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Ł\(\Pi\) logic with fixed points. (English) Zbl 1179.03031
The paper investigates the extension of a many-valued logic with fixed points. The logic under consideration is Ł\(\Pi\), the most expressive known logic based on a continuous t-norm. The author uses novel methods: the existence of a proper semantics being hinged on the Brouwer Theorem rather than the usual Tarski Theorem. The main results of the paper include “standard completeness” for the introduced logic (\(\mu\)Ł\(\Pi\)) and a categorical equivalence between its linearly ordered algebraic semantics and real closed fields. This equivalence is also extended to the full algebraic semantics of \(\mu\)Ł\(\Pi\) and a class of structures which suitably generalise real closed fields to non-linearly ordered structures.

MSC:
03B50 Many-valued logic
03B52 Fuzzy logic; logic of vagueness
03G25 Other algebras related to logic
06F25 Ordered rings, algebras, modules
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