Forensic Dynamic Lukasiewicz Logic
محورهای موضوعی : 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.)
کلید واژه: Lukasiewiz Logic, Dynamic Logic, Epistemic Logic, MV-algebra,
چکیده مقاله :
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.
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.
[1] G. Birkho and J. D. Lipson, Heterogeneous Algebras, Journal of Combinatorial Theory, 8 (1970), 115-133.
[2] C. C. Chang, Algebraic Analysis of Many-Valued Logics, Trans. Amer. Math. Soc., 88 (1958), 467-490.
[3] J. H. Conway, Regular Algebra and Finite Machines, Chapman and Hall, London, (1971).
[4] M. J. Fischer and R. E. Ladner, Propositional dynamic logic of regular programs, JCSS, 18(2) (1979).
[5] G. Gratzer, Univarsal algebra, Springer, New York, (1979).
[6] R. Grigolia, Algebraic analysis of Lukasiewicz-Tarski n-valued logical systems, Selected papers on Lukasiewicz Sentential Calculi, Wroclaw, (1977), 81-91.
[7] G. Hansoul and B. Teheux, Completeness results for many-valued Lukasiewicz modal systems and relational semantics, (2006).
[8] D. Kozen, A representation theorem for models of *-free PDL, Technical Report RC7864, IBM, September, (1979).
[9] D. Kozen and R. Parikh, An Elementary Proof of the completeness of PDL, Theoretical Computer Science, North-Holland Publishing Company, 14 (1981), 113-118.
[10] R. Parikh, A completeness result for PDL, in Symposium on Mathematical Foundations of Computer Science, Zakopane, Warsaw, Sept., (1978).
[11] V. R. Pratt, Dynamic algebras and the nature of induction, 12th ACM Symposium on Theory of Computation, Los Angeles, April, (1980).
[12] V. Pratt, Dynamic algebras: Examples, constructions, applications, Stud Logica 50, (1991), 571-605.
[13] K. Segerberg, A completeness theorem in the modal logic of programs, Notices AMS, 24(6) (1977), A-522.
[14] K. Segerberg, An Essay in Classical Modal Logic, Ph.D. Thesis, Stanford University, May, (1971).
