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## Munich Center for Mathematical Philosophy (MCMP)

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Kristina Liefke (LMU/MCMP) gives a talk at the Workshop on Five Years MCMP: Quo Vadis, Mathematical Philosophy? (2-4 June, 2016) titled "Relating Theories of Intensional Semantics: Established Methods and Surprising Results". Abstract: Formal semantics comprises a plethora of ‘intensional’ theories which model propositional attitudes through the use of different ontological primitives (e.g. possible/impossible worlds, partial situations, 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 reduced to 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’ theories (e.g. extensional semantics) which do not contain intensional objects like possible worlds.
This talk surveys my recent work on ontological reduction relations between the above theories. This work has shown 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. Our talk illustrates this observation by two examples: (i) the relation between Montague-/possible world-style intensional semantics and extensional semantics, and (ii) the relation between intensional semantics and situation-based single-type semantics. The relations between these theories are established through the use of associates from higher-order recursion theory (cf. (i)) and of type-coercion from programming language theory (cf. (ii)).
Part of this work is joined with Markus Werning (RUB Bochum) and Sam Sanders (LMU Munich/MCMP).

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