## 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

https://projecteuclid.org/euclid.ndjfl/1039700742

Digital Object Identifier
doi:10.1305/ndjfl/1039700742

Mathematical Reviews number (MathSciNet)
MR1624942

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. https://projecteuclid.org/euclid.ndjfl/1039700742

#### References

• Kearns, J. T., “Modal semantics without possible worlds," The Journal of Symbolic Logic, vol. 46 (1981), pp. 77–86. Zbl 0479.03011 MR 82f:03015
• Kearns, J. T., “A more satisfactory description of the semantics of justification," Notre Dame Journal of Formal Logic, vol. 22 (1981), pp. 109–19. Zbl 0452.03045 MR 82d:03034
• Kearns, J. T., “Lesniewski's strategy and modal logic," Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 291–307. Zbl 0694.03004 MR 91e:03020
• Vanderveken, D., and J. Searle, Foundations of Illocutionary Logic, Cambridge University Press, Cambridge, 1985. Zbl 0577.03011 MR 87k:03025
• Vanderveken, D., Meaning and Speech Acts, Cambridge University Press, Cambridge, 1990.