Natural Language Semantic Representations as Types

Tim Fernando


Can we view natural languages as programming languages fit for computers? This course surveys 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 labelled `dynamic semantics' (DS), and investigations into what T. Parsons calls `sub-atomic semantics' (SS), delving into, for example, verbs. DS has a proof-theoretic formulation (detailed by A. 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.

The bulk of the course covers a formulation of propositions-as-types for SS, pushing systems of typed-lambda calculi/functional programming down to regular languages to analyze the notion of an event(-type). Events are conceived as sequences of observations (much like comics and movies) that are accepted by finite automata. Mereological approaches to events are reconstructed in terms of suitable entailments between the regular languages, grounded in time. Forcing conditions are formed from strings in the languages, relative to which worlds and models are derived from generic sets. Ideas about temporality from Reichenbach and Vendler discussed by Steedman in connection with the frame problem from AI are analyzed in a finite-state setting. Notions of causation and inertia are considered, and related to recent work on M. Shanahan's event calculus by Hamm and van Lambalgen, inspired by Moschovakis' view of sense-as-algorithm and denotation-as-value.

Finally, adverbs of quantification are re-considered, and conservativity in generalized quantifiers is linked to presupposition filtering under a propositions-as-types analysis.



1, 4 slides/page . There are also these two papers: more linguistic + more technical
2, 4 slides/page . Plus from SuB 2003 and from SALT 2004
3, 4 slides/page (abridged)
4 in preparation.
5 in preparation. In the meantime, there's this paper (from SALT 2001, pp 172-191).

Last modified: 22 July 2004.