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Journal of Logic and Computation 2004 14(3):395-403; doi:10.1093/logcom/14.3.395
© 2004 by Oxford University Press
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Original Article

Concept Equations

Radim Belohlávek

Department of Computer Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic. E-mail: radim.belohlavek{at}upol.cz and Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Czech Republic

Studied in the paper are systems of equations which naturally arise in the formalization of the Port-Royal theory of concepts. The unknown quantity is a relation between objects and attributes. We study the case where the relation is fuzzy with truth values in a complete residuated lattice, covering therefore the special cases of complete Boolean algebras, Heyting algebras, MV-algebras etc. We answer the question of solvability, structure of solutions, and show how solvability of non-solvable systems may be attained by so-called decrease of logical precision.

Keywords: Port-Royal logic, formal concept, relational equation, fuzzy logic

Received 9 September 2002.


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