Full Nonassociative Lambek Calculus with Distribution: Models and Grammars
نویسندگان
چکیده
We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Full Nonassociative Lambek Calculus with Distribution DFNL). We prove that formal grammars based on DFNL, also with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, employed in [13] in the proof of Strong Finite Model Property of DFNL. We obtain analogous results for different variants of DFNL, e.g. BFNL, which admits negation ¬ such that ∧,∨,¬ satisfy the laws of boolean algebra, and HFNL whose underlying lattice is a Heyting algebra. Our proof also yields Finite Embeddability Property for boolean and Heyting algebras, supplied with an additional residuation structure.
منابع مشابه
Lambek Grammars, Tree Adjoining Grammars and Hyperedge Replacement Grammars
Two recent extension of the nonassociative Lambek calculus, the LambekGrishin calculus and the multimodal Lambek calculus, are shown to generate class of languages as tree adjoining grammars, using (tree generating) hyperedge replacement grammars as an intermediate step. As a consequence both extensions are mildly context-sensitive formalisms and benefit from polynomial parsing algorithms.
متن کاملOn Commutative and Nonassociative Syntactic Calculi and Categorial Grammars
Two axiomatizations of the nonassociative and commutative Lambek syntactic calculus are given and their equivalence is proved. The rst axiomatization employs Permutation as the only structural rule, the second one, with no Permutation rule, employs only unidirectional types. It is also shown that in the case of the Aj-dukiewicz calculus an analogous equivalence is valid only in the case of a re...
متن کاملConjoinability and unification in Lambek categorial grammars
Recently, learning algorithms in Gold’s model have been proposed for some particular classes of classical categorial grammars [Kan98]. We are interested here in learning Lambek categorial grammars. In general grammatical inference uses unification and substitution. In the context of Lambek categorial grammars it seems appropriate to incorporate an operation on types based both on deduction (Lam...
متن کاملNonassociative Lambek Calculus with Additives and Context-Free Languages
We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Distributive Full Nonassociative Lambek Calculus DFNL). We prove that categorial grammars based on DFNL, also enriched with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, earlier employed in [11] in the proof of Fi...
متن کامل