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 rmal 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 Pea arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, n-rmal 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.
Product Identifiers
Publisher
Springer
ISBN-10
9027715734
ISBN-13
9789027715739
eBay Product ID (ePID)
95046050
Product Key Features
Author
M. Fitting
Format
Hardcover
Language
English
Subject
Philosophy
Dimensions
Weight
2140g
Height
297mm
Width
210mm
Additional Product Features
Place of Publication
Dordrecht
Series Part/Volume Number
169
Series Title
Synthese Library
Content Note
VIII, 555 P.
Date of Publication
29/04/1983
Imprint
Kluwer Academic Publishers
Edition Statement
1983 Edition
Country of Publication
Netherlands
Genre
Philosophy
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