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Trakhtenbrot theorem and firstorder axiomatic extensions of MTL
"... Abstract. In 1950, B.A. Trakhtenbrot showed that the set of firstorder tautologies associated to finite models is not recursively enumerable. In 1999, P. Hájek generalized this result to the firstorder versions of Lukasiewicz, Gödel and Product logics, w.r.t. their standard algebras. In this tal ..."
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. In this talk we extend the analysis to the firstorder versions of axiomatic extensions of MTL. Our main result is the following. Let K be a class of nontrivial MTLchains: then the set of all firstorder tautologies associated to the finite models over chains in K, fTAUTK ∀ , is Π01hard. Let TAUTK
Firstorder Gödel logics
, 2006
"... Firstorder Gödel logics are a family of infinitevalued logics where the sets of truth values V are closed subsets of [0,1] containing both 0 and 1. Different such sets V in general determine different Gödel logics GV (sets of those formulas which evaluate to 1 in every interpretation into V). It i ..."
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Cited by 14 (5 self)
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). It is shown that GV is axiomatizable iff V is finite, V is uncountable with 0 isolated in V, or every neighborhood of 0 in V is uncountable. Complete axiomatizations for each of these cases are given. The r.e. prenex, negationfree, and existential fragments of all firstorder Gödel logics are also
Adding modalities to MTL and its extensions
 Proceedings of the Linz Symposium
, 2005
"... Abstract. Monoidal tnorm logic MTL and related fuzzy logics are extended with various modalities distinguished by the axiom (A ∨ B) → (A ∨ B). Such modalities include Linear logiclike exponentials, the globalization (or Delta) operator, and truth stressers like “very true”. Extensions of MTL with ..."
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Cited by 7 (1 self)
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Abstract. Monoidal tnorm logic MTL and related fuzzy logics are extended with various modalities distinguished by the axiom (A ∨ B) → (A ∨ B). Such modalities include Linear logiclike exponentials, the globalization (or Delta) operator, and truth stressers like “very true”. Extensions of MTL
Adding Modalities to MTL and its Extensions
"... Abstract. Monoidal tnorm logic MTL and related fuzzy logics are extendedwith various modalities distinguished by the axiom \Lambda (A. B) ! (\Lambda A. \Lambda B).Such modalities include Linear logiclike exponentials, the globalization (or Delta) operator, and truth stressers like "very t ..."
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;quot;very true". Extensions of MTL with modalities are presented here via axiomatizations, hypersequent calculi, and algebraic semantics, and related to standard algebras based on tnorms. Embeddings oflogics, decidability, and the finite embedding property are also investigated.
Standard completeness for extensions of MTL: an automated approach
, 2012
"... We provide general conditions on hypersequent calculi that guarantee standard completeness for the formalized logics. These conditions are implemented in the PROLOG system AxiomCalc that takes as input any suitable axiomatic extension of Monoidal Tnorm Logic MTL and outputs a hypersequent calculus ..."
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Cited by 3 (3 self)
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We provide general conditions on hypersequent calculi that guarantee standard completeness for the formalized logics. These conditions are implemented in the PROLOG system AxiomCalc that takes as input any suitable axiomatic extension of Monoidal Tnorm Logic MTL and outputs a hypersequent
Density Elimination and Rational Completeness for FirstOrder Logics
"... Density elimination by substitutions is introduced as a uniform method for removing applications of the TakeutiTitani density rule from proofs in firstorder hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cutel ..."
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elimination. Moreover, adding the density rule to any axiomatic extension of a simple firstorder logic gives a logic that is rational complete; i.e., complete with respect to linearly and densely ordered algebras: a precursor to showing that it is a fuzzy logic (complete for algebras with a real unit interval lattice
Equality and Monodic FirstOrder Temporal Logic
 Studia Logica
, 2002
"... It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic twovari ..."
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Cited by 17 (7 self)
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It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two
Two Variable FirstOrder Logic over Ordered Domains
 Journal of Symbolic Logic
, 1998
"... The satisfiability problem for the twovariable fragment of firstorder logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wel ..."
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Cited by 25 (0 self)
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The satisfiability problem for the twovariable fragment of firstorder logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary
Results 1  10
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576