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Boolean Semantics for Natural Language : STUDIES IN LINGUISTICS AND PHILOSOPHY - Edward L. Keenan

Boolean Semantics for Natural Language



Published: 31st December 1984
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In the spring of 1978, one of the authors of this book was sitting in on a course in logic for linguists given by the other author. In attempting to present some of Montague's insights in an elementary way (hopefully avoid- ing the notation which many find difficult at first), the authors began dis- cussions aimed towards the construction of a simple model-theoretical semantic apparatus which could be applied directly to a small English-like language and used to illustrate the methods of formal logical interpretation. In these discussions two points impressed themselves on us. First, our task could be simplified by using boolean algebras and boolean homomorphisms in the models; and second, the boolean approach we were developing had much more widespread relevance to the logical structure of English than we first thought. During the summer and fall of 1978 we continued work on the system, proving the more fundamental theorems (including what we have come to call the Justification Theorem) and outlining the way in which an intensional interpretation scheme could be developed which made use of the boolean approach (which was originally strictly extensional). We presented our findings in a monograph (Keenan and Faltz, 1978) which the UCLA Linguistics Department kindly published as part of their series called Occa- sional Papers in Linguistics; one of the authors also presented the system at a colloquium held at the Winter Meeting of the Linguistic Society of America in December 1978.

`... Keenan & Faltz have written an impressive book, in its originality, scope, and sheer intellectual bravado. I found it intensely stimulating, and hope that many others will come to share that feeling.' Language, 62:4 (1986) `Being of capital interest for (mathematical and computational) linguists, logicians and algebrists, we believe that the book is, at least for natural language semantics, one of the most valuable of the present decade and will strongly influence the forthcoming researchers in the field.' Zentralblatt fur Mathematik/Mathematics Abstracts, 556 (1985)

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.

ISBN: 9789027717689
ISBN-10: 9027717680
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 387
Published: 31st December 1984
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 2.3
Weight (kg): 1.64