This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. This new edition includes material on AE calculus, Herbrand's theorem, Gentzen's theorem, and related topics.
Melvin Fitting Boeken
Melvin Fitting is een logicus wiens werk zich verdiept in filosofische logica en tableau-bewijssystemen. Hij onderzoekt hoe redeneerprincipes verschuiven afhankelijk van context en onderwerp, en beschouwt logica als een waardevol instrument om de coherentie van filosofische posities te belichamen en aan te tonen. Zijn uitgebreide academische carrière omvatte onderwijs en onderzoek, waarmee hij zowel studenten als het vakgebied vormde. Fitting's benadering benadrukt het vermogen van logica om gedachten te formaliseren en hun onderliggende structuren te onthullen.
Fitting and Mendelsohn offer an in-depth exploration of first-order modal logic, utilizing possible world models, tableau proofs, and philosophical discussions. Key topics include quantification, equality, existence, non-rigid constants, predicate abstraction, and definite descriptions, addressing significant philosophical issues.
Justification Logic
- 268bladzijden
- 10 uur lezen
Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a framework for the reliability of assertions. This book, the first in the area, is a systematic and modern account that will appeal to readers from a variety of disciplines to which the theory applies.
Beyond two: theory and applications of multiple valued logic
- 384bladzijden
- 14 uur lezen
This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.
Types, tableaus, and Gödel's God
- 196bladzijden
- 7 uur lezen
Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and the Prawitz/Takahashi completeness proof is given. Then modal machinery is added to produce a modified version of Montague/Gallin intensional logic. Finally, various ontological proofs for the existence of God are discussed informally, and the Gödel argument is fully formalized. Parts of the book are mathematical, parts philosophical.
First-Order Logic and Automated Theorem Proving
- 348bladzijden
- 13 uur lezen
Focusing on automated theorem proving in classical logic, this book serves computer scientists while also appealing to philosophers and mathematicians. It provides a theoretical treatment of formal logic, emphasizing truth in mathematical discourse and exploring models and their properties. Although not a practical guide, it addresses how-to issues and covers essential proof techniques, including completeness, making it suitable for those seeking a comprehensive understanding of formal logic within various fields of computer science.