On Reduction Systems Equivalent to the Non-associative Lambek Calculus with the Empty String

2007 ◽  
Vol 17 (2) ◽  
pp. 299-310 ◽  
Author(s):  
W. Zielonka
Keyword(s):  
Lambek Calculus ◽  
Empty String

scholarly journals Involutive Nonassociative Lambek Calculus: Sequent Systems and Complexity

2017 ◽  
Vol 46 (1/2) ◽  
Author(s):  
Wojciech Buszkowski
Keyword(s):  
Cut Elimination ◽  
Lambek Calculus ◽  
Double Negation ◽  
Sequent Systems ◽  
Sequent System

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 Grooté 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 PTIME.

scholarly journals Undecidability of the Lambek Calculus with a Relevant Modality

2016 ◽  
pp. 240-256 ◽  
Author(s):  
Max Kanovich ◽  
Stepan Kuznetsov ◽  
Andre Scedrov
Keyword(s):  
Lambek Calculus

scholarly journals Correction to: Lambek Calculus with Conjugates

Studia Logica ◽  
2020 ◽  
Author(s):  
Igor Sedlár ◽  
Andrew Tedder
Keyword(s):  
Lambek Calculus
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