Two Weak Lambek-Style Calculi: DNL and DNL

Logic and Logical Philosophy 21 (1):53-64 (2012)
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Abstract

The calculus DNL results from the non-associative Lambek calculus NL by splitting the product functor into the right (⊲) and left (⊳) product interacting respectively with the right (/) and left () residuation. Unlike NL, sequent antecedents in the Gentzen-style axiomatics of DNL are not phrase structures (i.e., bracketed strings) but functor-argument structures. DNL − is a weaker variant of DNL restricted to fa-structures of order ≤ 1. When axiomatized by means of introduction/elimination rules for / and , it shows a perfect analogy to NL which DNL lacks.

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10.12775/llp.2012.004

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References found in this work

The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Linear logic displayed.Nuel Belnap - 1989 - Notre Dame Journal of Formal Logic 31 (1):14-25.
Interdefinability of Lambekian functors.Wojciech Zielonka & W. Zielonka - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):501-507.

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