# The concept of logic entropy on D-posets

Document Type : Research Paper

Author

University of Jiroft

Abstract

In this paper, a new invariant called {\it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {\it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {\it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $m$-generator of a dynamical system is introduced and a version of the Kolmogorov-Sinai theorem is given.

Keywords

#### References

[1] G. Birkhoff, J. Von Neumann, The logic of quantum mechanics, Ann. Math. 37, 823–842 (1936).
[2] M. Ebrahimi, B. Mosapour, The concept of entropy on D-posets, Cankaya University Journal of Science and Engineering, 10, 137–151 (2013).
[3] F. Kopka and F. Chovanec, D-posets, Mathematica Slovaca 44, 21–34 (1994).
[4] T. Kroupa, Conditional probability on MV-algebras, Fuzzy Sets and Systems. 369–381 (2005).
[5] U. Mohammadi, Weighted entropy function as an extension of the Kolmogorov-Sinai entropy, U. P. B. Sci. Series A, no. 4, 117–122 (2015).
[6] U. Mohammadi, Relative entropy functional of relative dynamical systems, Cankaya University Journal of Science and Engineering, no. 2, 29–38 (2014).
[7] P. Walters, An Introduction to Ergodic Theory, Springer Verlag, 1982.