| 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 a variant of System R of Relevance 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.
To download, click here. |