Incompletezza - Saggi su Kurt Godel

Heinz-Otto Peitgen, Peter H. Richter
Bollati Boringhieri editore

Eric S. Roberts
Franco Angeli

Marcello Frixione, Dario Palladino
Carocci editore

Nata nel corso degli anni Trenta del secolo scorso nel contesto delle ricerche sui fondamenti della matematica, con lo sviluppo dei calcolatori digitali la teoria della computabilità ha assunto il ruolo di disciplina fondamentale per l'informatica teorica. Attraverso di essa, la sua influenza culturale si è estesa ad ambiti quali l'intelligenza artificiale, le scienze cognitive, la linguistica. Questo volume vuole rendere accessibili, con un adeguato approfondimento, i principali risultati della teoria della computabilità ad un pubblico non specializzato.

H.M. Cundy, A.P. Rollett
Feltrinelli

Ludwig von Bertalanffy
Arnoldo Mondadori Editore

Michael R. Genesereth, Nils J. Nilsson
Morgan Kaufmann Publishers

Intended both as a text for advanced undergraduates and graduate students, and as a key reference work for AI researchers and developers, Logical Foundations of Artificial Intelligence is a lucid, rigorous, and comprehensive account of the fundamentals of artificial intelligence from the standpoint of logic.

The first section of the book introduces the logicist approach to AI--discussing the representation of declarative knowledge and featuring an introduction to the process of conceptualization, the syntax and semantics of predicate calculus, and the basics of other declarative representations such as frames and semantic nets. This section also provides a simple but powerful inference procedure, resolution, and shows how it can be used in a reasoning system.

The next several chapters discuss nonmonotonic reasoning, induction, and reasoning under uncertainty, broadening the logical approach to deal with the inadequacies of strict logical deduction. The third section introduces modal operators that facilitate representing and reasoning about knowledge. This section also develops the process of writing predicate calculus sentences to the metalevel--to permit sentences about sentences and about reasoning processes. The final three chapters discuss the representation of knowledge about states and actions, planning, and intelligent system architecture.

End-of-chapter bibliographic and historical comments provide background and point to other works of interest and research. Each chapter also contains numerous student exercises (with solutions provided in an appendix) to reinforce concepts and challenge the learner. A bibliography and index complete this comprehensive work.

Saunders Mac Lane, Garrett Birkhoff
Mursia

Bruno D'Amore
Zanichelli

Charles S. Chihara
Oxford University Press

Chihara here develops a mathematical system in which there are no existence assertions but only assertions of the constructibility of certain sorts of things. He utilizes this system in the analysis of the nature of mathematics, and discusses many recent works in the philosophy of mathematics from the viewpoint of the constructibility theory developed. This innovative analysis will appeal to mathematicians and philosophers of logic, mathematics, and science.

Stefano Donati
Firenze Atheneum

La filosofia della matematica di Bertrand Russell nella sua fase matura e definitiva: la fase logicista, in cui egli sostenne che tutta la matematica pura deriva da premesse puramente logiche e utilizza solo concetti logici, o definibili in termini puramente logici.

Enrico Rufini
Feltrinelli

Guido Castelnuovo
Feltrinelli