Course Proposal: Computational Semantics

Jørgen Villadsen

I am interested in giving a course on Computational Semantics and Natural Language Processing (NLP).

It should provide an introduction to modern logical and grammatical theories for natural language.

A possible textbook is Bob Carpenter: Type-Logical Semantics, MIT Press 1997.

Based on an introductory course on natural-language semantics, this book provides an introduction to type-logical grammar and the range of linguistic phenomena that can be handled in categorial grammar.

It also contains a great deal of original work on categorial grammar and its application to natural-language semantics.

The author chose the type-logical categorial grammar as his grammatical basis because of its broad syntactic coverage and its strong linkage of syntax and semantics.

Although its basic orientation is linguistic, the book should also be of interest to logicians and computer scientists seeking connections between logical systems and natural language.

Table of Contents

1	Introduction	
	    	1.1	Truth and Reference	
	    	    	1.1.1	Truth	
	    	    	1.1.2	Reference	
	    	    	1.1.3	Conventionalism and Realism	
	    	1.2	Topics in Semantics	
	    	    	1.2.1	Synonymy, Entailment, and Contradiction	
	    	    	1.2.2	Presupposition	
	    	    	1.2.3	Ambiguity and Vagueness	
	    	    	1.2.4	Indexicality and the Situation of an Utterance	
	    	    	1.2.5	Sense and Reference	
	    	    	1.2.6	Lexical Semantics	
	    	1.3	Topics in Pragmatics	
	    	    	1.3.1	Conversational Implicature	
	    	    	1.3.2	Speech Acts	
	    	    	1.3.3	Discourse Structure	
	    	    	1.3.4	Metaphors, Idioms, and Language Change	
	    	1.4	Methodology	
	    	    	1.4.1	Productivity	
	    	    	1.4.2	Compositionality	
	    	    	1.4.3	Model Theory and Grammar Fragments	
2	Simply Typed l-Calculus	
	    	2.1	Simple Types	
	    	2.2	l-Terms	
	    	2.3	Functional Models	
	    	    	2.3.1	Frames	
	    	    	2.3.2	Models	
	    	2.4	Proof Theory for Simply Typed l-Calculus	
	    	2.5	Combinators and Variable-Free Logic	
	    	2.6	Products	
	    	2.7	Sums	
3	Higher-Order Logic	
	    	3.1	Higher-Order Syntax	
	    	3.2	Higher-Order Models	
	    	3.3	Quantifiers in Natural Language	
	    	    	3.3.1	A Compositional Approach to Quantifiers	
	    	    	3.3.2	Properties of Natural-Language Quantifiers	
	    	3.4	Negative Polarity Items	
	    	3.5	Definite Descriptions	
	    	    	3.5.1	Quantificational Definites	
	    	    	3.5.2	Referential Definites	
	    	    	3.5.3	Contextual Elaboration	
	    	    	3.5.4	Nominal Type Shifting	
	    	3.6	Proof Theory for Higher-Order Logic	
4	Applicative Categorial Grammar	
	    	4.1	The Category System	
	    	4.2	Semantic Domains	
	    	4.3	Categorial Lexicons	
	    	4.4	Phrase Structure	
	    	4.5	A Categorial Lexicon	
	    	4.6	Tree Admissibility	
	    	4.7	Ambiguity, Vagueness, and Meaning Postulates	
	    	    	4.7.1	Lexical Ambiguity and Vagueness	
	    	    	4.7.2	Derivational Ambiguity	
	    	    	4.7.3	Local and Global Ambiguity	
	    	    	4.7.4	Meaning Postulates	
5	The Lambek Calculus	
	    	5.1	Lambek's Sequent Calculus	
	    	    	5.1.1	Applicative Fragment	
	    	    	5.1.2	Abstraction Schemes	
	    	    	5.1.3	Associativity, Cut Elimination, and Decidability	
	    	5.2	The Natural-Deduction Lambek Calculus	
	    	    	5.2.1	Applicative Natural Deduction	
	    	    	5.2.2	The Natural-Deduction Lambek Calculus	
	    	    	5.2.3	Proof Normalization	
	    	5.3	Products	
	    	5.4	Categorial Grammar Aas Logic	
	    	    	5.4.1	Substructural Logic	
	    	    	5.4.2	The Curry-Howard Isomorphism	
6	Coordination and Unbounded Dependencies	
	    	6.1	Coordination	
	    	    	6.1.1	Boolean Coordination	
	    	    	6.1.2	Distributivity and Type Raising	
	    	    	6.1.3	Nonconstituent Coordination	
	    	6.2	Conjunctive and Disjunctive Categories	
	    	    	6.2.1	The Conjunction Constructor	
	    	    	6.2.2	The Disjunction Constructor	
	    	    	6.2.3	Natural-Deduction Conjunction and Disjunction	
	    	    	6.2.4	Copular Complements and Predicatives	
	    	    	6.2.5	Incompleteness of Conjunction and Disjunction	
	    	6.3	Unbounded Dependency Constructions	
	    	    	6.3.1	The Lambek Calculus and Unbounded Dependencies	
	    	    	6.3.2	"Disharmonic" Combinations	
	    	    	6.3.3	Moortgat's Approach to Unboundedness	
	    	    	6.3.4	Islands and Extractability	
	    	    	6.3.5	Incompleteness of the Extraction Constructor	
7	Quantifiers and Scope	
	    	7.1	Quantifying In	
	    	7.2	Cooper Storage	
	    	7.3	Scoping Constructor	
	    	7.4	Type Raising and Quantifier Coordinations	
	    	7.5	Embedded Quantifiers	
	    	7.6	Quantifiers and Coordinate Structures	
	    	7.7	Quantification and Negation	
	    	7.8	Quantification and Definite Descriptions	
	    	7.9	Possessives	
	    	7.10	Indefinites	
	    	7.11	Generics	
	    	7.12	Comparatives	
	    	    	7.12.1	Gradability and Measurability	
	    	    	7.12.2	The Grammar of Comparatives	
	    	7.13	Expletives and the Unit Type	
8	Plurals	
	    	8.1	An Ontology of Groups	
	    	8.2	A Plural Grammar	
	    	8.3	Distributors and Collectors	
	    	8.4	Coordination, Negation, and Argument Lowering	
	    	8.5	Adverbial Distribution	
	    	8.6	Plural Quantification	
	    	8.7	Partitives and Pseudopartitives	
	    	8.8	Nonboolean Coordination	
	    	8.9	Comitative Complements	
	    	8.10	Mass Terms	
9	Pronouns and Dependency	
	    	9.1	Pronouns and Reflexives	
	    	9.2	Pronouns and Agreement	
	    	9.3	Pronouns as Variables	
	    	9.4	A Quantificational Approach to Reflexives	
	    	9.5	Plural Pronouns	
	    	9.6	Reciprocals and Generalized Quantification	
	    	9.7	Pied Piping	
	    	9.8	Ellipsis and Sloppy Anaphora	
	    	9.9	Interrogatives	
10	Modal Logic	
	    	10.1	Modes of Truth	
	    	10.2	S5: A Modal Logic of Necessity	
	    	    	10.2.1	The Model Theory of S5	
	    	    	10.2.2	S5 Proof Theory	
	    	10.3	Indexicality	
	    	10.4	General Modal Logics	
	    	    	10.4.1	Classifying Modal Logics	
	    	10.5	Strict Implication and Counterfactuals	
	    	10.6	First-Order Tense Logics	
	    	10.7	Tense Logic And Natural Language	
	    	10.8	Temporal-Period Structures	
	    	    	10.8.1	Constructing Periods from Moments	
	    	    	10.8.2	Constructing Moments from Periods	
	    	    	10.8.3	Duration and Measure	
	    	10.9	Higher-Order Modal Logic	
11	Intensionality	
	    	11.1	An Intensional Grammar	
	    	    	11.1.1	Type Logic and Categorial Grammar	
	    	    	11.1.2	Propositional Attitudes	
	    	    	11.1.3	Complementized Sentences	
	    	    	11.1.4	Sentential, Infinitival, and Gerundive Subjects	
	    	    	11.1.5	Nominalization, Self-Reference, and Semantic Paradoxes	
	    	    	11.1.6	Gerunds, Naked Infinitives, and Event-Based Semantics	
	    	    	11.1.7	Modal Adverbs and Modal Auxiliaries	
	    	    	11.1.8	Control Verbs	
	    	    	11.1.9	Control Predicatives	
	    	    	11.1.10	Nonobligatory Control and Purpose Clauses	
	    	    	11.1.11	Intensional Transitive Verbs	
	    	    	11.1.12	Intensional Adjectives	
	    	11.2	Individual Concepts and Quantificational Definites	
	    	    	11.2.1	Definite Descriptions and Scope	
	    	    	11.2.2	Individual Concepts and Rigid Designation	
	    	11.3	Alternatives to Possible Worlds	
	    	    	11.3.1	Logical Omniscience and the Granularity of Propositions	
	    	    	11.3.2	Quotational Theories	
	    	    	11.3.3	Structured Meanings and General Intensional Models	
	    	    	11.3.4	Situation Semantics	
	    	    	11.3.5	Truth-Value Gaps and Partial Possible Worlds	
	    	11.4	Lexical Relations	
12	Tense and Aspect	
	    	12.1	Reichenbach's Approach to Simple and Perfect Tenses	
	    	12.2	Tense and Discourse	
	    	12.3	Vendler's Verb Classes	
	    	12.4	A Semantic Approach to Aspect	
	    	12.5	A Grammar of Tense and Aspect	
	    	    	12.5.1	Verb Forms	
	    	    	12.5.2	Simple Finite Verbs and Auxiliary Verbs	
	    	    	12.5.3	Intersective Temporal Modifiers	
	    	    	12.5.4	The Perfect	
	    	    	12.5.5	The Progressive	
	    	    	12.5.6	Tense and Nominal Quantification	
	    	    	12.5.7	Tense, Nominals, and Quantification	
	    	    	12.5.8	Adverbs of Quantification and Negation	
	Appendix A Mathematical Preliminaries	
	    	A.1	Set Theory	
	    	A.2	Functions and Relations	
	    	A.3	Orderings, Well Orderings, and Lattices	
	    	A.4	Proof by Induction	
	    	A.5	Formal Languages	
	    	A.6	Trees	
	    	A.7	First-Order Logic	
	    	    	A.7.1	First-Order Terms and Formulas	
	    	    	A.7.2	First-Order Model Theory	
	    	    	A.7.3	First-Order Proof Theory	
	    	A.8	Algebras and Equality	
	    	    	A.8.1	Algebras	
	    	    	A.8.2	Boolean Algebras	
	    	    	A.8.3	First-Order Logic with Equality	

Jørgen Villadsen 2008-01-13