Quantifiers and Cognition

Cham : : Springer International Publishing, , 2016.

1 online resource (210 p.)

1st ed. 2016.

Description based upon print version of record.. - Acknowledgments; Contents; Introduction; Part I Procedural Semantics; 1 Algorithmic Theory of Meaning; References; 2 Complexity in Linguistics; 2.1 Computational Complexity; 2.2 Syntax; 2.3 Descriptive Syntax; 2.4 Semantics; 2.5 Finite Universes; References; Part II Simple Quantifiers; 3 Basic Generalized Quantifier Theory; 3.1 Two Equivalent Concepts of Generalized Quantifiers; 3.2 Logic Enriched by Generalized Quantifiers; 3.3 Definability of Generalized Quantifiers; 3.4 Semantic Universals; 3.4.1 Boolean Combinations of Quantifiers; 3.4.2 Relativization of Quantifiers. - 3.4.3 Domain Independence3.4.4 Conservativity; 3.4.5 CE-Quantifiers; 3.5 Monotonicity; References; 4 Computing Simple Quantifiers; 4.1 Representation of Finite Models; 4.2 Quantifier Automata; 4.3 Characterization Results; References; 5 Cognitive Processing of Quantifiers; 5.1 Processing Time; 5.1.1 Experiment 1; 5.1.2 Experiment 2; 5.2 Accuracy; 5.2.1 Probabilistic Semantic Automata; 5.2.2 Modeling the Data; 5.3 Working Memory; 5.3.1 Neurocognitive Evidence; 5.3.2 Concurrent Tasks; 5.3.3 Schizophrenic Patients; 5.3.4 Intelligence; 5.3.5 Executive Resources; 5.4 Corpora Distributions. - 5.4.1 Power Laws5.5 Monotonicity; 5.5.1 Comparison with Literature; 5.6 Approximate Number System; 5.7 Discussion; References; Part III Complex Quantifiers; 6 Standard Polyadic Lifts; 6.1 Iteration; 6.2 Cumulation; 6.3 Resumption; 6.4 Semantic Automata for Polyadic Quantifiers; 6.4.1 Experimental Direction; 6.5 The Frege Boundary; 6.5.1 Classic Characterization Results; 6.5.2 The Frege Boundary and the Chomsky Hierarchy?; 6.6 Summary; References; 7 Complexity of Polyadic Quantifiers; 7.1 Computational Complexity of Quantifiers. - 7.2 PTIME Generalized Quantifiers Are Closed Under It, Cum, and Res7.3 Branching Quantifiers; 7.3.1 Henkin's Quantifiers; 7.3.2 Proportional Branching Quantifiers; 7.4 Ramsey Quantifiers; 7.4.1 The Branching Reading of Hintikka's Sentence; 7.4.2 Clique Quantifiers; 7.4.3 Proportional Ramsey Quantifiers; 7.4.4 Tractable Ramsey Quantifiers; 7.4.5 Intermediate Ramsey Quantifiers; 7.4.6 Dichotomy Result; 7.5 Summary; References; 8 Complexity of Quantified Reciprocals; 8.1 Reciprocal Expressions; 8.1.1 Strong Meaning Hypothesis; 8.2 Reciprocals as Polyadic Quantifiers. - 8.2.1 Strong Reciprocal Lift8.2.2 Intermediate Reciprocal Lift; 8.2.3 Weak Reciprocal Lift; 8.2.4 The Reciprocal Lifts in Action; 8.3 Complexity of Strong Reciprocity; 8.3.1 Counting Quantifiers in the Antecedent; 8.3.2 Proportional Quantifiers in the Antecedent; 8.3.3 Tractable Strong Reciprocity; 8.4 Intermediate and Weak Lifts; 8.5 A Complexity Perspective on the SMH; 8.6 Empirical Evidence; 8.6.1 Cognitive Difficulty; 8.6.2 Distribution in English; 8.7 Summary; References; 9 Branching Quantifiers; 9.1 Hintikka's Thesis; 9.2 Other Hintikka-Like Sentences; 9.3 Theoretical Discussion. - 9.3.1 A Remark on Possible Readings. - This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition. Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, studying the possible meanings and the inferential power of quantifier expressions by logical means. The classic version was developed in the 1980s, at the interface of linguistics, mathematics and philosophy. Before this volume, advances in "classic" generalized quantifier theory mainly focused on logical questions and their applications to linguistics, this volume adds a computational component, the third pillar of language use and logical activity. This book is essential reading for researchers in linguistics, philosophy, cognitive science, logic, AI, and computer science.

Electronic books.

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9783319287478