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Concept Equations

2004; Oxford University Press; Volume: 14; Issue: 3 Linguagem: Inglês

10.1093/logcom/14.3.395

1465-363X

Radim Bělohlávek,

Rough Sets and Fuzzy Logic

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.