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.