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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.
Authors and Affiliations
Bibliographic Information
Book Title: Systems of Formal Logic
Authors: L. H. Hackstaff
DOI: https://doi.org/10.1007/978-94-010-3547-7
Publisher: Springer Dordrecht
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eBook Packages: Springer Book Archive
Copyright Information: D. Reidel Publishing Company 1966
Hardcover ISBN: 978-90-277-0077-3Due: 31 July 1966
Softcover ISBN: 978-94-010-3549-1Published: 12 October 2011
eBook ISBN: 978-94-010-3547-7Published: 06 December 2012
Edition Number: 1
Number of Pages: 372
Topics: Logic