Notre Dame Journal of Formal Logic

Propositional Logic of Supposition and Assertion

John T. Kearns


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

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

First available in Project Euclid: 12 December 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

Export citation


  • 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.