Equality propositional logic and its extensions

Gao, X. L.; Xin, X. L.

doi:10.22111/ijfs.2019.4912

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	Equality propositional logic and its extensions
Iranian Journal of Fuzzy Systems
مقاله 11، دوره 16، شماره 5، آذر و دی 2019، صفحه 125-137 اصل مقاله (184.96 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4912
نویسندگان
X. L. Gao^* ؛ X. L. Xin
School of Mathematics, Northwest University, Xi'an,710127, China
چکیده
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $\boldsymbol{\wedge}$ (conjunction) and $\equiv$ (equivalence). Moreover, the $\Rightarrow$ (implication) connective can be derived as $A\Rightarrow B:=(A\boldsymbol{\wedge}B)\equiv A$. 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 $\Delta$(delta) in equality propositional logic and demonstrate that the resulting logic holds soundness and completeness.
کلیدواژه‌ها
Equality algebra؛ equality propositional logic؛ completeness؛ delta equality propositional logic

مراجع
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Equality propositional logic and its extensions