Notre Dame Journal of Formal Logic

Propositional Logic of Supposition and Assertion

John T. Kearns

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.

Article information

Source
Notre Dame J. Formal Logic Volume 38, Number 3 (1997), 325-349.

Dates
First available in Project Euclid: 12 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039700742

Mathematical Reviews number (MathSciNet)
MR1624942

Digital Object Identifier
doi:10.1305/ndjfl/1039700742

Zentralblatt MATH identifier
0904.03004

Subjects
Primary: 03B60: Other nonclassical logic
Secondary: 03B05: Classical propositional logic

Citation

Kearns, John T. Propositional Logic of Supposition and Assertion. Notre Dame J. Formal Logic 38 (1997), no. 3, 325--349. doi:10.1305/ndjfl/1039700742. http://projecteuclid.org/euclid.ndjfl/1039700742.


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References

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  • [3] Kearns, J. T., ``Lesniewski's strategy and modal logic," Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 291--307.
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