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38
Mapping problems with finitedomain variables into problems with boolean variables
 In SAT 2004
, 2004
"... Abstract. We define a collection of mappings that transform manyvalued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks with stateoftheart SAT solvers. Our results provide empirical evidence that enc ..."
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Cited by 31 (9 self)
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Abstract. We define a collection of mappings that transform manyvalued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks with stateoftheart SAT solvers. Our results provide empirical evidence that encoding combinatorial problems with the mappings defined here can lead to substantial performance improvements in complete SAT solvers. 1
Elimination of Cuts in Firstorder Finitevalued Logics
 J. Inform. Process. Cybernet. (EIK
, 1994
"... A uniform construction for sequent calculi for finitevalued firstorder logics with distribution quantifiers is exhibited. Completeness, cutelimination and midsequent theorems are established. As an application, an analog of Herbrand's theorem for the fourvalued knowledgerepresentation logic ..."
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Cited by 19 (4 self)
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A uniform construction for sequent calculi for finitevalued firstorder logics with distribution quantifiers is exhibited. Completeness, cutelimination and midsequent theorems are established. As an application, an analog of Herbrand's theorem for the fourvalued knowledgerepresentation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report
 IN PROC. NMR02
, 2002
"... Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Previous results show that nested logic programs can be transformed into standard (unnested) disjunctive logic pro ..."
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Cited by 14 (3 self)
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Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Previous results show that nested logic programs can be transformed into standard (unnested) disjunctive logic programs in an elementary way, applying the negationasfailure operator to body literals only. This is of great practical relevance since it allows us to evaluate nested logic programs by means of offtheshelf disjunctive logic programming systems, like DLV. However, it turns out that this straightforward transformation results in an exponential blowup in the worstcase, despite the fact that complexity results indicate that there is a polynomial translation among both formalisms. In this paper, we take up this challenge and provide a polynomial translation of logic programs with nested expressions into disjunctive logic programs. Moreover, we show that this translation is modular and (strongly) faithful. We have implemented both the straightforward as well as our advanced transformation; the resulting compiler serves as a frontend to DLV and is publicly available on the Web.
Probabilistic and TruthFunctional ManyValued Logic Programming
 IN PROCEEDINGS OF THE 29TH IEEE INTERNATIONAL SYMPOSIUM ON MULTIPLEVALUED LOGIC
, 1998
"... We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that a ..."
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Cited by 13 (9 self)
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We introduce probabilistic manyvalued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic manyvalued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are Pcomplete for classical logic programs are shown to be coNPcomplete for probabilistic manyvalued logic programs. We then focus on manyvalued logic programming in Pr ? n as an approximation of probabilistic manyvalued logic programming. Surprisingly, manyvalued logic programs in Pr ? n have both a probabilistic semantics in probabilities over a set of possible worlds and a truthfunctional semantics in the finitevalued Łukasiewicz logics Łn . Moreover, manyvalued logic programming in Pr ? n has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming. We especially introduce the proof...
Automated Theorem Proving by Resolution for FinitelyValued Logics Based on Distributive Lattices with Operators
 An International Journal of MultipleValued Logic
, 1999
"... In this paper we present a method for automated theorem proving in manyvalued logics whose algebra of truth values is a nite distributive lattice with operators. This class of manyvalued logics includes many logics that occur in a natural way in applications. The method uses the Priestley dual of t ..."
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Cited by 11 (2 self)
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In this paper we present a method for automated theorem proving in manyvalued logics whose algebra of truth values is a nite distributive lattice with operators. This class of manyvalued logics includes many logics that occur in a natural way in applications. The method uses the Priestley dual of the algebra of truth values instead of the algebra itself; this dual is used as a finite set of possible worlds. We first present a procedure that constructs, for every formula in the language of such a logic, a set of signed clauses such that is a theorem if and only if is unsatisfiable. Compared to related approaches, the method presented here leads in many cases to a reduction of the number of clauses that are generated, especially when the set of truth values is not linearly ordered. We then discuss several possibilities for checking the unsatisfiability of , among which a version of signed hyperresolution, and give several examples.
Commodious Axiomatization of Quantifiers in MultipleValued Logic
, 1997
"... . We provide tools for a concise axiomatization of a broad class of quantifiers in manyvalued logic, socalled distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantif ..."
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. We provide tools for a concise axiomatization of a broad class of quantifiers in manyvalued logic, socalled distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite distributive lattices are used to derive tableaustyle axiomatizations of distribution quantifiers. Introduction The aim of this paper 1 is to provide concise axiomatizations of certain quantifiers in manyvalued logic which were introduced by Mostowski (1961) and baptized distribution quantifiers by Carnielli (1987). The task of axiomatizing such quantifiers has been solved satisfactorily in theor...
Mechanising Partiality without ReImplementation
 IN 21ST ANNUAL GERMAN CONFERENCE ON ARTIFICIAL INTELLIGENCE, VOLUME 1303 OF LNAI
, 1997
"... Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a threevalued logic decades ago. This approach allows rejecting certain unwanted formul ..."
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Cited by 10 (5 self)
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Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a threevalued logic decades ago. This approach allows rejecting certain unwanted formulae as faulty, which the simpler twovalued ones accept. We have developed resolution and tableau calculi for automated theorem proving that take the restrictions of the threevalued logic into account, which however have the severe drawback that existing theorem provers cannot directly be adapted to the technique. Even recently implemented calculi for manyvalued logics are not wellsuited, since in those the quantification does not exclude the undefined element. In this work we show, that it is possible to enhance a twovalued theorem prover by a simple strategy so that it can be used to generate proofs for the theorems of the threevalued setting. By this we are able to use an existing t...
Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
MUltlog 1.0: Towards an Expert System for Manyvalued Logics
, 1996
"... MUltlog is a system which takes as input the specification of a finitelyvalued firstorder logic and produces a sequent calculus, a natural deduction system, and a calculus for transforming a manyvalued formula to clauses suitable for manyvalued resolution. All generated rules are optimized r ..."
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Cited by 9 (3 self)
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MUltlog is a system which takes as input the specification of a finitelyvalued firstorder logic and produces a sequent calculus, a natural deduction system, and a calculus for transforming a manyvalued formula to clauses suitable for manyvalued resolution. All generated rules are optimized regarding their branching degree. The output is in the form of a scientific paper, written in L A T E X.
Automated theorem proving by resolution in nonclassical logics
 Annals of Mathematics and Artificial Intelligence
, 2007
"... This paper is an overview of a variety of results, all centered around a common theme, namely embedding of nonclassical logics into first order logic and resolution theorem proving. We present several classes of nonclassical logics, many of which are of great practical relevance in knowledge repre ..."
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Cited by 9 (6 self)
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This paper is an overview of a variety of results, all centered around a common theme, namely embedding of nonclassical logics into first order logic and resolution theorem proving. We present several classes of nonclassical logics, many of which are of great practical relevance in knowledge representation, which can be translated into tractable and relatively simple fragments of classical logic. In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures. 1