Abstract
The axiomatic approach to a logic is quite different from that of tableaus. Certain formulas are simply announced to be theorems (they are called axioms), and various rules are adopted for adding to the stock of theorems by deducing additional ones from those already known. An axiom system is, perhaps, the most traditional way of specifying a logic, though proof discovery can often be something of a fine art. Historically, almost all of the best-known modal logics had axiomatic characterizations long before either tableau systems or semantical approaches were available. While early modal axiom systems were somewhat circuitous by today’s standards, Gödel (1933) introduced the modern axiomatic approach and this is now used by almost everybody, including us.
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© 1998 Springer Science+Business Media Dordrecht
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Fitting, M., Mendelsohn, R.L. (1998). Axiom Systems. In: First-Order Modal Logic. Synthese Library, vol 277. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5292-1_3
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DOI: https://doi.org/10.1007/978-94-011-5292-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-5335-5
Online ISBN: 978-94-011-5292-1
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