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portada Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra
Type
Physical Book
Author
Publisher
Language
English
Pages
70
Format
Paperback
Dimensions
22.9x15.2x0.4 cm
Weight
0.10 kg.
ISBN13
9781792949616
Categories

Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra

Alexej P. Pynko (Author) · Independently Published · Paperback

Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra - Pynko, Alexej P.

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Delivery: 19 Oct - 30 Oct Shipping: 16 to 20 business days.
R 1,252
R 1,252

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Synopsis "Deduction Theorem and Peirce Law in General Algebraic Logic: Constructive Proofs in General Sentential Logic and Universal Algebra"

In this book we study the issues of Deduction Theorem and Peirce Law within the context of finitary universal Horn theories andequivalence between them. As basic general results, we first obtain a model-theoretic chracterization of sushtheories having Deduction Theorem with Peirce Law and then prove that equivalence between them preserves both Deduction Theorem and Peirce law. Next, we argue that our Deduction Theorem scema for enlargable multiple-conclusionsequent calculi with structural rules found earlier respects Peirce Law.As a consequence, we provide a natural and quite useful semanticsof such calculi. Finally, we explore the issues involved within the context of the Weak Contraposition extensions of so-called contraposable propositional calculi of the mentioned kind.After all, we successfully apply our generic elaborationto both certain sentential logics and varieties of algebras, providing constructive and quite transparent proofsof Deduction Theorem with Peirce Law for the formers as well asimplicativity (or, at least, restricted equational definabilityof principal congruences) for the latters.

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