The present book, whose parents are previous similar (but distinct) books of B. Partee and R. Wall, is a fundamental, multifunctional issue: a reference book for computational linguistics (CL) teachers and researchers, a basic textbook for CL students, and a general handbook (or guide) for anyone interested in the principles of the CL field. The book contains the fundamental current theories, from mathematics, logic, and computer science.
The book contains 22 chapters, grouped in five parts (A to E), with some important appendices to parts A, B, and E, with exercises at the end of each chapter and part, with a rich bibliography and a complex index.
Part A is devoted to set theory (Chapters 1-4), including four appendices on the set-theoretic construction of number systems.
Part B is the largest (and really substantial) one: logic and formal systems. The four chapters enclose: Chapter 5: Basic concepts of logic and formal systems; Chapter 6: Statement logic (including natural deduction, Beth tableaux); Chapter 7: Predicate logic (including elements of proof theory); Chapter 8: Formal systems, axiomatization, and model theory (Kleene’s three-valued logic is introduced in Appendix B-2).
Part C is devoted to algebra. Chapter 9: Basic concepts; Chapter 10: Operational structures (groups, semigroups, monoids, and morphisms); Chapter 11: Lattices (filters, ideals, special lattices); Chapter 12: Boolean and Hayting algebras (including Kripke semantics). Part D investigated English as a formal language. Chapter 13: Basic concepts (on the model-theoretic semantics of natural language meaning); Chapter 14: Generalized quantifiers; Chapter 15: Intensionality.
Part E examines the basic concepts and properties in computer science, related to (formal) languages, grammars, and automata. Chapter 16: Basic concepts (Chomsky hierarchy); Chapter 17: Finite automata, regular languages, and type-3 grammars; Chapter 18: Pushdown automata, context- free grammars and languages; Chapter 19: Turing machines, r.e. languages, and type-O grammars; Chapter 20: Linear bounded automata, context- sensitive languages, and type-1 grammars; Chapter 21: Languages between context-free and context-sensitive (indexed, tree-adjoining, head, and categorial grammars); Two appendices comprise the Chomsky hierarchy and semantic automata.
The solutions to selected exercises end this book which can be labelled as a guide into the necessary formal universe of the present CL.