Proof Methods for Modal and Intuitionistic Logics (Hardcover)

M. Fitting

ISBN 10: 9027715734 / ISBN 13: 9789027715739

Editore: Springer, Dordrecht, 1983

Riguardo questo articolo

Hardcover. "Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.

Codice articolo 9789027715739

Dati bibliografici

• Titolo: Proof Methods for Modal and Intuitionistic Logics (Hardcover)
• Editore: Springer, Dordrecht
• Data di pubblicazione: 1983
• Lingua: Inglese
• ISBN 10: 9027715734
• ISBN 13: 9789027715739
• Rilegatura: Hardcover
• Condizione: new

Descrizione articolo

Riassunto

"Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.

Contenuti

One / Background.- Two / Analytic Modal Tableaus and Consistency Properties.- Three / Logical Consequence, Compactness, Interpolation, and Other Topics.- Four / Axiom Systems and Natural Deduction.- Five / Non-Analytic Logics.- Six / Non-Normal Logics.- Seven / Quantifiers.- Eight / Prefixed Tableau Systems.- Nine / Intuitionistic Logic.- Special Notation.