Ł\(\Pi\) logic with fixed points
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.
scientific article; zbMATH DE number 5366795
scientific article