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22nd March 2005: Tim Fernando
Computer Laboratory > Research > TSG > Logic and Semantics Seminar > 22nd March 2005: Tim Fernando

Speaker: Tim Fernando, TrinityCollege, Dublin
Title: Propositions-as-Types and Regular Languages for Natural Language Semantics
Time: 22nd March 2005, 12:00
Venue: SW01
Abstract:

Can we view natural languages as programming languages fit for computers? This talks looks at some topics in linguistic semantics where such a view has arguably advanced Montague's slogan `English as a formal language.' These include work on anaphora and presupposition commonly labeled `dynamic semantics' (DS), and investigations into what Terry Parsons calls `sub-atomic semantics' (SS), delving into, for example, verbs. DS has a proof-theoretic formulation (detailed by Aarne Ranta within intuitionistic type theory) that equates a proposition with the type of its proofs, providing a declarative alternative to the imperative (assignment-based) languages of Quantified Dynamic Logic. But `propositions-as-types' says nothing about what proofs of atomic formulae are, or where models interpreting such formulae come from. Nor does time or change (often crucial to the information conveyed by a verb) receive any special treatment under `propositions-as-types.'

With an eye to SS, we push systems of typed-lambda calculi/functional programming down to finite-state machines, formulating an event-type as a regular regular language. The strings in such a language are sequences of observations (much like comics and movies) that for an event-type given by a discrete temporal logic formula can be viewed not only as events but also as proofs.