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**1 - 3**of**3**### CATEGORIAL VERSUS MODAL INFORMATION THEORY

, 2009

"... In this very brief note, I raise a few worries about interpreting the Lambek Calculus, admired and cherished as it may be by all connoisseurs, as a base logic of information flow. ..."

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In this very brief note, I raise a few worries about interpreting the Lambek Calculus, admired and cherished as it may be by all connoisseurs, as a base logic of information flow.

### Noname manuscript No. (will be inserted by the editor) Discontinuous Lambek Calculus

"... Abstract The search for a full treatment of wrapping in type logical grammar has been a task of long-standing. In this paper we present a calculus for discontinuity addressing this challenge, ω-DL. The calculus allows an unbounded number of points of discontinuity (hence the prefix ω-) and includes ..."

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Abstract The search for a full treatment of wrapping in type logical grammar has been a task of long-standing. In this paper we present a calculus for discontinuity addressing this challenge, ω-DL. The calculus allows an unbounded number of points of discontinuity (hence the prefix ω-) and includes both deterministic and nondeterministic discontinuous connectives. We believe that it constitutes a general and natural extension of the Lambek calculus L. Like the Lambek calculus it has a sequent calculus which is a sequence logic without structural rules, and it enjoys such properties as Cut-elimination, the subformula property and decidability. By n-DL we refer to ω-DL restricted to at most n points of discontinuity. 0-DL is the original Lambek calculus L. Of particular interest is 1-DL in which the unicity of the point of discontinuity means that the deterministic and nondeterministic discontinuous connectives coincide. We illustrate 1-DL with linguistic applications to medial extraction, discontinuous idioms, parentheticals, gapping, VP ellipsis, reflexivization, quantification, pied-piping, appositive relativisation, comparative subdeletion, and cross-serial dependencies. We further illustrate deterministic 2-DL with linguistic

### Categorial Grammars and Substructural Logics

"... Substructural logics are formal logics whose Gentzen-style sequent systems abandon some/all structural rules (Weakening, Contraction, Exchange, Associativity). They have extensively been studied in current literature on nonclassical logics from different points of view: as sequent axiomatizations of ..."

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Substructural logics are formal logics whose Gentzen-style sequent systems abandon some/all structural rules (Weakening, Contraction, Exchange, Associativity). They have extensively been studied in current literature on nonclassical logics from different points of view: as sequent axiomatizations of relevant,