Ł\(\Pi\) logic with fixed points
type: Item
instance of: scholarly article
title: Ł\(\Pi\) logic with fixed points
zbMATH Open document ID: 1179.03031
author: Luca Spada
published in: Archive for Mathematical Logic
publication date: 2008-11-17T00:00:00Z
review text: 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.
reviewed by: Agata Ciabattoni
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 5366795
zbMATH Keywords: Ł\(\Pi\) logic
zbMATH Keywords: fixed point
zbMATH Keywords: many-valued logic
zbMATH Keywords: ordered algebraic semantics
zbMATH Keywords: real closed fields
MaRDI profile type: Publication
full work available at URL: s00153-008-0105-3
OpenAlex ID: W2048287546
cites work: Groupes et anneaux reticules
cites work: Algebraizable logics
cites work: Linear Kripke frames and Gödel logics
cites work: Algebraic Analysis of Many Valued Logics
cites work: A note to the definition of the Ł\(\Pi\)-algebras
cites work: Fixed Point Logics
cites work: Q4485195
cites work: The \(L\Pi\) and \(L\Pi\frac 12\) logics: Two complete fuzzy systems joining Łukasiewicz and product logics
cites work: A logical and algebraic treatment of conditional probability
cites work: Algebraization, parametrized local deduction theorem and interpolation for substructural logics over FL
cites work: Metamathematics of fuzzy logic
cites work: Results on the propositional \(\mu\)-calculus
cites work: Complexity and Definability Issues in LFormula
cites work: On spectra, and the negative solution of the decision problem for identities having a finite nontrivial model
cites work: Q3751631
cites work: An algebraic approach to propositional fuzzy logic
cites work: Interpolation and Beth's property in propositional many-valued logics: a semantic investigation
cites work: Elementary induction on abstract structures
cites work: Kripke‐style semantics for many‐valued logics
cites work: Continuous approximations of product implication in MV-algebras with product
cites work: A constructive proof of McNaughton's theorem in infinite-valued logic
cites work: Tensor products and the Loomis-Sikorski theorem for MV-algebras
cites work: A lattice-theoretical fixpoint theorem and its applications
DOI: 10.1007/S00153-008-0105-3
description: scientific article; zbMATH DE number 5366795