Compositionality and model-theoretic interpretation

Abstract

The present paper studies the general implications of the principle of compositionality for the organization of grammar. It will be argued that Janssen's (1986) requirement that syntax and semantics be similar algebras is too strong, and that the more liberal requirement that syntax be interpretable into semantics leads to a formalization that can be motivated and applied more easily, while it avoids the complications that encumber Janssen's formalization. Moreover, it will be shown that this alternative formalization even allows one to further complete the formal theory of compositionality, in that it is capable of clarifying the role played by translation, model-theoretic interpretation and meaning postulates, of which the latter two aspects received little or no attention in Montague (1970) and Janssen (1986).