Boolean Semantics for Natural Language

Boolean Semantics: An Overview.- 1. Sketch of the Semantics.- 1.1. Characterizing English Denotations and Entailments.- 1.2. Characterizing Possible Semantic Systems for Natural Language.- 2. On the Relation between English Form and Logical Form.- 3. An Ontological Innovation.- I: The Extensional Logic.- A. The Core Language, L.- 1. Syntax of the Core Language L.- Defining CAT.- Defining V and PEV.- Defining L.- Remarks on the Definitions.- 2. The Semantics for L.- Defining the Types for L.- The Type for P0 or Formulas.- The Types for N, $$bar N$$, and $$bar N$$prop.- Eliminating the Universe.- Characterizing TN.- Completeness of boolean algebras.- Atomicity of boolean algebras.- Defining TN Without a Universe.- Defining Proper Noun Denotations without U.- The Ontology and Some Basic Types for L: Summary.- Discussion.- Why should TN Be Complete and Atomic?.- Defining TDet.- Defining the Types for the Pn's.- Defining $${T_{{P_n}}}$$, all n.- Defining Types for Predicative Hierarchies in General.- Summary Definition of the Types.- Defining Interpretations for L.- Advantages of the Generalized Entailment Relation.- A Concluding Remark on Comparative Ontologies.- Proofs of the Theorems.- Notes.- I: The Extensional Logic.- B. Extending the Core Language.- 1. Modifiers.- Adjective Phrases.- Comparative Adjectives.- Predicate Adjectives.- Proofs of Theorems from This Section.- 2. Predicate Modifiers.- Proofs of Theorems from This Section.- 3. Predicatives.- Preliminary Remarks on Case Marking.- Transitive Common Noun Phrases.- Modifiers of n-place Common Nouns.- Some Relations Between Nominals and Predicates.- Subcategories of Nn.- Transitive Adjective Phrases.- Ditransitive Verb Phrases (P3s).- Prepositions and Predicate Modifier Hierarchies.- Prepositions as Formers of Predicate Modifiers.- Prepositions as Verbal Extensors.- 4. Valency Affecting Operations.- Passives.- A Generalized Passive Operator.- Sentence level views.- Predicate level views.- Generalizing Passive.- Agent Phrases.- Extending Passive to Nominals and Other Predicative Hierarchies.- Nominals.- Passive Adjectives?.- Passive Prepositions??.- 5. Extending and Subcategorizing the Class of Determiners.- Numerical Determiners.- Non-Logical Determiners.- Characterizing 'Logical' Determiners.- Vague Determiners.- Determiners Compared to Other Categories.- Generalizing Determiners.- Extending Possessive Determiners.- 6. Variables and Variable Binding Operators.- The Lambda Operator.- The Reflexive Operator.- The Relative Clause Operator.- 7. Non-homomorphic Predicates?.- Numerical Predicates.- Collective Predicates.- Reciprocal Predicates.- Intensional Predicates.- II: The Intensional Logic.- 1. Introduction to the Intensional System.- Proofs of the Theorems.- 2. The Intensional System for the Core Language.- Proofs of the Theorems.- Notes for II.2.- 3. The Intensional Logic for APs.- Proofs of the Theorems.- 4. Predicate Modifiers and Prepositions in the Intensional System.- 5. Variables and Variable Binding Operators in the Intensional System.- 6. Sentential Predicates in the Intensional System.- Syntax of Sentence Taking Predicates.- A Semantics for $$bar S$$ and $$bar S$$-Taking Predicates.- Formal Definitions of the New Types.- Lexical Constraints on the Interpreting Function m.- Subcategories of $$bar S$$-Taking Predicates.- Argument Categories in Addition to $$bar N$$ and $$bar S$$.- Extraposition.