# [FOM] combining probability and logic

Jon Williamson jon.williamson at kcl.ac.uk
Fri Sep 6 05:23:42 EDT 2002

```> > To this matter the ideas of polyvalued truth value space is quite
relevant and
> > the formalisam of polyvalued logic is isomorf to Baysian logic, that is
a
> > combining of probability and logic.
>
> I want to add: The polyvalued logic is a quantity relation logic, like
> Baysian logic, but provides also a natural definition of modal concepts,
> i.e. modal logic is an integrated part of this logic. The difference
between
> probabilities, factual truths and logical truths is only the strengh in
> truth - the logic (the consequece relations between things) remains still
> the same and is independent of what kind of truth concept we applies.
> Probability must be apprehended as a truth concept - weaker than factual
> truth - like logical truth is a stronger concept.
>

One has to be a bit careful about this. Many-valued logics (such as the
logics of Lukasiewicz) tend to be truth functional (for example value(a&b)
is a function of value(a) and value(b)), often employing similar rules to
fuzzy logic for determining values. Probabilities are not truth-functional,
so many-valued logic as it is normally developed is not a logic of
probability. Many-valued logics can be thought of as logics for reasoning
about partial truth or vagueness, but if these concepts are explicated using
many-valued logics, then probability cannot be interpreted as partial truth.

All those interested in this subject are welcome at "combining probability
and logic", 4th-6th November, King's College London.
http://www.kcl.ac.uk/progic

All the best,
Jon
.......................
Jon Williamson
Department of Philosophy, King's College, Strand, London, WC2R 2LS, UK
http://www.kcl.ac.uk/jw

----- Original Message -----
From: "Åke Persson" <ok.person at swipnet.se>
To: <fom at cs.nyu.edu>
Sent: Friday, September 06, 2002 12:29 AM
Subject: Re: [FOM] combining probability and logic

>
> >> Jon Williamson wrote:
> >>
> >> Those FOMers around London at the beginning of November might be
> >> interested in the workshop "combining probability and logic":
> >> http://www.kcl.ac.uk/progic
>
> > Åke Persson wrote:
> >
> > To this matter the ideas of polyvalued truth value space is quite
relevant and
> > the formalisam of polyvalued logic is isomorf to Baysian logic, that is
a
> > combining of probability and logic.
>
> I want to add: The polyvalued logic is a quantity relation logic, like
> Baysian logic, but provides also a natural definition of modal concepts,
> i.e. modal logic is an integrated part of this logic. The difference
between
> probabilities, factual truths and logical truths is only the strengh in
> truth - the logic (the consequece relations between things) remains still
> the same and is independent of what kind of truth concept we applies.
> Probability must be apprehended as a truth concept - weaker than factual
> truth - like logical truth is a stronger concept.
>