Two Weak Lambek-Style Calculi: DNL and DNL

• Authors: Wojciech Zielonka
• Languages of publication: EN

Abstracts

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.

Keywords

EN

Lambek calculus; Gentzen formalism; axiomatization

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2012
• Volume: 21
• Issue: 1
• Pages: 53-64

Dates

published

2012-03-01

online

2013-07-02

Contributors

author

Wojciech Zielonka

• University of Warmia and Mazury Faculty of Mathematics and Computer Science Żołnierska 14a, 10-561 Olsztyn, Poland

References

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Identifiers

DOI

10.12775/LLP.2012.004