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Negations in conflict

Erkenntnis 38 (1):115 - 129 (1993)

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  1. Juxtaposition: A New Way to Combine Logics.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):560-606.
    This paper develops a new framework for combining propositional logics, called "juxtaposition". Several general metalogical theorems are proved concerning the combination of logics by juxtaposition. In particular, it is shown that under reasonable conditions, juxtaposition preserves strong soundness. Under reasonable conditions, the juxtaposition of two consequence relations is a conservative extension of each of them. A general strong completeness result is proved. The paper then examines the philosophically important case of the combination of classical and intuitionist logics. Particular attention is (...)
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  • Natural Semantics: Why Natural Deduction is Intuitionistic.James W. Garson - 2001 - Theoria 67 (2):114-139.
    In this paper investigates how natural deduction rules define connective meaning by presenting a new method for reading semantical conditions from rules called natural semantics. Natural semantics explains why the natural deduction rules are profoundly intuitionistic. Rules for conjunction, implication, disjunction and equivalence all express intuitionistic rather than classical truth conditions. Furthermore, standard rules for negation violate essential conservation requirements for having a natural semantics. The standard rules simply do not assign a meaning to the negation sign. Intuitionistic negation fares (...)
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  • Sentence connectives in formal logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
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