Equality propositional logic and its extensions

Q: How can I download an article?

To download an article from SID, first log in to the site, search for the article title, and click on the 'Download Article' option.

Q: How can I download an ISI article?

To download an ISI article on SID, enter the keyword or article title in the search bar, view the relevant results, click on the desired article, and select the 'Download Article' option.

Q: How can I access the SID database?

To access the SID database, visit SID.ir, create an account, and log in to access scientific resources.

Q: Is downloading articles from SID free?

Some articles on SID are available for free, while others require payment. Details are specified on the article's page.

Gao X.L.; Xin X.L.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2019 | Volume:16 | Issue:5 Page(s): 125-137

Download Full-Text

Persian Verion

View:

588

Download:

202

Cites:

Information Journal Paper

Title

Equality propositional logic and its extensions

Author(s)

Gao X.L. | Xin X.L. | Issue Writer Certificate

Keywords

Equality algebraQ2

equality propositional logicQ2

completenessQ2

delta equality propositional logicQ2

Abstract

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, ^ (conjunction) and ≡ (equivalence). Moreover, the ⇒ (implication) connective can be derived as A ⇒ B: = (A ^ B) ≡ A. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such as Modus Ponens(MP) rule, Hypothetical Syllogism(HS) rule and completeness, etc. Especially, we provide two ways to prove the completeness of this logic system. We also introduce two extensions of equality propositional logic. The first one is involutive equality propositional logic, which is equality propositional logic with double negation. The second one adds prelinearity which is rich enough to enjoy the strong completeness property. Finally, we introduce additional connective Δ (delta) in equality propositional logic and demonstrate that the resulting logic holds soundness and completeness.

Cites

No record.

References

No record.

Cite

APA: Copy

Gao, X.L., & Xin, X.L.. (2019). Equality propositional logic and its extensions. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(5 ), 125-137. SID. https://sid.ir/paper/113421/en

Vancouver: Copy

Gao X.L., Xin X.L.. Equality propositional logic and its extensions. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2019;16(5 ):125-137. Available from: https://sid.ir/paper/113421/en

IEEE: Copy

X.L. Gao, and X.L. Xin, “Equality propositional logic and its extensions,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 16, no. 5 , pp. 125–137, 2019, [Online]. Available: https://sid.ir/paper/113421/en

Related Journal Papers