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Infinitesimals and Pavelka logic

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Details

Original languageEnglish
Title of host publicationPROCEEDINGS OF THE 2015 CONFERENCE OF THE INTERNATIONAL FUZZY SYSTEMS ASSOCIATION AND THE EUROPEAN SOCIETY FOR FUZZY LOGIC AND TECHNOLOGY
EditorsJM Alonso, H Bustince, M Reformat
Place of PublicationPARIS
PublisherAtlantis Press
Pages1027-1033
Number of pages7
ISBN (Electronic)978-94-62520-77-6
DOIs
Publication statusPublished - 2015
Publication typeA4 Article in a conference publication
EventConference of the European Society for Fuzzy Logic and Technology -
Duration: 1 Jan 1900 → …

Publication series

NameAdvances in Intelligent Systems Research
PublisherATLANTIS PRESS
Volume89
ISSN (Print)1951-6851

Conference

ConferenceConference of the European Society for Fuzzy Logic and Technology
Period1/01/00 → …

Abstract

Rational Pavelka Logic does not admit infinitesimals. We argue that infinitesimals are important in logic and we present an alternative approach which admits them. It is built up in a similar style, but based on the Chang's perfect MV-algebra. We prove a partial result towards the completeness of this logic. We also discuss a combined approach using more complex perfect MV-algebras.

Keywords

  • Mathematical fuzzy logic, Rational Pavelka Logic, Lukasiewicz operations, MV-algebra, perfect MV-algebra, Chang's MV-algebra, FUZZY LOGIC, PROPOSITIONAL CALCULI, TRUTH-CONSTANTS, COMPLETENESS

Publication forum classification

Field of science, Statistics Finland