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Vol. 1. Propositional Logic
Vol. 2. Predicate Logic
Logic is a foundational mathematical discipline for Computer Science. This unique compendium provides the main ideas and techniques originating from logic. It is divided into two volumes - propositional logic and predicate logic. The volume presents some of the most important concepts starting with a variety of logic formalisms - Hilbert/Frege systems, tableaux, sequents, and natural deduction in both propositional and first-order logic, as well as transformations between these formalisms. Topics like circuit design, resolution, cutting planes, Hintikka sets, paramodulation, and program verification, which do not appear frequently in logic books are discussed in detail. The useful reference text has close to 800 exercises and supplements to deepen understanding of the subject. It emphasizes proofs and overcomes technical difficulties by providing detailed arguments. Computer scientists and mathematicians will benefit from this volume.
In scientifc reasoning, one starts with a collection of statements, the premises, in order to justify another statement, via a process of inference. Therefore, the study of logic is essential for students of Computer Science, mathematics, and all who use mathematical proofs.
Many of the fundamental computing concepts were created by logicians. The most famous such concept is the idea of a general-purpose computer, the Turing Machine. Computer programs are written in symbolic languages, e.g., Python, Java, and Lisp, that contain features of logical notations and symbolisms. Through such connections, the study of logic helps in the design of programs. Logic also has a role in the design of new programming languages, and it is essential for work in Artificial Intelligence (AI).
Propositional Logic:
Preliminaries
Propositional Logic–Syntax and Semantics
Propositional Logic–Formal Systems
Predicate Logic:
First-Order Logic–Syntax and Semantics
First-Order Logic–Formal Systems
Program Verification