tailieunhanh - A note on entropy of logic

We propose an entropy based classification of propositional calculi. Our method can be applied to finite–valued propositional logics and then, extended asymptotically to infinite–valued logics. In this paper we consider a classification depending on the number of truth values of a logic and not on the number of its designated values. Furthermore, we believe that almost the same approach can be useful in classification of finite algebras. | Yugoslav Journal of Operations Research 27 (2017), Number 3, 385–390 DOI: A NOTE ON ENTROPY OF LOGIC ˇ C ´ Marija BORICI Faculty of Organizational Sciences, University of Belgrade, Serbia Received: October 2015 / Accepted: April 2016 Abstract: We propose an entropy based classification of propositional calculi. Our method can be applied to finite–valued propositional logics and then, extended asymptotically to infinite–valued logics. In this paper we consider a classification depending on the number of truth values of a logic and not on the number of its designated values. Furthermore, we believe that almost the same approach can be useful in classification of finite algebras. Keywords: Many–valued Propositional Logics, Lindenbaum–Tarski Algebra, Partition, Entropy. MSC: 03B50, 03B05, 94A17, 37A35. 1. INTRODUCTION We present one way of logical systems classification based on their entropies (see [2] and [3]). The concept of generalized Shannons entropy, entropy of a partition and the logical system represented by its Linednbaum–Tarski algebra, make it possible to define the entropy of a many–valued propositional logic, and then to extend it asymptotically to infinite–valued logics. Our finite measure of uncertainty H of a finite–valued logic monotonically increases with the growth of truth values number. This measure is sensitive to both the number of truth values of a finite–valued logic and the number of its designated (true) values (see [2] and [3]). In this paper we deal with a classification depending only on the number of truth values. 2. LINDEBAUM–TARSKI ALGEBRA Let us keep in mind the following two well–known facts. The first is related n to the number 22 of mutually non–equivalent formulae over the finite set of propositional letters {p1 , . . . , pn } in the classical two–valued logic. The second one 386 Marija Boriˇci´c / A Note on Entropy of Logic is that Nishimura has shown that in case of .

• Toán học
• Many valued propositional logics
• Lindenbaum–Tarski algebra
• Based classification
• Propositional calculi
• Propositional calculi