composed from the output of its component programs in a direct manner. In this paper, we consider these aspects for the stablemodel semantics of disjunctive logic programs (DLPs). We define the notion of a DLPfunction, where a welldefined input/output interface is provided, and establish a novel module theorem enabling a suitable compositional semantics for modules. The module theorem extends the wellknown splittingset theorem and allows also a generalisation of a shifting technique for splitting shared disjunctive rules among components.
Discovering Classes of Strongly Equivalent Logic Programs
 In: Proc. of the Intl. Joint Conf. on Artificial Intelligence (IJCAI’05
, 2005
"... In this paper we apply computeraided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that pre ..."
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Cited by 19 (5 self)
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In this paper we apply computeraided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules. 1.
Some (in)translatability results for normal logic programs and propositional theories
 Journal of Applied NonClassical Logics
, 2006
"... ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation f ..."
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Cited by 14 (5 self)
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ABSTRACT. In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ≤ 2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ≤ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but nonmodular translation function from normal programs to propositional theories. We consider this as a breakthrough due to subquadratic time complexity (of the order of P   × log 2 Hb(P)). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.
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 13 (10 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.
SELP  a system for studying strong equivalence between logic programs
 In Proceedings of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning(LPNMR 2005
, 2005
"... Abstract. This paper describes a system called SELP for studying strong equivalence in answer set logic programming. The basic function of the system is to check if two given ground disjunctive logic programs are equivalent, and if not, return a counterexample. This allows us to investigate some in ..."
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Cited by 12 (1 self)
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Abstract. This paper describes a system called SELP for studying strong equivalence in answer set logic programming. The basic function of the system is to check if two given ground disjunctive logic programs are equivalent, and if not, return a counterexample. This allows us to investigate some interesting properties of strong equivalence, such as a complete characterization for a rule to be strongly equivalent to another one, and checking whether a given set of rules is strongly equivalent to another, perhaps simpler set of rules. 1
Replacements in nonground answerset programming
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2006
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