[FOM] Defined truth

[Joao Marcos]

Sandy Hodges wrote:
> I wonder if anyone can direct me to references concerning defined
truth
> predicates.   I have a couple of references (Taisuke Sato, e.g.) on
the
> logic programming side, but none on the philosophical side.


   By your usage of the expression "truth predicate" it seems to me you
are actually looking for "truth operators", or "truth connectives", is
that right?  If that is the case, you might be interested in having a
look at the following paper:

von Wright, Georg Henrik
Truth-logics.
Logique et Analyse, Nouv. Sér. 30, No.120, 311-334 (1987).

Review by L.Löfgren, for the Zentralblatt Math:
A variety of logical calculi are developed. Their vocabulary is that of
traditional propositional logic (PL) enriched with a symbol T for a
truth operator, ``it is true that''. Formally, the role of T in the
calculus is similar to the role of modal operators in a propositional
modal logic. The use of the operator allows distinction between ways of
negating a proposition, $\sim Tp$ ``it is not true that p'', and $T\sim
p$ ``it is true that not p''. The author develops nonclassical truth
logics, TL, $T'L$, and $T''L$ to admit, respectively, truth-value gaps
(propositions neither true nor false), truth-value overlaps
(propositions both true and false), and both gaps and overlaps. TL is
called paracomplete and $T'L$ is a paraconsistent logic. TL resembles
intuitionist logic in that, if a proposition is true then it is false
that it is false, TP$\to T\sim T\sim p$, but not conversely. In $T'L$
the reverse implication holds. TLM, $T'LM$, and $T''LM$ are
corresponding logics extended to handle ``mixed'' formulas, i.e.,
formulas composed of T-expressions (of the previous logics) and
PL-expressions (of ordinary propositional logic). By way of example,
Tp$\leftrightarrow p$ is a mixed formula, in fact one with a well known
role for a general discussion of truth. The use of truth- logics in
studying antinomies is discussed. For reasoning with vague concepts the
author suggests that a logic like TL which allows truth- value gaps is
better suited than classical logic. And for reasoning about processes
and the flux of a changing world the use of a paraconsistent type of
logic may be more commendable. There are other possibilities still. A
good many of them may be systematized within a general theory of what
the author calls truth-logic(s).


   There were at least two other much older papers by von Wright ("On
the idea of logical truth, I and II") on the theme at the Soc. Sci.
Fennica.

   Yours, JM

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