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Computational Logic: Volume 1

Classical Deductive Computing with Classical Logic

Luis M. Augusto

This is the first of a two-volume work combining two fundamental components of contemporary computing into classical deductive computing, a powerful form of computation, highly adequate for programming and automated theorem proving, which, in turn, have fundamental applications in areas of high complexity and/or high security such as mathematical proof, software specification and verification, and expert systems. Deductive computation is concerned with truth-preservation: This is the essence of the satisfiability problem, or SAT, the central computational problem in computability and complexity theory. The Turing machine provides the classical version of this theory—classical computing—with its standard model, which is physically concretized—and thus spatial-temporally limited and restricted—in the von Neumann, or digital, computer.

Although a number of new technological applications require classical deductive computation with non-classical logics, many key technologies still do well—or exclusively, for that matter—with classical logic. In this first volume, we elaborate on classical deductive computing with classical logic. The objective of the main text is to provide the reader with a thorough elaboration on both classical computing and classical deduction with the classical first-order predicate calculus with a view to computational implementations.

As a complement to the mathematical-based exposition of the topics we offer the reader a very large selection of exercises. This selection aims at not only practice of discussed material, but also creative approaches to problems, for both discussed and novel contents, as well as at research into further relevant topics.

19 June 2018


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