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Traditional winter session MIAN–POMI devoted to the topic "Mathematical logic"
December 25, 2018 14:30–15:05, Moscow, Steklov Mathematical Institute, Gubkina, 8, Conference hall, 9 floor
 


Исчисление Ламбека, обогащенное субэкспоненциалами

A. Scedrov

University of Pennsylvania
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MP4 385.2 Mb

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A. Scedrov
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Abstract: In Lafont's soft linear logic the rule of contraction is replaced by the so-called rule of multiplexing. Here we consider a version of multiplexing where !A implies any positive number of copies of A. The weakening rule is not allowed. We also borrow the ! introduction rule from Girard's light linear logic. Here we study Lambek calculus enriched with these rules. We prove that Lambek calculus so enriched satisfies cut elimination, substitution, and Lambek’s non-emptiness restriction, that is, the left-hand side of any provable sequent is non-empty. We show that this calculus is undecidable. If a number of copies of A in the multiplexing rule is bounded by a fixed constant, then the calculus becomes decidable.

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