Forensic Dynamic Lukasiewicz Logic

Subject Areas : Transactions on Fuzzy Sets and Systems

Antonio  Di Nola ¹ (Department of Mathematics, University of Salerno, Italy.)
Revaz  Grigolia ² (Department of Mathematics, Tbilisi State University, Department of Mathematical Cybernetics,Georgian Technical University, Georgia.)

Received: 2022-05-30 Accepted : 2022-06-12 Published : 2022-11-07

Keywords: Lukasiewiz Logic‎, ‎Dynamic Logic‎, ‎Epistemic Logic‎, ‎MV-algebra,

Abstract :

A forensic dynamic $n$-valued {\L}ukasiewicz logic $FD{\L}_n$ is introduced on the base of $n$-valued {\L}ukasiewicz logic ${\L}_n$ and corresponding to it forensic dynamic $MV_n$-algebra ($FDL_n$-algebra)‎, ‎$1 < n < \omega$‎, ‎which are algebraic counterparts of the logic‎, ‎that in turn represent two-sorted algebras $(\mathcal{M}‎, ‎\mathcal{R}‎, ‎\Diamond)$ that combine the varieties of $MV_n$-algebras $\mathcal{M} = (M‎, ‎\oplus‎, ‎\odot‎, ‎\sim‎, ‎0,1)$ and regular algebras $\mathcal{R} = (R,\cup‎, ‎;‎, ‎^\ast)$ into a single finitely axiomatized variety resemblig $R$-module with‎ ‎"scalar"‎ ‎multiplication $\Diamond$‎. ‎Kripke semantics is developed for forensic dynamic {\L}ukasiewicz logic $FD{\L}_n$ with application to Digital Forensics‎.

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