SOME IDEAS ON SOFT LOGIC PROGRAMMING
Jorma K. Mattila
Lappeenranta University of Technology
E-mail: Jorma.K.Mattila@lut.fi
Date: Thursday, July 2nd, 1998
Time: 4-5pm
Location : 310 Soda Hall
Abstract
Some basic ideas for logic programs based on multimodal logics are presented.
The purpose is to apply them using resolution method. The leading example
is to find out whether the inference
a is small.
a and b are approximately equal.
So, b is more or less small.
is correct, and what is the logical system where it is correct. (This inference
has been mentioned in several text books of fuzzy systems without further
consideration.) Thus the aim is also to find a logical system (at least one)
which is both logically correct and intuitively acceptable. It appears that the
inference is correct in MultiS5+I, but this system includes some few features
which are not intuitively acceptable (e.g. the sentence "If a and b are
approximately equal then a and b are equal" is provable in it).
Brief introduction to multimodal systems, like MultiT+I, MultiS4+I, and MultiB+I
is given, and graded modifier systems by means of accessibility relations are
presented. Also some ideas about intuitively acceptable systems are considered.
Especially logical systems with identity are very interesting, and there are
many philosophical problems in them. The problem to find a logically
correct and intuitively acceptable system including identity may be solved
by using so-called contingent identity systems. In those systems the
method is to restrict or change some axioms concerning identity.
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