Computational logics and the philosophy of language: The problem of lexical meaning in formal semantics

This paper deals with the possible contributions that logical researches carried on in the field of artificial intelligence (AI) could give to formal theories of meaning developed by logically oriented philosophers of language within the tradition of analytic philosophy. In particular, I will take into account a topic which is problematic in many respects for traditional logical accounts of meaning, i.e., the problem of lexical semantics. My thesis is that AI logics could give useful instruments to face some aspects of the problem, whilst other aspects fall outside the scope of a logical treatment, and require other kinds of computational instruments. 1 Lexical semantics and formal theories of meaning The dominant formal paradigm in the philosophical study of meaning is so-called model theoretic semantics. Based on formal tools of a set theoretic nature, model theoretic semantics originated from the researches on the meaning of expressions of formal languages. The simplest and historically prior form of model theoretic approach is extensional Tarskian semantics for first order predicate logic. According to Tarskian semantics, an interpretation I for a first order theory is a ordered pair I = (φ, D). D is the domain of the interpretation, that is to say, a set of objects on which the constructs of the language are interpreted. φ is an interpretation function, associating a reference in D to the various constructs of the language (e.g., to every individual constant is associated an element of D, to one place predicative letters are associated subsets of D, and so on). Recursive compositional rules allow to establish the reference of syntactically complex expressions, given the reference of their components. In particular, the truth value of a closed formula can be established starting from the reference of the atomic symbols occurring in it. An interpretation I that makes true a certain formula α is said to be a model of α (in symbols, I |= α). A model of a set Γ of formulas is a model of all formulas in Γ. Model theoretic semantics allows to formally characterise such notions as the validity of a formula, or the relation of logical consequence between formulas. For example, a formula α is valid (|= α) if and only if it is true in all the interpretations. A formula β is logical consequence of a formula α (α |= β) if and only if β is true in all the models of α. Historically, after the development of Tarskian extensional theory, model theoretic semantics has been extended to deal with intensional aspects of meaning with the development of possible world semantics, due mainly to the researches of Rudolph Carnap and Saul Kripke. Possible world semantics showed to be a very flexible and powerful tool, which allowed one to face many aspects of the meaning not only of formal languages, but also of natural ones. The application of formal intensional