hadley@fornax.UUCP (Bob Hadley) (07/17/90)
Reasoning with Truth Ascriptions, Self-Reference and Embedded Sentences in First-Order Logic by Robert F. Hadley School of Computing Science Simon Fraser University Burnaby, Canada V5A 1S6 hadley@cs.sfu.ca Abstract A first-order logic, T-FOL, is presented, which at once sanctions inferences involving truth ascriptions, while also permitting self-reference and arbitrary nesting of sentences within propositional attitudes. T-FOL includes a distinguished truth predicate and special inference rules which permit inferences involving truth-ascriptions to be drawn in a natural, intuitive fashion, while avoiding explicit contradictions of the kind noted by Tarski (1936). Explicitly self-referential sentences (such as the famous `Liar' sentence) cannot be represented in T-FOL, but standard, implicit self-reference is included. The adoption of a (Fregean-based) context-sensitive semantics allows self-reference, and arbitrary nesting of sentences to be achieved without the encumbrance of quotation marks and concatenation devices. Within T-FOL, the objects of which truth, knowledge, and belief are predicated are intensions, rather than particular sentences. This approach enables a many-to-one mapping between particular sentences and the beliefs they express. Applications of T-FOL to inferences involving truth are described. The soundness and completeness of T-FOL have been established and are provided within.