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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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Semantics for Logical Necessity

Semantics for Logical Necessity

(p.61) Chapter 4 Semantics for Logical Necessity
Modal Logic

Nino B. Cocchiarella

Max A. Freund

Oxford University Press

This chapter initially describes possible-worlds semantics, which was first introduced by Rudolf Carnap in 1946 in terms of his state-description semantics, for sentential modal logic. Carnap was not concerned with different notions of necessity and possibility, but only with logical necessity and logical possibility. He proposed a criterion of adequacy that any formal semantics for these notions must satisfy in his account of logical necessity and logical possibility. The authors construct a formal semantics and modal logic that satisfies Carnap's criterion in terms of the ontology of logical atomism — an ontology that was implicit in Carnap's state-description semantics.

Keywords:   possible-worlds semantics, Rudolf Carnap, logical necessity, logical possibility, semantics, modal logic, logical atomism

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