Abstract

:The Lambek Calculus was introduced by Lambek [2] in order to obtain effective rules to allow forming sentences and distinguishing sentences from nonsentences. Two primitives types are defined in this calculus and from these types is allowed to construct compound types to the words of the sentence. We construct a -calculus for the Lambek Calculus, Curry-Howard isomorphic to the sequent calculus. Some proof-theoretical results and a denotational semantic for this calculus, showing its adequacy with regard to the calculus, are shown. A phase semantics, based on Girard's phase semantics for the Linear Logic, searching to implement a verificationistic approach for meaning in construtivism, is also shown for this calculus. Keywords: Lambek Sintactic Calculus, -Calculus, Denotational Semantic, Phase Semantic, Linear Logic. Resumo: O Lambek Calculus foi introduzido por Lambek [2] com o objetivo de obter regras efetivas que permitam formar sentencas e distinguir sentencas de n~ao-sentencas...

Citations