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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.
A Solver for QBFs in Nonprenex Form
, 2006
"... Various problems in AI 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 fo ..."
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Cited by 11 (6 self)
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Various problems in AI 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 implement 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 normalform provers on problems from the area of AI.
A Solver for QBFs in Negation Normal Form
, 2006
"... 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 8 (2 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.
Reasoning in argumentation frameworks using quantified boolean formulas
 Proc. COMMA, volume 144 of FAIA, 133–144. IOS
, 2006
"... Abstract. This paper describes a generic approach to implement propositional argumentation frameworks by means of quantified Boolean formulas (QBFs). The motivation to this work is based on the following observations: Firstly, depending on the underlying deductive system and the chosen semantics (i. ..."
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Abstract. This paper describes a generic approach to implement propositional argumentation frameworks by means of quantified Boolean formulas (QBFs). The motivation to this work is based on the following observations: Firstly, depending on the underlying deductive system and the chosen semantics (i.e., the kind of extension under consideration), reasoning in argumentation frameworks can become computationally involving up to the fourth level of the polynomial hierarchy. This makes the language of QBFs a suitable target formalism since decision problems from the polynomial hierarchy can be efficiently represented in terms of QBF. Secondly, several practicably efficient solvers for QBFs are currently available, and thus can be used as blackbox engines in potential implementations of argumentation frameworks. Finally, the definition of suitable QBF modules provides us with a tool box in order to capture a broad range of reasoning tasks associated to formal argumentation. 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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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
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.
Program correspondence under the answerset semantics: The nonground case
 IN: ICLP’08. VOLUME 5366 OF LNCS
, 2008
"... The study of various notions of equivalence between logic programs in the area of answerset programming (ASP) gained increasing interest in recent years. The main reason for this undertaking is that ordinary equivalence between answerset programs fails to yield a replacement property similar to ..."
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Cited by 3 (2 self)
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The study of various notions of equivalence between logic programs in the area of answerset programming (ASP) gained increasing interest in recent years. The main reason for this undertaking is that ordinary equivalence between answerset programs fails to yield a replacement property similar to the one of classical logic. Although many refined program correspondence notions have been introduced in the ASP literature so far, most of these notions were studied for propositional programs only, which limits their practical usability as concrete programming applications require the use of variables. In this paper, we address this issue and introduce a general framework for specifying parameterised notions of program equivalence for nonground disjunctive logic programs under the answerset semantics. Our framework is a generalisation of a similar one defined previously for the propositional case and allows the specification of several equivalence notions extending wellknown ones studied for propositional programs. We provide semantic characterisations for instances of our framework generalising uniform equivalence, and we study decidability and complexity aspects. Furthermore, we consider axiomatisations of such correspondence problems by means of polynomial translations into secondorder logic.
Some questions for institutions to consider further in their own context • To what extent are current or developing institutional strategies for learning and teaching seen to incorporate the underlying principles of ‘information literacy’ among their stud
 In Proc. NMR’06
, 1989
"... Abstract. In recent work, a general framework for specifying program correspondences under the answerset semantics has been defined. The framework allows to define different notions of equivalence, including the wellknown notions of strong and uniform equivalence, as well as refined equivalence no ..."
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Cited by 2 (2 self)
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Abstract. In recent work, a general framework for specifying program correspondences under the answerset semantics has been defined. The framework allows to define different notions of equivalence, including the wellknown notions of strong and uniform equivalence, as well as refined equivalence notions based on the projection of answer sets, where not all parts of an answer set are of relevance (like, e.g., removal of auxiliary letters). In the general case, deciding the correspondence of two programs lies on the fourth level of the polynomial hierarchy and therefore this task can (presumably) not be efficiently reduced to answerset programming. In this paper, we give an overview about an implementation to compute program correspondences in this general framework. The system, called eqcheck, relies on lineartime constructible reductions to quantified propositional logic using extant solvers for the latter language as backend inference engines. We provide some preliminary performance evaluation, which shed light on some crucial design issues. 1
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
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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Cited by 2 (2 self)
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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