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50A formalization of Sambins's normalization for GLMathematical Logic Quarterly 39 (1): 133-142. 1993.Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arith…Read more
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21The semantics of falsity and negationManuscrito 27 (1): 183-191. 2004.In Logical Forms Chateaubriand offers a realist semantics for false elementary propositions and for true negative propositions that appeals to negative facts. Although he does not refer to Wittgenstein, he rules out “possibilist” solutions such as that of the Tractatus. In this paper I will critically discuss Chateaubriand’s solution and compare it with the semantics of the Tractatus
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102A short note on intuitionistic propositional logic with multiple conclusionsManuscrito 28 (2): 317-329. 2005.A common misconception among logicians is to think that intuitionism is necessarily tied-up with single conclusion calculi. Single conclusion calculi can be used to model intuitionism and they are convenient, but by no means are they necessary. This has been shown by such influential textbook authors as Kleene, Takeuti and Dummett, to cite only three. If single conclusions are not necessary, how do we guarantee that only intuitionistic derivations are allowed? Traditionally one insists on restri…Read more
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44A New Normalization Strategy for the Implicational Fragment of Classical Propositional LogicStudia Logica 96 (1): 95-108. 2010.The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to…Read more
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269Considerações sobre a Noção Construtiva de VerdadeO Que Nos Faz Pensar 17 107-123. 2003.This paper deals with the recent Swedish proposals of a Intuitionistic notion of Truth, by Dag Prawitz and Per Martin-Löf.
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249th Workshop on Logic, Language, Information and ComputationLogic Journal of the IGPL 10 (6): 679-688. 2002.