Forensic Dynamic Lukasiewicz Logic

Transactions on Fuzzy Sets and Systems

مقاله 8، دوره 1، شماره 2، بهمن 2022، صفحه 59-71   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.1959658.1035

نویسندگان

Antonio Di Nola¹؛ Revaz Grigolia^{* 2}

¹Department of Mathematics, University of Salerno, Italy.

²Department of Mathematics Tbilisi State University, Department of Mathematical Cybernetics, Georgian Technical University, Georgia.

چکیده

A forensic dynamic $n$-valued Lukasiewicz logic $FDL_n$ is introduced on the base of $n$-valued Lukasiewicz 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 Lukasiewicz logic $FDL_n$ with application to Digital Forensics‎.

کلیدواژه‌ها

Lukasiewiz Logic‎؛ ‎Dynamic Logic‎؛ ‎Epistemic Logic‎؛ ‎MV-algebra

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