TY - JOUR AU - Buszkowski, Wojciech PY - 2017/06/30 Y2 - 2024/03/29 TI - Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity JF - Bulletin of the Section of Logic JA - B Sect Log VL - 46 IS - 1/2 SE - Research Article DO - 10.18778/0138-0680.46.1.2.07 UR - https://czasopisma.uni.lodz.pl/bulletin/article/view/2931 SP - 75–91 AB - <p style="margin: 0cm 0cm 10pt;"><span style="font-family: Calibri; font-size: medium;">In [5] we study Nonassociative Lambek Calculus (NL) augmented with De Morgan negation, satisfying the double negation and contraposition laws. This logic, introduced by de Groot<span style="line-height: 115%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-fareast-language: EN-US; mso-ansi-language: PL; mso-bidi-language: AR-SA; mso-ascii-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">é</span> and Lamarche [10], is called Classical Non-Associative Lambek Calculus (CNL). Here we study a weaker logic InNL, i.e. NL with two involutive negations. We present a one-sided sequent system for InNL, admitting cut elimination. We also prove that InNL is <em>PTIME</em>.</span></p> ER -