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Concept equations. (English) Zbl 1057.03021

Summary: The author studies systems of equations which naturally arise in the formalization of the Port-Royal theory of concepts. An 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.

MSC:

03B70 Logic in computer science
03B52 Fuzzy logic; logic of vagueness
68T30 Knowledge representation
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