Forensic Dynamic Lukasiewicz Logic
Subject Areas : Transactions on Fuzzy Sets and Systems
Antonio Di Nola
1
,
Revaz Grigolia
2
1 - Department of Mathematics, University of Salerno, Italy.
2 - Department of Mathematics, Tbilisi State University, Department of Mathematical Cybernetics,Georgian Technical University, Georgia.
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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