The Language Complexity Game (Artificial Intelligence)

This work elucidates the structure and complexity of human language in terms of the mathematics of information and computation. It strengthens Chomsky's early work on the mathematics of language, with the advantages of a better understanding of language and a more precise theory of structural complexity. Ristad argues that language is the process of constructing linguistic representations from the forms produced by other cognitive modules and that this process is NP-complete. This NP-completeness is defended with a phalanx of elegant and revealing proofs that rely only on the empirical facts of linguistic knowledge and on the uncontroverted assumption that these facts generalize in a reasonable manner. For this reason, these complexity results apply to all adequate linguistic theories and are the first to do so. Eric Sven Ristad is Assistant Professor of Computer Science at Princeton University. He is the coauthor of __Computational Complexity and Natural Language.__**Contents:** Foundation of the Investigation. Anaphora. Ellipsis. Phonology. Syntactic Agreement and Lexical Ambiguity. Philosophical Issues. Foreword / Robert C. Berwick -- 1. Introduction -- 1.1. Prior Motivation -- 1.2. The Language Complexity Game -- 1.3.1. Interpretation Of Human Language -- 1.3.2. Complexity Thesis For Human Language -- 2. The Anaphora Problem -- 2.1. Defining The Problem -- 2.3. Summary Of Anaphora Results -- 3. Anaphoric Agreement -- 3.1. The Standard Agreement Model -- 3.2. From Graph Coloring To Anaphoric Agreement -- 3.3. Agreement Reconsidered -- 3.3.1. Theory Of Paradigm Structure -- 3.3.2. Paradigms For Anaphoric Elements -- 3.4. An Upper Bound On Anaphoric Uniqueness -- 4. Referential Dependency -- 4.1. The Referential Dependence Model -- 4.1.1. Local C-command Configuration -- 4.1.2. Control Configuration -- 4.1.3. Strong Crossover Configuration -- 4.1.4. Invisible Obviation Configuration -- 4.2. Prom Satisfiability To Referential Dependence -- 5. Ellipsis -- 5.1. Copy Model Of Ellipsis -- 5.2. Prom Qbf To Anaphoric Copying -- 5.3. Ellipsis Reconsidered -- 5.4. Function-sharing Model Of Ellipsis -- 5.5. An Np Algorithm For Anaphoric Sharing -- 6. Implications Of The Results -- 6.1. Interpretation Of Human Language -- 6.1.1. The Study Of Language -- 6.1.2. The Parsing Of E-languages -- 6.2. The Complexity Thesis -- 6.3. The Language Complexity Game -- 6.3.1. Methodological Suggestions -- 6.3.2. Technical Contributions To Linguistics -- A: Background. Eric Sven Ristad. Includes Bibliographical References (p. [139]-143) And Index. This work elucidates the structure and complexity of human language in terms of the mathematics of information and computation. It strengthens Chomsky's early work on the mathematics of language, with the advantages of a better understanding of language and a more precise theory of structural complexity. Ristad argues that language is the process of constructing linguistic representations from the forms produced by other cognitive modules and that this process is NP-complete. This NP-completeness is defended with a phalanx of elegant and revealing proofs that rely only on the empirical facts of linguistic knowledge and on the uncontroverted assumption that these facts generalize in a reasonable manner. For this reason, these complexity results apply to all adequate linguistic theories and are the first to do so. Eric Sven Ristad is Assistant Professor of Computer Science at Princeton University. He is the coauthor of Computational Complexity and Natural Language. Contents: Foundation of the Investigation. Anaphora. Ellipsis. Phonology. Syntactic Agreement and Lexical Ambiguity. Philosophical Issues