Gary Hardegree, Compositional Semantics
under continual construction
Categorial Syntax
Basic Categorial Syntax Introduction to the basic ideas of categorial syntax. Type-governed grammar.
Shortcomings of Standard Categorial Syntax Why we reject standard categorial grammar and the usual ways of patching it up, including movement and type-shifting.
Expanded Categorial Syntax Introduction to Expanded Categorial Syntax, including case-inflection and generalized-composition.
Examples of Expanded Categorial Syntax This chapter presents a few simple applications of Revised Categorial Syntax, including passives and function-like nouns. It also proposes a re-categorization of common-noun phrases and copular-be.
Categorial Logic (for Syntax) Standard categorial composition is modelled by a single logical argument form – modus ponens. By contrast, generalized-composition is modelled by all the valid argument forms of a logical calculus, which we dub Categorial Logic, which is sub-structural logic between Relevance Logic and Linear Logic. This chapter presents the details of Categorial Logic, including a natural deduction system.
Categorial Semantics
Basic Categorial Semantics Introduction to truth-conditional semantics. Denotation versus meaning.
Lambda-Abstraction Presentation of basic material on lambda-abstraction, both as used in type-theory, and as used in set-theory.
Expanded Categorial Semantics How semantic-composition works in Expanded Categorial Grammar.
Categorial Logic - Semantics More examples of Expanded Categorial Grammar
Scope and Ambiguity How expanded categorial grammar handles scope-ambiguities.
Applications
Pronouns - Basic Ideas Basic ideas. Overall classification. Treatment of demonstrative pronouns and lazy pronouns.
Reflexive Pronouns Reflexive pronouns are not NP-anaphoric, but are rather role-anaphoric.
Standard Anaphoric Pronouns These pronouns are logically bound by their antecedents, but need not be governed by them. Essentially-lazy pronouns.
Anaphoric Uses of Relative Pronouns Ultimately resulting in a unified treatment of restrictive and non-restrictive relative clauses. Restrictive versus non-restrictive adjectives.
Non-Standard Anaphoric Pronouns In one variety, the pronoun is anaphoric to a tacit NP. In the other variety, the pronoun is a lazy-copy of its antecedent, and is co-anaphoric with its antecedent. This technique also explains anaphoric uses of definite-determiner phrases.
'Any' and 'There' 'any', 'there' insertion
Numerical Quantifiers Numerical quantifiers and exclusive adverbs
Relational Nouns and Prepositions Inflectional (genitive) 'of' versus relational (posssessive) 'of'. Genitive 'have' versus possessive 'have'.
APPENDICES, Collateral Material
Set Theory
Overview/Summary Collateral material on set theory.
Basic Concepts
Relations
Functions
Natural Numbers
Cardinal Numbers
Basic Metalogical Issues
Formal Languages 1 Collateral material on metalogic. Use/mention. Object-language/meta-language. Recursive definitions. The use of semantic methods in metalogic.
Formal Languages 2
Mathematical Induction
Truth-Functional Logic
Semantic Characterization of Logics
Number Words
Morphology of Number Words Collateral material illustrating how the methods of categorial grammar can be applied to number words and numerals.
Appendix: Brief History of Numeration
Categorial Logic Tools (under construction)
Semantic Derivations This is a Microsoft Word File that contains key assignments, macros, and styles that simplify writing semantic derivations in the Kalish and Montague style.
These require Adobe Acrobat Reader.