TY - GEN
T1 - Proof Systems for Gödel Logics with an Involution
AU - Avron, Arnon
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/5
Y1 - 2021/5
N2 - G, the extension of Gödel logic G with an invo-lutive negation, has many applications, like its use as a fuzzy paraconsistent logic. In this paper we provide analytic proof systems for both the truth-preserving and the degree-preserving versions of G, as well as to its proper extensions in its language. In addition, we provide particularly simple Hilbert-type axiomatizations of these logics, which (unlike previous such axiomatizations) do not use Baaz' Δ operator. Instead, we follow a suggestion made (and left open) in [16], and base our systems on using, in addition to (MP), the rule (CP). (from ϕ → ψ infer ⇁ψ → ⇁ϕ). This establishes an interesting connection between G, and some major modal logics (like B and S 5).
AB - G, the extension of Gödel logic G with an invo-lutive negation, has many applications, like its use as a fuzzy paraconsistent logic. In this paper we provide analytic proof systems for both the truth-preserving and the degree-preserving versions of G, as well as to its proper extensions in its language. In addition, we provide particularly simple Hilbert-type axiomatizations of these logics, which (unlike previous such axiomatizations) do not use Baaz' Δ operator. Instead, we follow a suggestion made (and left open) in [16], and base our systems on using, in addition to (MP), the rule (CP). (from ϕ → ψ infer ⇁ψ → ⇁ϕ). This establishes an interesting connection between G, and some major modal logics (like B and S 5).
KW - Fuzzy Logics
KW - Godel Logics
KW - Proof Systems
UR - http://www.scopus.com/inward/record.url?scp=85113247153&partnerID=8YFLogxK
U2 - 10.1109/ISMVL51352.2021.00021
DO - 10.1109/ISMVL51352.2021.00021
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AN - SCOPUS:85113247153
T3 - Proceedings of The International Symposium on Multiple-Valued Logic
SP - 68
EP - 73
BT - Proceedings - 2021 IEEE 51st International Symposium on Multiple-Valued Logic, ISMVL 2021
PB - IEEE Computer Society
T2 - 51st IEEE International Symposium on Multiple-Valued Logic, ISMVL 2021
Y2 - 25 May 2021 through 27 May 2021
ER -