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Duality, projectivity, and unification in Lukasiewicz logic and MValgebras
"... We prove that the unification type of Lukasiewicz (infinitevalued propositional) logic and of its equivalent algebraic semantics, the variety of MValgebras, is nullary. The proof rests upon Ghilardi’s algebraic characterisation of unification types in terms of projective objects, recent progress ..."
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We prove that the unification type of Lukasiewicz (infinitevalued propositional) logic and of its equivalent algebraic semantics, the variety of MValgebras, is nullary. The proof rests upon Ghilardi’s algebraic characterisation of unification types in terms of projective objects, recent progress
GEOMETRICAL DUALITIES FOR LUKASIEWICZ LOGIC
"... Abstract. This article develops a general dual adjunction between MValgebras (the algebraic equivalents of Lukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MValgebras. Such a dual adjunction restricts to a duality between ..."
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Abstract. This article develops a general dual adjunction between MValgebras (the algebraic equivalents of Lukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MValgebras. Such a dual adjunction restricts to a duality between
Bounded Lukasiewicz Logics
"... Lukasiewicz logics were introduced for philosophical reasons by Jan Lukasiewiczin the 1920s [8] and are among the first examples of manyvalued logics. Currently they are of great importance in several areas of research. Firstly, in fuzzylogic [15], where infinitevalued Lukasiewicz logic ..."
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Lukasiewicz logics were introduced for philosophical reasons by Jan Lukasiewiczin the 1920s [8] and are among the first examples of manyvalued logics. Currently they are of great importance in several areas of research. Firstly, in fuzzylogic [15], where infinitevalued Lukasiewicz logic
Belief Functions on Formulas in Lukasiewicz Logic
"... Belief functions are generalized to formulas in Lukasiewicz logic. It is shown that they generalize probabilities on formulas (socalled states) and that they are completely monotone mappings with respect to the lattice operations. 1 ..."
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Belief functions are generalized to formulas in Lukasiewicz logic. It is shown that they generalize probabilities on formulas (socalled states) and that they are completely monotone mappings with respect to the lattice operations. 1
The Kakutani duality for MValgebras
"... In the context of Riesz spaces and Banach lattices, it is natural to consider the unital ones (i.e, those having a strong unit) as a distinct class: some main spectral representation theorems assume the existence of a strong unit, while basic examples such as C(X) and L1(X,µ) are naturally unital sp ..."
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spaces. Not only does the unit interval generate the entire algebra, it also has a structure of its own: it is an MValgebra with some additional properties. MValgebras were introduced by Chang in 1958 as the algebraic counterpart of ∞valued Lukasiewicz propositional logic. They are to Lukasiewicz
On Lukasiewicz's fourvalued modal logic
, 2000
"... . # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its algeb ..."
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. # Lukasiewicz's fourvalued modal logic is surveyed and analyzed, together with # Lukasiewicz's motivations to develop it. A faithful interpretation of it into classical (nonmodal) twovalued logic is presented, and some consequences are drawn concerning its classification and its
On the set of intermediate logics between the truth and degree preserving Lukasiewicz logics
"... The aim of this paper is to explore the class of intermediate logics between the truthpreserving Lukasiewicz logic L and its degreepreserving companion L≤. From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L ..."
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of finitevalued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A, F) such that A is a finite MValgebra and F is a lattice filter. 1
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