This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

Deduction: Automated Logic presents the broad topic of automated deductive reasoning in a concise and comprehensive manner. This book features broad coverage of deductive methods on the level of propositional and first-order logic, the strategic aspects of automated deduction, the applications of deduction mechanisms to a range of different areas, and their realization in concrete systems. This book can be used both by readers seeking a broad survey of the area, and by those requiring a reference for more detailed analysis on individual topics. It is an invaluable text for students of artificial intelligence, cognitive science, and theorum- proving at the advanced undergraduate and graduate level. Intended for readers who wish to become familiar with the area as a whole, or with selected topics, in a relatively short time Serves as a reference book for consultation on individual topics Contains one of the most comprehensive collections of different deduction mechanisms which has ever appeared in a single book, all presented in a uniform framework Contains extensive references and exercises Thoroughly cross-referenced

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

A notation called sets-as-signs is developed, and then it is demonstrated how it can be used to modify any known inference method to handle many-valued logics. Applications are discussed, both in pure mathematics, and in hardware verification and interval arithmetic. Concludes with a historical overview of activities in many-valued theorem proving. Annotation copyright by Book News, Inc., Portland, OR

The idea of mechanizing deductive reasoning can be traced all the way back to Leibniz, who proposed the development of a rational calculus for this purpose. But it was not until the appearance of Frege's 1879 Begriffsschrift-"not only the direct ancestor of contemporary systems of mathematical logic, but also the ancestor of all formal languages, including computer programming languages" ([Dav83])-that the fundamental concepts of modern mathematical logic were developed. Whitehead and Russell showed in their Principia Mathematica that the entirety of classical mathematics can be developed within the framework of a formal calculus, and in 1930, Skolem, Herbrand, and Godel demonstrated that the first-order predicate calculus (which is such a calculus) is complete, i. e. , that every valid formula in the language of the predicate calculus is derivable from its axioms. Skolem, Herbrand, and GOdel further proved that in order to mechanize reasoning within the predicate calculus, it suffices to Herbrand consider only interpretations of formulae over their associated universes. We will see that the upshot of this discovery is that the validity of a formula in the predicate calculus can be deduced from the structure of its constituents, so that a machine might perform the logical inferences required to determine its validity. With the advent of computers in the 1950s there developed an interest in automatic theorem proving.