Titlebook: Substructural Logics: A Primer; Francesco Paoli Book 2002 Springer Science+Business Media Dordrecht 2002 Algebraic structure.Cut-eliminati

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The Role of Structural Rules in Sequent Calculizen where one or more of the structural rules (weakening, contraction, exchange, cut) are suitably restricted or even left out. We do not assume the reader to be familiar with the terminology of the preceding sentence, which will be subsequently explained in full detail — but if only she has some ac

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Cut Elimination and the Decision Problemer, we did not . the cut elimination theorem for any of the systems so far introduced. This will be exactly the task of the present chapter. For a start, we shall present Gentzen’s proof of the . for .; coming to know how such a proof works is essential also from our perspective, for it allows to ap

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Algebraic Structuresof algebraic structures which verify exactly the provable formulae of S. Thus, for example, it turns out that the algebraic counterpart of classical propositional logic are Boolean algebras, while intuitionistic propositional logic corresponds to Heyting algebras. As a rule, these correspondences pa

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Relational Semanticsanother standpoint one can assume about the semantic value of sentences. In fact, a true sentence like “Brutus killed Caesar” could have been false if Brutus had not killed Caesar; it is true in the light of what actually happened, but could have been false if human history had been different — in a

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Basic Proof Systems for Substructural Logics some extent, arbitrary. However, a delicate tradeoff is involved: this system must be neither too weak, for it would lack any intrinsic interest, nor too strong, since its extensions would be too limited in number.

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