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. |