TY - JOUR AU - Zielonka, Wojciech PY - 2012/03/15 Y2 - 2024/03/29 TI - Two weak Lambek style calculi: DNL and DNL−∗ JF - Logic and Logical Philosophy JA - LLP VL - 21 IS - 1 SE - Articles DO - 10.12775/LLP.2012.004 UR - https://apcz.umk.pl/LLP/article/view/LLP.2012.004 SP - 53-64 AB - <p>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<sup>−</sup> 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.</p> ER -