### Propositional Logic of Supposition and Assertion

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

#### Abstract

This presentation of a system of propositional logic is a foundational paper for systems of illocutionary logic. The language contains the illocutionary force operators '' for assertion and ' ' for supposition. Sentences occurring in proofs of the deductive system must be prefixed with one of these operators, and rules of 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 (). Commitment valuations assign the values to sentences of ; 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.

First Page:
Primary Subjects: 03B60
Secondary Subjects: 03B05
Full-text: Open access

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

### References

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Mathematical Reviews (MathSciNet): MR82f:03015
Zentralblatt MATH: 0479.03011
Digital Object Identifier: doi:10.2307/2273259
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Mathematical Reviews (MathSciNet): MR82d:03034
Zentralblatt MATH: 0452.03045
Project Euclid: euclid.ndjfl/1093883395
Digital Object Identifier: doi:10.1305/ndjfl/1093883395
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Mathematical Reviews (MathSciNet): MR91e:03020
Zentralblatt MATH: 0694.03004
Project Euclid: euclid.ndjfl/1093635086
Digital Object Identifier: doi:10.1305/ndjfl/1093635086
[4]Vanderveken, D., and J. Searle, Foundations of Illocutionary Logic, Cambridge University Press, Cambridge, 1985.
Mathematical Reviews (MathSciNet): MR87k:03025
Zentralblatt MATH: 0577.03011
[5] Vanderveken, D., Meaning and Speech Acts, Cambridge University Press, Cambridge, 1990.