[FOM] paraconsistent logic and computer science + logical context

Antonino Drago drago at unina.it
Sun Oct 14 15:57:07 EDT 2007

On 12 Oct 2007 at 11:09, Arnon Avron wrote:
>  On Fri, Sep 28, 2007 at 11:34:32AM +0200, Joseph Vidal-Rosset wrote:

>> >  In what precise situations [of computer scinece] have we to allow $ p,
>> > \neg p \vdash q $ ?
>> >  It is very difficult for me to understand what is a "true
>> >  contradiction" and to admit "Dialetheism". I still believe that
>> >  rejecting contradiction as false is a sane methodological position in
>> >  science and in philosophy in general.

In my interpretation of Vasiliev's paraconsistent Logic ("Vasiliev's
paraconsistent logic interpreted by means of the dual role played by the
double negation law", J. Applied Non-Classical Logic, 11 (2001) 281-294),
third Vasiliev's statement  "S is and is not A" may be interpreted as "not
not A implies A and does not implies A".
This statement applies to a situation whose context is undefined; and
precisely when it is undefined to which kind organisation of the theory he
is building, one refers to; either the deductive organisation  (then, not
not A a implies A), or the problem-based organisation, which is
characteristic of an inductive research for finding out a new method of
solution to be apllied to the given problem (the, not not A does not imply
Hence, in computer science (likely as in science in general), this kind of
statement occurs in a situation in which one refer not to data, but to
hypothesis on data, i.e. to guesses with respect to a set of data, without
any specification of the kind of organisation he want to refer his theory.

My interpretation opens the question: at what extent a logical statement
depends from its context?

Best regards
Antonino Drago

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