Interpolation and Amalgamation in Many-Valued Logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F25%3A00638096" target="_blank" >RIV/67985807:_____/25:00638096 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.congressi.unisi.it/latd25/wp-content/uploads/sites/156/2025/07/LATD2025_Booklet-8.pdf" target="_blank" >https://www.congressi.unisi.it/latd25/wp-content/uploads/sites/156/2025/07/LATD2025_Booklet-8.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Interpolation and Amalgamation in Many-Valued Logics

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Interpolation and Amalgamation in Many-Valued Logics

Popis výsledku anglicky

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.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GM25-18306M" target="_blank" >GM25-18306M: Interpolace, amalgamace a výpočty</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů