Re: Difference between logics and theories

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Organization: Dipartimento di Informatica - Universita' di Pisa - Italy
Date: Tue, 13 Sep 1994 11:59:28 --100
From: attardi@di.unipi.it
Message-id: <9409130959.AA04607@omega>
To: sowa@ranch.poly.edu
Cc: cg@cs.umn.edu, interlingua@ISI.EDU, srkb@cs.umbc.edu, sowa@ranch.poly.edu,
        simi@di.unipi.it
In-reply-to: <9409101746.AA03702@ranch.poly.edu> (sowa@ranch.poly.edu)
Subject: Re: Difference between logics and theories
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   >From sowa@ranch.poly.edu Sat Sep 10 19:48:13 1994
   Date: Sat, 10 Sep 94 13:46:02 -0400
   From: sowa@ranch.poly.edu (John F. Sowa)
   Cc: sowa@ranch.poly.edu

   ...
   I will certainly admit that we, as definers of KIF and CGs, have a
   responsibility to demonstrate that our metalanguage is capable of
   supporting a theory of truth, modality, or whatever.  But if anyone
   writes inconsistent axioms in our formalism, it's not our fault.

But the problem is that writing such axioms in a consistent way is
very tricky.
If you need to invent axioms for every new modality you need, then you
have the problem not only of proving the resulting theory consistent,
but also of proving it consistent in connection with the axiomatizations
of the other modalities that you are also using.
This makes the situation completely unmanageable.

\begin{commercial}
To solve this problem, M. Simi and myself have been developing a framework
for expressing and reasoning relativized truth and propositional
attitudes, that we call theory of viewpoints (similar to McCarthy
contexts), which is first-order, has a model theory and a proof theory
and it is proven consistent.
The idea is not much different from Sowa "lightweight boxes", but with
a full formalization.
Using a basic construct for relitivized truth "In(formula, viewpoint)",
we show how to express various propositional attitudes: you must supply
your own preferred axioms, but you get consistency and proof theory for free.

There are several papers on the subject that I can send to interested
parties.
\end{commercial}

-- Beppe