🚀 go-pugleaf

In article <6921.26ebb2bb@abo.fi> hvirtanen@abo.fi (Harry Virtanen) writes:

>I'm planning to present a paper (if accepted) on this subject at the IFSA 91'
>Brussels congress. Any comments, or information on other existing Fuzzy Prolog
>systems are welcome (personal mail or in this newsgroup).

It would be interesting to consider the architectures that might support
your language.  If evaluation of Lukasiewicz sentences plays a significant
part in the execution of LukLog programs, you might find that the analog
VLSI Lukasiewicz logic arrays implemented at Indiana University could be
used in a hybrid machine.

I have been more interested in defining applications of these arrays to
connectionist networks, fuzzy controllers and expert systems.  Languages
for hybrid systems integrating connectionism & logic programming may also
be possible, using sentence schema in Lukasiewicz logic as targets for
network descriptions. To answer Richard's question, the VLSI LLAs are
continuous-valued theoretically, but can be resolved to L(64) in the
current test set-up (6 bits of precision).

Lukasiewicz logic connects a number of computational paradigms, and offers
a means to approach analog computation logically.

McNaughton noted the relationship between Lukasiewicz logic and polynomial
curves approximated by linear segments ("A theorem about infinite-valued
sentential logic," Journal of Symbolic Logic, Vol 16, pp. 1-13, 1951).

Robin Giles has published a series of papers from 1976 to 1985 discussing
the relationships between Lukasiewicz logic, fuzzy logic, and a game-theoretic
approach to truth.  His most recent paper, "A resolution logic for fuzzy
reasoning" appeared in the 1985 Proceedings of the IEEE 17th International
Symposium on Multiple-Valued Logic.

Lukasiewicz logic arrays are described in a paper of that title by Mills,
Daffinger and Beavers in the Proceedings of the 20th IEEE Symposium on
Multiple-valued Logic.  A discussion of the use of both the algebraic and
logical operational semantics of LLAs appeared as "An Analog VLSI Array
Processor for Classical and Connectionist AI," in the Proceedings of the
1990 Conference on Application-specific Array Processors.

Fuzzy Prologs are certainly interesting, but Lukasiewicz logic offers a
novel approach to extending Kowalski's paradigm, "algorithm = logic + control"
to other areas of AI, as well as developing languages and/or compilation
techniques for analog and hybrid processors.