Edinburgh, Scotland

Title and Abstract of Invited Talks

On the Descriptive Complexity of Linear Algebra

Quantum knots and mosaics

Prefix-correct Earley parsing of mildly context-sensitive languages

Inter-deriving semantic artifacts for object-oriented programming

On game semantics of the affine and intuitionistic logics

Applications of Proof Theory to Ergodic Ramsey Theory

The Grammar of Scope

The program of research that seeks a "Natural Logic" to which the forms of natural language are transparent has been frustrated by the existence of ambiguities of scope in interpretations for multiply quantified sentences, which appear to require grammatical operations that compromise the strong assumptions of syntactic/semantic transparency and monotonicity made under that program. Examples of such operations include covert movement at the level of logical form, abstraction or storage mechanisms, and proliferating type-changing operations.

The paper examines some interactions of scope alternation with syntactic phenomena including coordination, binding, and relativization. Starting from the assumption of Fodor and Sag, and others, that many expressions that have been treated as generalized quantifiers are in reality non-quantificational, expressions, and using Combinatory Categorial Grammar (CCG) as a grammatical framework, the paper presents an account of quantifier scope ambiguities according to which the available readings are projected directly from the lexicon by the combinatorics of the syntactic derivation, without any independent manipulation of logical form and without recourse to syntactically unmotivated type-changing operations.

The logic that results has a number of surprising features. It makes extensive use of (generalized) Skolem terms. The treatment of negation is unusual. The Philonian identification of the conditional with material implication is avoided. Some implications for natural language processing are considered.  

Last modified: 7 March 2008