Logical constants across varying types.

Abstract

We investigate the notion of "logicality" for arbitrary categories of linguistic expression, viewed as a phenomenon which they can all possess to a greater or lesser degree. Various semantic aspects of logicality are analyzed in technical detail: in particular, invariance for permutations of individual objects, and respect for Boolean structure. Moreover, we show how such properties are systematically related across different categories, using the apparatus of the typed lambda calculus.