The Mathematics of Language: 12th Biennial Conference, MOL by Andreas Maletti (auth.), Makoto Kanazawa, András Kornai,

By Andreas Maletti (auth.), Makoto Kanazawa, András Kornai, Marcus Kracht, Hiroyuki Seki (eds.)

This publication constitutes the complaints of the twelfth Biennial assembly on arithmetic in Language, MOL 12, held in Nara, Japan, in September 2011.

Presented during this quantity are 12 rigorously chosen papers, in addition to the paper of the invited speaker Andreas Maletti. The papers hide such assorted issues as formal languages (string and tree transducers, grammar-independent syntactic constructions, probabilistic and weighted context-free grammars, formalization of minimalist syntax), parsing and unification, lexical and compositional semantics, statistical language versions, and theories of truth.

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Lambda Grammars and the Syntax-Semantics Interface. , Stokhof, M. ) Proceedings of the Thirteenth Amsterdam Colloquium, Amsterdam, pp. : New Directions in Type-Theoretic Grammars. : Generation, lambek calculus, montague’s semantics and semantic proof nets. : The gf resource grammar library. : Probl`emes de filtrage et probl`emes d’analyse pour les grammaires cat´egorielles abstraites. : On the membership problem for non-linear abstract categorial grammars. In: Muskens, R. ) Proceedings of the Workshop on New Directions in Type-theoretic Grammars, Dublin, Ireland.

Y . 0 n 1 m Note that the Datalog variables {z1 , . . , zl } are associated to irrelevant positions in Γω γω ; this way, we ensure irrelevant positions are forced to belong to the desired set of atomic types (thanks to atom(zi )), and we ensure the safety condition on the rules of our Datalog program. For each constant c ∈ C1 , it is easy to see that the rule ρc is in fact associated γ is the mglt of H (c) and the relabeling to every typing Γ ·σ γ ·σ, where Γ σ maps atomic types in Irrat(Γ γ ) to atomic types in Potat(Γ γ) ∪ {ω}, such that Γ γ is a typing of the term to parse M .

Y would be a → b. Second, this restricted form of intersection types allows us to assign informative types to constants that are deleted during β-reduction. Given two countable sets of atomic types A and B, we define (Uα (B))α∈T (A) , where Uα (B) is the set of types built on B and uniform with α, to be the least subsets of T (B) that verify the following identities: 1. Uα (B) = B when α is atomic, 2. Uα→β (B) = {γ → δ | γ ∈ Uα (B) and δ ∈ Uβ (B)}. Lemma 1. Two types γ1 and γ2 in Uα (B) are always unifiable and their most general unifier is a relabeling.

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