Theoretical Computer Science
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
From Semantics to Rules: A Machine Assisted Analysis
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Normal form theorem proving for the Lambek Calculus
COLING '90 Proceedings of the 13th conference on Computational linguistics - Volume 2
Forcing-Based Cut-Elimination for Gentzen-Style Intuitionistic Sequent Calculus
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
The logical basis of evaluation order and pattern-matching
The logical basis of evaluation order and pattern-matching
Continuation semantics for the Lambek--Grishin calculus
Information and Computation
Polarities in logic and semantics
AC'11 Proceedings of the 18th Amsterdam colloquim conference on Logic, Language and Meaning
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While initially motivated for studying natural language syntax, the intuitionistic bias underlying traditional Lambek calculi renders them particularly suitable to a Montagovian formal semantics through the Curry-Howard correspondence. Several recent proposals, however, have departed from the intuitionistic tradition, seeking instead to formulate 'classical' Lambek calculi. We show that this classical turn need not come at the cost of the tight connection with formal semantics, concentrating on De Groote and Lamarche's Classical Non-Associative Lambek calculus (CNL). Our work is founded in Girard's and Andreoli's research into polarities and focused proofs, suggesting the definition of polarized CNL, its connection to De Groote and Lamarche's original proposal explicated through the use of phase spaces. We conclude with a discussion of related literature, particularly Moortgat's Lambek-Grishin calculus.