The Lambek-Grishin Calculus Is NP-Complete
نویسنده
چکیده
The Lambek-Grishin calculus LG is the symmetric extension of the non-associative Lambek calculus NL. In this paper we prove that the derivability problem for LG is NP-complete.
منابع مشابه
Relational Semantics for the Lambek-Grishin Calculus
We study ternary relational semantics for symmetric versions of the Lambek calculus with interaction principles due to Grishin (1983). We obtain completeness on the basis of a Henkin-style weak filter construction. 1 Background, motivation The categorial calculi proposed by Lambek and their current typelogical extensions respect an “intuitionistic” restriction: in a Gentzen presentation, Lambek...
متن کاملLambek calculus is NP-complete
We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L∗ the derivability problem is NP-complete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NP-complete.
متن کاملProduct-Free Lambek Calculus Is NP-Complete
In this paper we prove that the derivability problems for productfree Lambek calculus and product-free Lambek calculus allowing empty premises are NP-complete. Also we introduce a new derivability characterization for these calculi.
متن کاملParsing for Semidirectional Lambek Grammar is NP-Complete
We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional. In semidirectional Lambek calculus SDL there is an additional nondirectional abstraction rule allowing the formula abstracted over to appear anywhere in the premise sequent’s left-hand side, thus permitting non-peripheral extraction. SDL grammars are able to gener...
متن کاملPolarized Montagovian Semantics for the Lambek-Grishin Calculus
Grishin ([9]) proposed enriching the Lambek calculus with multiplicative disjunction (par) and coresiduals. Applications to linguistics were discussed by Moortgat ([14]), who spoke of the Lambek-Grishin calculus (LG). In this paper, we adapt Girard’s polarity-sensitive double negation embedding for classical logic ([7]) to extract a compositional Montagovian semantics from a display calculus fo...
متن کامل