Annals of Pure and Applied Logic 172 (3):102916 (2021)

Authors
Abstract
Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value.
Keywords Mathematical fuzzy logic  Lindström theorem  Abstract model theory  Many-valued predicate logics
Categories (categorize this paper)
DOI 10.1016/j.apal.2020.102916
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,645
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Model Theory.C. C. Chang & H. Jerome Keisler - 1992 - Studia Logica 51 (1):154-155.
Axioms for Abstract Model Theory.K. Jon Barwise - 1974 - Annals of Mathematical Logic 7 (2-3):221-265.
Omitting Uncountable Types and the Strength of [0,1]-Valued Logics.Xavier Caicedo & José N. Iovino - 2014 - Annals of Pure and Applied Logic 165 (6):1169-1200.

View all 10 references / Add more references

Citations of this work BETA

Fuzzy Logic.Petr Hajek - 2008 - Stanford Encyclopedia of Philosophy.

Add more citations

Similar books and articles

Fraïssé Classes of Graded Relational Structures.Guillermo Badia & Carles Noguera - 2018 - Theoretical Computer Science 737:81–90.
Uniform Short Proofs for Classical Theorems.Kees Doets - 2001 - Notre Dame Journal of Formal Logic 42 (2):121-127.
A New Modal Lindström Theorem.Johan van Benthem - 2007 - Logica Universalis 1 (1):125-138.
A Logical Framework for Graded Predicates.Petr Cintula, Carles Noguera & Nicholas J. J. Smith - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction: LORI 2017. Berlin: Springer. pp. 3-16.
A Note on Graded Modal Logic.Maarten De Rijke - 2000 - Studia Logica 64 (2):271 - 283.
A Lindström Theorem for Intuitionistic Propositional Logic.Guillermo Badia - 2020 - Notre Dame Journal of Formal Logic 61 (1):11-30.
A Note on Graded Modal Logic.Maarten de Rijke - 2000 - Studia Logica 64 (2):271-283.
Grading Modal Judgement.Nate Charlow - 2020 - Mind 129 (515):769-807.
On Models with Variable Universe.Bernd Ingo Dahn - 1975 - Studia Logica 34 (1):11 - 23.

Analytics

Added to PP index
2020-11-05

Total views
10 ( #882,542 of 2,462,267 )

Recent downloads (6 months)
2 ( #299,023 of 2,462,267 )

How can I increase my downloads?

Downloads

My notes