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  1. 1 Logic and Logical Philosophy

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  1. 1 Zielonka W.

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  1. 1 2012

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Two Weak Lambek-Style Calculi: DNL and DNL

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Zielonka W.
Logic and Logical Philosophy
|
2012
|
vol. 21
|
issue 1
53-64
EN
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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