Confluence and termination of fuzzy relations

Authors:
Radim Belohlavek;Tomas Kuhr;Vilem Vychodil
Affiliations:
Watson School, State University of New York at Binghamton, Parkway E, Vestal, NY 13902-6000, NY, USA and Dept. Computer Science, Palacky University, Olomouc 17. listopadu 12, CZ-771 46 Olomouc, Cz ...;Dept. Computer Science, Palacky University, Olomouc 17. listopadu 12, CZ-771 46 Olomouc, Czech Republic;Watson School, State University of New York at Binghamton, Parkway E, Vestal, NY 13902-6000, NY, USA and Dept. Computer Science, Palacky University, Olomouc 17. listopadu 12, CZ-771 46 Olomouc, Cz ...
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

Confluence and termination are essential properties connected to the idea of rewriting and substituting which appear in abstract rewriting systems. The aim of the present paper is to investigate confluence, termination, and related properties from the point of view of fuzzy logic leaving the ordinary notions a particular case when the underlying structure of truth degrees is two-valued Boolean algebra. The main motivation of this study is the fact that in several natural situations, the notion of substitutability is inherently fuzzy rather than crisp.