Emms, Martin Thomas

2018-01-31T11:20:09Z

2018-01-31T11:20:09Z

1995

The thesis presents research in the field of model theoretic semantics on the problem of ambiguity, especially as it arises for sentences that contain junctions (and,or) and quantifiers (every man, a woman). A number of techniques that have been proposed are surveyed, and I conclude that these ought to be rejected because they do not make ambiguity 'emergent': they all have the feature that subtheories would be able to explain all syntactic facts yet would predict no ambiguity. In other words these accounts have a special purpose mechanism for generating ambiguities.

It is argued that categorial grammars show promise for giving an 'emergent' account. This is because the only way to take a subtheory of a particular categorial grammar is by changing one of the small number of clauses by which the categorial grammar axiomatises an infinite set of syntactic rules, and such a change is likely to have a wider range of effects on the coverage of the grammar than simply the subtraction of ambiguity.

Of categorial grammars proposed to date the most powerful is Lambek Categorial Grammar, which defines the set of syntactic rules by a notational variant of Gentzen's sequent calculus for implicational propositional logic, and which defines meaning assignment by using the Curry- Howard isomorphism between Natural Deduction proofs in implicational propositional logic and terms of typed lambda calculus. It is shown that no satisfactory account of the junctions and quantifiers is possible in Lambek categorial grammar.

I introduce then a framework that I call Polymorphic Lambek Categorial Grammar, which adds variables and their universal quantification, to the language of categorisation. The set of syntac¬ tic rules is specified by a notational variant of Gentzen's sequent calculus for quantified proposi¬ tional logic, and which defines meaning assignment by using Girard's Extended Curry-Howard isomorphism between Natural Deduction proofs in quantified implicational propositional logic and terms of 2nd order polymorphic lambda calculus. It is shown that this allows an account of the junctions and quantifiers, and one which is 'emerge

http://hdl.handle.net/1842/26487

The University of Edinburgh

Annexe Thesis Digitisation Project 2017 Block 15

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Logical ambiguity

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