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Summer 1997 Propositional Logic of Supposition and Assertion
John T. Kearns
Notre Dame J. Formal Logic 38(3): 325-349 (Summer 1997). DOI: 10.1305/ndjfl/1039700742

Abstract

This presentation of a system of propositional logic is a foundational paper for systems of illocutionary logic. The language $\mathcal{L}_{.75}$ contains the illocutionary force operators '$\vdash$' for assertion and '⨽' for supposition. Sentences occurring in proofs of the deductive system $\mathcal{S}_{.75}$ must be prefixed with one of these operators, and rules of $\mathcal{S}_{.75}$ take account of the forces of the sentences. Two kinds of semantic conditions are investigated; familiar truth conditions and commitment conditions. Accepting a statement A or rejecting A commits a person to accepting some statements (the symbol '$+$' marks this value), to rejecting some statements ($-$), and will leave the person uncommitted with respect to others ($n$). Commitment valuations assign the values $+, -, n$ to sentences of $\mathcal{L}_{.75}$; such a valuation is conceived as reflecting the beliefs/knowledge of a particular person. This paper explores the relations between truth conditions and commitment conditions, and between semantic concepts defined in terms of these conditions.

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John T. Kearns. "Propositional Logic of Supposition and Assertion." Notre Dame J. Formal Logic 38 (3) 325 - 349, Summer 1997. https://doi.org/10.1305/ndjfl/1039700742

Information

Published: Summer 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0904.03004
MathSciNet: MR1624942
Digital Object Identifier: 10.1305/ndjfl/1039700742

Subjects:
Primary: 03B60
Secondary: 03B05

Rights: Copyright © 1997 University of Notre Dame

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Vol.38 • No. 3 • Summer 1997
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