Applied Logic for Computer Scientists and Mathematicians

This book provides an introduction to logic and mathematical induction, which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern interactive proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians, and engineers to enhance their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of "logic," placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS as well as mechanizations of proofs of mathematical theorems.

Needs to build certificates of correctness and robustness of software and hardware systems Provides mathematicians with the logical background to develop mechanized proofs of mathematical theorems Clarifies the differences between constructive and classical deduction

Autorentext

Mauricio Ayala-Rincón is a professor in the theory of computing at the Universidade Federal de Goiás and an associated researcher at the University of Brasília. He received his doctorate in informatics from the Universität Kaiserslautern. His primary research interests are in the logic and semantics of computation. His publications are related to rewriting and lambda calculus and to the applications of these frameworks in theorem proving and automated reasoning.

Flávio L. C. de Moura is an Associate Professor in computer science at the Universidade de Brasília, where he received his Ph.D. in mathematics (theory of computing). He has done long-term research programs at Heriot-Watt University and Université Paris Diderot. His research focuses on lambda calculus and explicit substitutions, as well as on the application of proof assistants to the formalization of computation and mathematics.

Thaynara Arielly de Lima is an Adjunct Professor in mathematics at the Universidade Federal de Goiás. She received his Ph.D. in mathematics (theory of computing) from the Universidade de Brasília. She has conducted long-term research at the Research Institute for Symbolic Computation (Hagenberg) at the Johannes Kepler University in Linz. Her research is focused on the formalization of combinatorial and algebraic theorems.

Inhalt

Introduction.- Derivation and proofs in the propositional logic.- Derivations and proofs in the predicate logic.- Deductions in the style of Gentzen's sequent calculus.- Derivations and formalizations.- Algebraic and computational examples.- Interactive theorem proving.- Suggested readings.