Covers first-order language in method appropriate for first and second courses in logic. CD-ROM consists of a new book, 3 programs,and an Internet-based grading service.

Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's (...) Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (shrink)

The original proof of the four-color theorem by Appel and Haken sparked a controversy when Tymoczko used it to argue that the justification provided by unsurveyable proofs carried out by computers cannot be a priori. It also created a lingering impression to the effect that such proofs depend heavily for their soundness on large amounts of computation-intensive custom-built software. Contra Tymoczko, we argue that the justification provided by certain computerized mathematical proofs is not fundamentally different from that provided by surveyable (...) proofs, and can be sensibly regarded as a priori. We also show that the aforementioned impression is mistaken because it fails to distinguish between proof search (the context of discovery) and proof checking (the context of justification). By using mechanized proof assistants capable of producing certificates that can be independently checked, it is possible to carry out complex proofs without the need to trust arbitrary custom-written code. We only need to trust one fixed, small, and simple piece of software: the proof checker. This is not only possible in principle, but is in fact becoming a viable methodology for performing complicated mathematical reasoning. This is evinced by a new proof of the four-color theorem that appeared in 2005, and which was developed and checked in its entirety by a mechanical proof system. (shrink)

This book argues that (1) AI will continue to produce machines with the capacity to pass stronger and stronger versions of the Turing Test but that (2) the "Person Building Project" (the attempt by AI and Cognitive Science to build a machine which is a person) will inevitably fail. The defense of (2) rests in large part on a refutation of the proposition that persons are automata -- a refutation involving an array of issues, from free will to Godel to (...) introspection to Searle and beyond. The defense of. (shrink)

Artificial Intelligence: A Modern Approach, 3e offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. Number one in its field, this textbook is ideal for one or two-semester, undergraduate or graduate-level courses in Artificial Intelligence. Dr. Peter Norvig, contributing Artificial Intelligence author and Professor Sebastian Thrun, a Pearson author are offering a free online course at Stanford University on artificial intelligence. According to an article in The New York Times, the course on artificial intelligence is (...) “one of three being offered experimentally by the Stanford computer science department to extend technology knowledge and skills beyond this elite campus to the entire world.” One of the other two courses, an introduction to database software, is being taught by Pearson author Dr. Jennifer Widom. Artificial Intelligence: A Modern Approach, 3e is available to purchase as an eText for your Kindle™, NOOK™, and the iPhone®/iPad®. (shrink)

Presenting a look at the human mind's capacity while criticizing artificial intelligence, the author makes suggestions about classical and quantum physics and ..

When Ken Malone investigates a case of something causing mental static across the United States, he is teleported to a world that doesn't exist.

Church's and Turing's theses dogmatically assert that an informal notion of effective calculability is adequately captured by a particular mathematical concept of computability. I present an analysis of calculability that is embedded in a rich historical and philosophical context, leads to precise concepts, but dispenses with theses. To investigate effective calculability is to analyze symbolic processes that can in principle be carried out by calculators. This is a philosophical lesson we owe to Turing. Drawing on that lesson and recasting work (...) of Gandy, I formulate boundedness and locality conditions for two types of calculators, namely, human computing agents and mechanical computing devices (discrete machines). The distinctive feature of the latter is that they can carry out parallel computations. The analysis leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of these axioms to Turing machines. Cellular automata and a variety of artificial neural nets can be shown to satisfy the axioms for machine computations. (shrink)

An Introduction to G¨ odel’s Theorems now exists in two versions – the original 2007 printing, and a corrected reprint in 2008. The quick way of telling these apart is to glance at the imprints page (the verso of the title page): the later version notes, halfway down that page, “Reprinted with corrections 2008”. Corrections marked with marginal side-bars as here are those that have been noted after the second printing went to press, and hence still need correction/improvement. If you (...) have the corrected reprint, then these marked corrections are the only errors you need care about! This complete list of corrections is divided, for convenience, into two sections. (shrink)

Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof.