Interpolation and Amalgamation in Many-Valued Logics

Authors: Daniel Wesley Fussner
Publication year: 2025
Publication type: Abstrakt
Periodical: Abstract Booklet: The Logic Algebra and Truth Degrees (LATD) 2025
Projects: Interpolation, Amalgamation, and Computation
Bibliographic citation: FUSSNER, Daniel Wesley. Interpolation and Amalgamation in Many-Valued Logics. In: Abstract Booklet: The Logic Algebra and Truth Degrees (LATD) 2025. Siena: Università degli Studi di Siena, DIISM, 2025, S. 8-8. Dostupné z: https://www.congressi.unisi.it/latd25/wp-content/uploads/sites/156/2025/07/LATD2025_Booklet-8.pdf
ID: 638096
Online record: View online record

Abstract

ZÁKLADNÍ ÚDAJE: Abstract Booklet: The Logic Algebra and Truth Degrees (LATD) 2025. Siena: Università degli Studi di Siena, DIISM, 2025. s. 8-8. [LATD 2025: Logic Algebra and Truth Degrees. 21.07.2025-25.07.2025, Siena]. ABSTRAKT: Fuzzy logics have long enjoyed a fruitful symbiosis with algebraic methods. In this talk, I will discuss some recent successes of this symbiosis in the context of interpolation and amalgamation. We will see both how the advancement of algebraic techniques have enabled rapid progress on interpolation in fuzzy logics, as well as how the challenges posed by fuzzy logics have illuminated the path to new tools for the study of amalgamation in general algebraic systems. The centerpiece of this discussion will be my recent classification with S. Santschi of varieties of BL-algebras with the amalgamation property, which yields also an exhaustive classification of axiomatic extensions of Hájek’s basic fuzzy logic with the deductive interpolation property. I will discuss the main ideas and technical challenges of this classification, and what it can teach us about interpolation and amalgamation writ large.