CLASP
The Centre for Linguistic Theory and Studies in Probability

Relating Theories of Formal Semantics: established methods and surprising results

Formal semantics comprises a plethora of theories which interpret natural language through the use of di¿erent ontological primitives (e.g. possible worlds, situations, individual concepts, unanalyzable propositions). The ontological relations between these theories are, today, still largely unexplored. In particular, it remains unclear whether the basic objects of some of these theories can be coded in terms of objects from other theories (s.t. phenomena which are modeled by one theory can also be modeled by the other theories) or whether some of these theories can even be reduced to ontologically poor(er) theories (e.g. extensional semantics) which do not contain ¿special¿ objects like possible worlds.

This talk surveys my recent work on ontological reduction relations between formal semantic theories. This work shows that, more than preserving the modeling success of the reduced theory, some reductions even improve upon the theory’s modeling adequacy or widen the theory’s modeling scope. My talk illustrates this observation by two examples: (i) the relation between Montague-/possible world-style intensional semantics and extensional semantics (cf. Liefke and Sanders 2016), and (ii) the relation between intensional semantics and situationbased single-type semantics (cf. Liefke and Werning, in revision). The first relation established through the use of associates from higher-order recursion theory.