Munich Center for Mathematical Philosophy (MCMP)

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Unity and Unification in Intensional Semantics

Natural languages presuppose a rich semantic ontology: To interpret the sentence Every boy admires Mary, we assume the existence of individuals (i.e. boys, Mary), propositions (Every boy admires Mary), properties of individuals (being a boy), relations between individuals (admire), and other types of objects. Formal models for natural language semantics (esp. Montague 1970a, 1970b, 1973) tame this zoo of objects by assuming only a small number of primitive objects, and obtaining all other objects from these primitives via constructions out of these primitives. In this way, Montague (1970a) reduces the referents of a basic fragment of English to constructions out of three types of primitives: individuals, possible worlds, and truth-values. However, in the last thirty years, attempts at revising and extending Montague’s model have introduced a plethora of models, which assume greatly varying sets of primitives. As a result, the zoo of primitive objects has been traded for a zoo of models.

This project seeks to unify the different models for natural language semantics. In particular, it aims to identify the commonalities of these models with respect to their choice of primitives, disclose coding relations between the different primitives, and use these relations to identify reductions between models. These reductions achieve a unification of the different semantic models. I expect that the reductions will further yield insights into the requirements on minimal models of a given linguistic phenomenon and that they will contribute to a better understanding of the linguistic type system. Apart from some isolated reductions, such an effort has never been undertaken. However, only this effort allows us to transfer the interpretive success of one model to another model.

To ensure the feasibility of this project in the proposed time frame, I will focus on one particular class of models (called ‘intensional models’) whose members interpret the standard fragment of English from (Montague 1973). This fragment contains propositional attitude verbs (e.g. believe), and intensional nouns (e.g. temperature, price) and intransitive verbs (e.g. rise, change). Different models of this fragment assume as their primitives some subset of the set of individuals, individual concepts, worlds, situations, propositions, and truth-values.

To unify these models, I will combine techniques from formal semantics and type theory with methods for comparative ontology analysis. To show the possibility of reducing pairs of intensional models, I demonstrate that primitive objects in the reduced model can be coded as objects in the reducing model. The use of coding for this purpose is supported by earlier results in formal semantics and by my own related work. These results further suggest that ‘the’ unifying model is, in fact, a class of models whose members are equivalent up to coding. The robustness of these models with respect to their choice of primitives explains the emergence of the large number of intensional models.


Subject area

  • Philosophy of language


  • Foundations of Montague semantics, Intensional logic, Natural language metaphysics, Type-logical semantics, Unification