TY - JOUR
ID - 4912
TI - Equality propositional logic and its extensions
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Gao, X. L.
AU - Xin, X. L.
AD - School of Mathematics, Northwest University, Xi'an,710127, China
Y1 - 2019
PY - 2019
VL - 16
IS - 5
SP - 125
EP - 137
KW - Equality algebra
KW - Equality propositional logic
KW - completeness
KW - Delta equality propositional logic
DO - 10.22111/ijfs.2019.4912
N2 - 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 $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. 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.
UR - http://ijfs.usb.ac.ir/article_4912.html
L1 - http://ijfs.usb.ac.ir/article_4912_f333b256a3857446705654eb1cb0a78a.pdf
ER -