On the compactness property of extensions of first-order G"{o}del logic

Document Type : Research Paper

Authors

1 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

2 Department of Mathematics and Computer Science, Amirk- abir University of Technology, Tehran, Iran

Abstract

We study three kinds of compactness in some variants of G"{o}del logic: compactness,
entailment compactness, and approximate entailment compactness.
For countable first-order underlying language we use the Henkin
construction to prove the compactness property of extensions of
first-order g logic enriched by nullary connective or the Baaz's
projection connective. In the case of uncountable first-order language
we use the ultraproduct method to derive the compactness theorem.

Keywords

References

1] M. Baaz and R. Zach, Compact propositional Godel logics, Multiple-Valued Logic, 28th IEEE
International Symposium on, (1998), 108-113.
[2] I. Ben-Yaacov and A. Usvyatsov, Continuous rst order logic and local stability, Transactions
of the American Mathematical Society, 362(10) (2010), 5213-5259.
[3] R. Cignoli, F. Esteva and L. Godo, On Lukasiewicz logic with truth constants, Theoretical
Advances and Applications of Fuzzy Logic and Soft Computing, Springer, (2007), 869-875.
[4] P. Cintula, Two notions of compactness in Godel logics, Studia Logica, 81(1) (2005), 99-123.
[5] P. Cintula and M. Navara, Compactness of fuzzy logics, Fuzzy Sets and Systems, 143(1)
(2004), 59-73.
[6] F. Esteva, J. Gispert, L. Godo and C. Noguera, Adding truth-constants to logics of continuous
t-norms: Axiomatization and completeness results, Fuzzy Sets and Systems, 158(6) (2007),
597-618.
[7] F. Esteva, L. Godo and C. Noguera. First-order t-norm based fuzzy logics with truthconstants:
Distinguished semantics and completeness properties, Annals of Pure and Applied
Logic, 161(2) (2009), 185-202.
[8] G. Gerla, Abstract fuzzy logic, Fuzzy Logic, Springer (2001), 19-44.
[9] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Pub, (1998).
[10] S. M. A. Khatami, M. Pourmahdian and N. R. Tavana, From rational Godel logic to ultrametric
logic, Journal of Logic and Computation, doi: 10.1093/logcom/exu065, 2014.
[11] M. Navara and U. Bodenhofer, Compactness of fuzzy logics, Neural Network World, Citeseer,
2001.
[12] J. Pavelka, On fuzzy logic i, ii, iii, Mathematical Logic Quarterly, 25(3-6,7-12,25-29)
(1979), 45-52,119-134,447-464.
[13] M. Pourmahdian and N. R. Tavana, Compactness in rst-order Godel logics, Journal of Logic
and Computation, 23(3) (2013), 473-485.
[14] N. Preining, Complete recursive axiomatizability of Godel logics, PhD thesis, Technische
Universitat Wien, 2003.
[15] N. R. Tavana, M. Pourmahdian and F. Didevar, Compactness in rst-order Lukasiewicz
logics, Journal of Logic and Computation, 20(1) (2012), 254-265.
[16] S. Willard. General topology, Courier Dover Publications, 2004.
Iranian Journal of Fuzzy Systems
Volume 12, Issue 4 - Serial Number 4
July and August 2015
Pages 101-121

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