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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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Relational World Systems

Relational World Systems

Chapter:
(p.81) Chapter 6 Relational World Systems
Source:
Modal Logic
Author(s):

Nino B. Cocchiarella

Max A. Freund

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195366587.003.0006

The authors develop semantics for sentential modal logic in terms of relational world systems, i.e. systems of possible worlds that stand in various kinds of relations of accessibility to one another. The semantic systems described in this chapter make use of the notion of a possible world is basic to the semantics for logical truth and implication in both a primary and secondary sense, but based on two new factors. One new factor is the idea of the class of possible worlds being indexed — e.g. by different “possible” reference frames — so that in principle the same possible world could be indexed by two or more different indices. The other factor is the inclusion of a relation between some or all of the indices of an indexed system of worlds.

Keywords:   sentential modal logic, relational world systems, semantic systems, logical truth, implication, possible worlds

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