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Towards Implementations for Advanced Equivalence Checking in AnswerSet Programming
 ICLP 2005. LNCS
, 2005
"... 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 ba ..."
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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 describe an approach to compute program correspondences in this general framework by means of lineartime constructible reductions to quantified propositional logic. We can thus use extant solvers for the latter language as backend inference engines for computing program correspondence problems. We also describe how our translations provide a method to construct counterexamples in case a program correspondence does not hold.
Inferring with inconsistent OWL DL ontology: A multivalued logic approach
 EDBT WORKSHOPS. VOLUME 4254 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Web ontology language OWL DL has twovalued model theory semantics so that ontologies expressed by it become trivial when contradictions occur. Based on classical description logic SHOIN (D), we propose the fourvalued description logic SHOIN (D)4 which has the ability to reason with inconsistencies ..."
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Web ontology language OWL DL has twovalued model theory semantics so that ontologies expressed by it become trivial when contradictions occur. Based on classical description logic SHOIN (D), we propose the fourvalued description logic SHOIN (D)4 which has the ability to reason with inconsistencies. By transformation technic, we convert the reasoning problems of SHOIN (D)4 to the counterparts of SHOIN (D). So SHOIN (D)4 provides us with an approach to deal with contradictions by classical reasoning mechanism.
Computational methods for database repair by signed formulae
 Ann. Math. Artif. Intell
"... Abstract. We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and ..."
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Abstract. We introduce a simple and practical method for repairing inconsistent databases. Given a possibly inconsistent database, the idea is to properly represent the underlying problem, i.e., to describe the possible ways of restoring its consistency. We do so by what we call signed formulae, and show how the ‘signed theory ’ that is obtained can be used by a variety of offtheshelf computational models in order to compute the corresponding solutions, i.e., consistent repairs of the database. 1.
Representing Paraconsistent Reasoning via Quantified Propositional Logic
 In Inconsistency Tolerance, volume 3300 of LNCS
, 2005
"... Abstract. Quantified propositional logic is an extension of classical propositional logic where quantifications over atomic formulas are permitted. As such, quantified propositional logic is a fragment of secondorder logic, and its sentences are usually referred to as quantified Boolean formulas (QB ..."
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Abstract. Quantified propositional logic is an extension of classical propositional logic where quantifications over atomic formulas are permitted. As such, quantified propositional logic is a fragment of secondorder logic, and its sentences are usually referred to as quantified Boolean formulas (QBFs). The motivation to study quantified propositional logic for paraconsistent reasoning is based on two fundamental observations. Firstly, in recent years, practicably efficient solvers for quantified propositional logic have been presented. Secondly, complexity results imply that there is a wide range of paraconsistent reasoning problems which can be efficiently represented in terms of QBFs. Hence, solvers for QBFs can be used as a core engine in systems prototypically implementing several of such reasoning tasks, most of them lacking concrete realisations. To this end, we show how certain paraconsistent reasoning principles can be naturally formulated or reformulated by means of quantified Boolean formulas. More precisely, we describe polynomialtime constructible encodings providing axiomatisations of the given reasoning tasks. In this way, a whole variety of a priori distinct approaches to paraconsistent reasoning become comparable in a uniform setting. 1
Paraconsistent reasoning and preferential entailments by signed quantified boolean formulae
 2007. Maier, Yue Ma, Pascal Hitzler / Paraconsistent OWL and Related Logics 33 hal00705876, version 1  8 Jun 2012
"... We introduce a uniform approach of representing a variety of paraconsistent nonmonotonic formalisms by quantified Boolean formulae (QBFs) in the context of multiplevalued logics. We show that this framework provides a useful platform for capturing, in a simple and natural way, a wide range of met ..."
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Cited by 5 (2 self)
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We introduce a uniform approach of representing a variety of paraconsistent nonmonotonic formalisms by quantified Boolean formulae (QBFs) in the context of multiplevalued logics. We show that this framework provides a useful platform for capturing, in a simple and natural way, a wide range of methods for preferential reasoning. The outcome is a subtle approach to represent the underlying formalisms, which induces a straightforward way to compute the corresponding entailments: by incorporating offtheshelf QBF solvers it is possible to simulate within our framework various kinds of preferential formalisms, among which are Priest’s logic LPm of reasoning with minimal inconsistency, Batens ’ adaptive logic ACLuNs2, Besnard and Schaub’s inference relation =n, a variety of formulapreferential systems, some bilatticebased preferential relations (e.g., =I1 and =I2), and consequence relations for reasoning with graded uncertainty (such as the fourvalued logic =4c).
Distancebased semantics for multiplevalued logics
 In Proc. 11th Int. Workshop on NonMonotonic Reasoning
, 2006
"... We show that the incorporation of distancebased semantics in the context of multiplevalued consequence relations yields a general, simple, and intuitively appealing framework for reasoning with incomplete and inconsistent information. ..."
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Cited by 2 (1 self)
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We show that the incorporation of distancebased semantics in the context of multiplevalued consequence relations yields a general, simple, and intuitively appealing framework for reasoning with incomplete and inconsistent information.
FourValued Semantics for Default Logic ⋆
"... Abstract. Reiter’s default logic suffers the triviality, that is, a single contradiction in the premise of a default theory leads to the only trivial extension which everything follows from. In this paper, we propose a default logic based on fourvalued semantics, which endows default logic with the ..."
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Abstract. Reiter’s default logic suffers the triviality, that is, a single contradiction in the premise of a default theory leads to the only trivial extension which everything follows from. In this paper, we propose a default logic based on fourvalued semantics, which endows default logic with the ability of handling inconsistency without leading to triviality. We define fourvalued models for default theory such that the default logic has the ability of nonmonotonic paraconsistent reasoning. By transforming default rules in propositional language L into language L +, a onetoone relation between the fourvalued models in L and the extensions in L + is proved, whereby the proof theory of Reiter’s default logic is remained. 1
an der
"... i Acknowledgements First, I would like to thank Hans Tompits for supervising this work and for his excellent introduction to scientific research. Furthermore, I want to thank Martina Seidl and Stefan Woltran for their collaboration on many paper projects related to this thesis. Also, I am graceful ..."
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i Acknowledgements First, I would like to thank Hans Tompits for supervising this work and for his excellent introduction to scientific research. Furthermore, I want to thank Martina Seidl and Stefan Woltran for their collaboration on many paper projects related to this thesis. Also, I am graceful to Elfriede Nedoma, Eva Nedoma, and Matthias Schlögel for their important administrative and technical support. Finally, I would like to thank my parents, Elke Oetsch and Hans Oetsch, for all the support and for not giving up hope that I would eventually finish my master thesis.