Eliminating the Universe (eBook)
by edward l keenan (Author)

 56,155 Words
 184 Pages
This book synthesizes the author's work (1980s–2015) on the logical expressive power of natural language. It extends the tools and concepts of model theory as used in (higher order) predicate logic to the study of natural language semantics. It focuses on boolean structure, generalized quantification (separated from variable binding), covering some cases of anaphora. Different categories — predicates, adjective, quantifiers — are modeled by nonisomorphic boolean lattices.
Of empirical linguistic interest is the expressibility of many natural classes of quantifiers defined in terms of their logical (automorphism invariant) properties. Some of these correlate with classes used syntactically in generative grammar. In other cases we find general (possibly universal) constraints on possible quantifier denotations in natural language.
Also of novel logical interest are entailment paradigms that depend on relations between pairs or triples of generalized quantifier denoting expressions, ones that are in some cases inherently vague. In addition we note novel binary quantifiers that lie beyond the "Frege boundary" in that they are provably not identical to any iterated application of unary quantifiers.
Of philosophical interest is the existence of models which make the same sentences true as standard models but which lack a universe and hence, seemingly, a notion of "reference". Moreover, these models generalize to ones in which we can represent (some) intensional expressions without the use of novel ontological objects, such as "possible worlds" or "propositions".
Contents:
 The Linguistic Prescience of George Boole
 Logic as Universal Grammar
 Classifying Nominal Quantifiers in English
 Generalized Quantifiers and Logical Expressive Power
 The Midpoint Theorems
 Three Linguistic Generalizations
 Mathematical Analysis of English Quantifiers
 Characterizing Syntactic Categories Semantically?
 English is Inherently Sortal
 Logical Operators and Structure Maps
 Beyond the Frege Boundary
 Eliminating the Universe
Readership: Researchers in mathematical logic and artificial intelligence.
Natural Logic;Logical Expressive Power (of Natural Language);Boolean Structure;Generalized Quantifiers and Anaphora;Formal Semantics;Entailment Paradigms in Natural Language0Key Features:
 The work applies well understood boolean notions to an extended study of the meaning system of natural language — of interest then to computational linguistics and philosophical and mathematical studies of linguistically motivated logical systems
 Its treatment of nonextensional evaluative adjectives is novel and ontologically more parsimonious than standard intensional systems
 And the novel entailment paradigms involving multiple arguments invites further investigation into the study of inference in natural language
 Released: July 6, 2018
 Categories: Computers & Internet, Education, Reference
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9814719854
 ISBN13: 9789814719858