Natural Language Semantics and Computability

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a (non-empty) set of logical formulasbecause a statement can be ambiguous, it can correspond to multiple formulas, one for each reading. We argue that as long as we do not explicitly compute the interpretation in terms of possible world models, one can compute the semantic representation(s) of a given statement, including aspects of lexical meaning. This is a very generic process, so the results are, at least in principle, widely applicable. We also discuss the algorithmic complexity of this process.