Propositional Logic of Supposition and Assertion
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.
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