Polarities in logic and semantics

Authors:
Arno Bastenhof
Affiliations:
Utrecht University, The Netherlands
Venue:
AC'11 Proceedings of the 18th Amsterdam colloquim conference on Logic, Language and Meaning
Year:
2011

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Polarized classical non-associative Lambek calculus and formal semantics

LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics

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Abstract

We ask to what extent a satisfactory categorial analysis of non-local scope construal can already be realized while restricting to a non-commutative, non-associative setting, and without relaxing compositionality to a relation. In response, we show a variety of data on the topic can be dealt with through an adaptation of classical non-associative Lambek calculus (CNL , [3]) that incorporates Girard's concept of polarity ([5]). The latter notion originated in the constructivization of classical logic, recognizable by computer scientists as the definition of continuation-passing style (CPS) translations.