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Discovering Classes of Strongly Equivalent Logic Programs
 Proceedings of the 19th International Joint Conference on Articial Intelligence (IJCAI05
, 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 p ..."
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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.
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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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.
Strongly equivalent temporal logic programs
"... This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, t ..."
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This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, the intermediate logic of HereandThere (HT). Trivially, equivalence in this temporal extension of HT provides a sufficient condition for temporal strong equivalence and, as we show in the paper, it can be transformed into a provability test into the standard Linear Temporal Logic (LTL), something that can be automatically checked using any of the LTL available provers. The paper shows an example of the potential utility of this method by detecting some redundant rules in a simple actions reasoning scenario.
cc⊤: A tool for checking advanced correspondence problems in answerset programming
 In Proceedings of the 15th International Conference on Computing (CIC 2006 ), A. Gelbukh
"... In recent work, a general framework for specifying correspondences between logic programs under the answerset semantics has been defined. The framework allows to define different notions of equivalence, including wellknown notions like strong equivalence as well as refined ones based on the projec ..."
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In recent work, a general framework for specifying correspondences between logic programs under the answerset semantics has been defined. The framework allows to define different notions of equivalence, including wellknown notions like strong equivalence as well as refined ones based on the projection of answer sets, where not all parts of an answer set are of relevance. In this paper, we describe a system, called cc⊤, to verify program correspondences in this general framework, relying on lineartime constructible reductions to quantified propositional logic using extant solvers for the latter language as backend inference engines. We provide a preliminary performance evaluation which sheds light on some crucial design issues. 1.
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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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
An extension of the system cc⊤ for testing relativised uniform equivalence under answerset projection
 IN PROCEEDINGS OF THE 16TH INTERNATIONAL CONFERENCE ON COMPUTING (CIC
, 2007
"... The system cc ⊤ is a tool for testing correspondence between nonmonotonic logic programs under the answerset semantics with respect to different refined notions of program correspondence. The basic architecture of cc ⊤ is to reduce a given correspondence problem into the satisfiability problem for ..."
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The system cc ⊤ is a tool for testing correspondence between nonmonotonic logic programs under the answerset semantics with respect to different refined notions of program correspondence. The basic architecture of cc ⊤ is to reduce a given correspondence problem into the satisfiability problem for quantified propositional logic and to employ offtheshelf solvers for the latter language as backend inference engines. In a previous incarnation of cc⊤, the system was designed to test correspondence between logic programs based on relativised strong equivalence under answerset projection. Such a setting generalises the usual notion of strong equivalence by taking the alphabet of the context programs as well as the projection of the compared answer sets to a set of designated output atoms into account. In this paper, we describe an extension of cc⊤ for testing similarly parameterised correspondence problems but generalising uniform equivalence, which have recently been introduced in previous work. Besides reviewing the formal underpinnings of the new component of cc⊤, we discuss an alternative encoding as well as optimisations for special problem classes. Furthermore, we give a prelimi
cc ⊤ on Stage: Generalised Uniform Equivalence Testing for Verifying Student Assignment Solutions ⋆
"... Abstract. The tool cc ⊤ is an implementation for testing various parameterised notions of program correspondence between logic programs under the answerset semantics, based on reductions to quantified propositional logic. One such notion is relativised uniform equivalence with projection, which exte ..."
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Abstract. The tool cc ⊤ is an implementation for testing various parameterised notions of program correspondence between logic programs under the answerset semantics, based on reductions to quantified propositional logic. One such notion is relativised uniform equivalence with projection, which extends standard uniform equivalence via two additional parameters: one for specifying the input alphabet and one for specifying the output alphabet. In particular, the latter parameter is used for projecting answer sets to the set of designated output atoms, i.e., ignoring auxiliary atoms during answerset comparison. In this paper, we discuss an application of cc ⊤ for verifying the correctness of students ’ solutions drawn from a laboratory course on logic programming, employing relativised uniform equivalence with projection as the underlying program correspondence notion. We complement our investigation by discussing a performance evaluation of cc⊤, showing that discriminating among different backend solvers for quantified propositional logic is a crucial issue towards optimal performance. 1
Strong Equivalence of Nonmonotonic Temporal Theories∗
"... In this paper we solve the following open problem: we prove that equivalence in the logic of Temporal HereandThere (THT) is not only a sufficient, but also a necessary condition for strong equivalence of two Temporal Equilibrium Logic (TEL) theories. This result has allowed constructing a tool, AB ..."
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In this paper we solve the following open problem: we prove that equivalence in the logic of Temporal HereandThere (THT) is not only a sufficient, but also a necessary condition for strong equivalence of two Temporal Equilibrium Logic (TEL) theories. This result has allowed constructing a tool, ABSTEM, that can be used to check different types of equivalence between two arbitrary temporal theories. More importantly, when the theories are not THTequivalent, the system provides a context theory that makes them behave differently, together with a Büchi automaton showing the temporal stable models that arise from that difference.
WASP WP3 report: Language extensions and software engineering for ASP, http://www.tcs.hut.fi/Research/Logic/wasp/wp3/waspwp3web
, 2003
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cc⊤: A correspondencechecking tool for logic programs under the answerset semantics
 In Proceedings of the 10th European Conference on Logics in Artificial Intelligence (JELIA 2006
"... Abstract. In recent work, a general framework for specifying correspondences between logic programs under the answerset semantics has been defined. The framework captures different notions of equivalence, including wellknown ones like ordinary, strong, and uniform equivalence, as well as refined o ..."
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Abstract. In recent work, a general framework for specifying correspondences between logic programs under the answerset semantics has been defined. The framework captures different notions of equivalence, including wellknown ones like ordinary, strong, and uniform equivalence, as well as refined ones based on the projection of answer sets where not all parts of an answer set are of relevance. In this paper, we describe an implementation to verify program correspondences in this general framework. The system, called cc⊤, relies on lineartime constructible reductions to quantified propositional logic and uses extant solvers for the latter language as backend inference engines. 1 General Information To support engineering tasks in answerset programming (ASP) [4], an important issue is to determine the equivalence of different problem encodings, given by two logic programs. Various notions of equivalence between programs have been studied in the literature [7, 2, 11] including the recently proposed framework by Eiter et al. [3], which subsumes most of the previously introduced notions. Within this framework, correspondence