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Canonical Propositional GentzenType Systems
 in Proceedings of the 1st International Joint Conference on Automated Reasoning (IJCAR 2001) (R. Goré, A Leitsch, T. Nipkow, Eds), LNAI 2083
, 2001
"... . Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connectiv ..."
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Cited by 29 (16 self)
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. Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connective is mentioned anywhere else in their formulation. We provide a constructive coherence criterion for the nontriviality of such systems, and show that a system of this kind admits cut elimination i it is coherent. We show also that the semantics of such systems is provided by nondeterministic twovalued matrices (2Nmatrices). 2Nmatrices form a natural generalization of the classical twovalued matrix, and every coherent canonical system is sound and complete for one of them. Conversely, with any 2Nmatrix it is possible to associate a coherent canonical Gentzentype system which has for each connective at most one introduction rule for each side, and is sound and complete for th...
Hypersequent calculi for Gödel logics: a survey
 Journal of Logic and Computation
, 2003
"... Hypersequent calculi arise by generalizing standard sequent calculi to refer to whole contexts of sequents instead of single sequents. We present a number of results using hypersequents to obtain a Gentzenstyle characterization for the family of Gödel logics. We first describe analytic calculi for ..."
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Cited by 13 (4 self)
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Hypersequent calculi arise by generalizing standard sequent calculi to refer to whole contexts of sequents instead of single sequents. We present a number of results using hypersequents to obtain a Gentzenstyle characterization for the family of Gödel logics. We first describe analytic calculi for propositional finite and infinitevalued Gödel logics. We then show that the framework of hypersequents allows one to move straightforwardly from the propositional level to firstorder as well as propositional quantification. A certain type of modalities, enhancing the expressive power of Gödel logic, is also considered. 1
The Inverse Method
, 2001
"... this paper every formula is equivalent to a formula in negation normal form ..."
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Cited by 13 (1 self)
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this paper every formula is equivalent to a formula in negation normal form
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.
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 8 (4 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
Cutfree Ordinary Sequent Calculi for Logics Having FiniteValued Semantics
 LOGICA UNIVERSALIS
, 2006
"... ..."
Chaining Techniques for Automated Theorem Proving in ManyValued Logics
 In Proc. 30th ISMVL
, 2000
"... We apply chaining techniques to automated theorem proving in manyvalued logics. In particular, we show that superposition specializes to a refined version of the manyvalued resolution rules introduced by Baaz and Ferm uller, and that ordered chaining can be specialized to a refutationally complete ..."
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Cited by 6 (2 self)
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We apply chaining techniques to automated theorem proving in manyvalued logics. In particular, we show that superposition specializes to a refined version of the manyvalued resolution rules introduced by Baaz and Ferm uller, and that ordered chaining can be specialized to a refutationally complete inference system for regular clauses. 1. Introduction A general method for automated theorem proving in finitelyvalued logics is the manyvalued resolution method by Baaz and Fermuller [1]. Their results have been extended in [7, 8], [10], and [2], where various versions of signed resolution are defined. Signed resolution rules have also been proposed for annotated logics by Kifer and Lozinskii [9] and Lu, Murray and Rosenthal [10]. Hahnle [8] has developed a hyperresolution method for the socalled regular logics which is directly modeled after classical hyperresolution. The completeness proofs are more or less directly derived from those for classical logic. The calculi in [10] are obt...
Classiclike analytic tableaux for finitevalued logics
 in Proceedings of the XVI Workshop on Logic, Language, Information and Computation (WoLLIC 2009), held in Tokyo, JP, June 2009, ser. Lecture Notes in Artificial Intelligence
, 2009
"... Abstract. The paper provides a recipe for adequately representing a very inclusive class of finitevalued logics by way of tableaux. The only requisite for applying the method is that the object logic received as input should be sufficiently expressive, in having the appropriate linguistic resources ..."
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Cited by 6 (6 self)
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Abstract. The paper provides a recipe for adequately representing a very inclusive class of finitevalued logics by way of tableaux. The only requisite for applying the method is that the object logic received as input should be sufficiently expressive, in having the appropriate linguistic resources that allow for a bivalent representation. For each logic, the tableau system obtained as output has some attractive features: exactly two signs are used as labels in the rules, as in the case of classical logic, providing thus a uniform framework in which different logics can be represented and compared; the application of the rules is analytic, in that it always reduces complexity, providing thus an immediate prooftheoretical decision procedure together with a countermodel builder for the given logic. Key words: manyvalued logics, proof theory 1
Sequent of Relations Calculi: A Framework for Analytic Deduction in ManyValued Logics
 Beyond Two: Theory and applications of MultipleValued Logics
, 2003
"... We present a general framework that allows to construct systematically analytic calculi for a large family of (propositional) manyvalued logics  called projective logics  characterized by a special format of their semantics. All finitevalued logics as well as infinitevalued Godel logic ..."
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Cited by 5 (3 self)
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We present a general framework that allows to construct systematically analytic calculi for a large family of (propositional) manyvalued logics  called projective logics  characterized by a special format of their semantics. All finitevalued logics as well as infinitevalued Godel logic are projective. As a casestudy, sequent of relations calculi for Godel logics are derived. A comparison with some other analytic calculi is provided.