Self-reference and Chaos in Fuzzy Logic

IEEE Transactions on Fuzzy Systems 1:237-253 (1993)
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Abstract

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of mutually referential triples.

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Patrick Grim
University of Michigan, Ann Arbor

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