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Modal LogicAn Introduction to its Syntax and Semantics$
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Nino B. Cocchiarella and Max A. Freund

Print publication date: 2008

Print ISBN-13: 9780195366587

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195366587.001.0001

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The Syntax of Modal Sentential Calculi

The Syntax of Modal Sentential Calculi

Chapter:
(p.15) Chapter 2 The Syntax of Modal Sentential Calculi
Source:
Modal Logic
Author(s):

Nino B. Cocchiarella

Max A. Freund

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195366587.003.0002

The authors construct different modal calculi in this chapter. These cover all the well-known systems, S1–S5, of Lewis and Langford's 1932 classic Symbolic Logic. These systems are constructed first on the level of sentential (or propositional) logic. Every sentential modal logic that they consider is also closed under tautologous transformations, in addition to be being based on the same formal language. These systems are called modal CN-calculi and are classified in terms of an order of increasing specificity as (quasi-)classical, (quasi-)regular, and (quasi-)normal modal CN-calculi.

Keywords:   modal calculi, Symbolic Logic, Lewis, Langford, sentential logic, modal CN-calculi

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