Formalizing the IMA Language: Toward the Minimalist Program for Compositional Semantics

Computational semantics via logical approach mainly focuses on the composition of meanings. Traditional approaches to it are based on typed logic via categorial grammar, which are not so successful when applied to very different languages than English. Recently, some alternative approaches with flatter types and underspecified semantics have been proposed. This paper is in the same line of these alternatives, but goes further and thoroughly. To avoid the presumed grammatical and semantic rules which are not universal across languages, we give a logic for a hypothetical language called the Isolating-Monocategorial-Associational (IMA) language, which can be assumed to be a prototype of natural languages with minimal grammar and semantics. We also give several extensions of the logic, motivated by different specifications. By formalizing the IMA language, we intend to reveal the universal mechanism of semantic composition in natural languages and to propose a general framework for compositional semantics.