applying two definitions of the union of if-events, p. grzegorzewski gave two generalizations of the inclusion-exclusion principle for if-events.in this paper we prove an inclusion-exclusion principle for if-states based on a method which can also be used to prove grzegorzewski's inclusion-exclusion principle for probabilities on if-events.finally, we give some applications of this principle by...

The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Boo...

Burris, Stanley. ‘‘George Boole.’’ In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. 2010. Available from http://plato.stanford.edu/archives/sum2010/entries/boole/ Krantz, Steven G. Discrete Mathematics Demystified. New York: McGraw-Hill, 2009. Nahin, Paul J. The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. Princeton, NJ: Princ...

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials. Finally, we derive some new identities of those poly-nomials from the Witt-type formulas which are related to Euler polynomials.

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

In this paper we show that the usual intuitionistic characterization of the decidability of the propositional function B(x) prop [x : A], i.e. to require that the predicate (∀x ∈ A)B(x)∨¬B(x) is provable, is equivalent, when working within the framework of Martin-Löf’s Intuitionistic Type Theory, to require that there exists a decision function φ : A → Boole such that (∀x ∈ A) (φ(x) =Boole true...

The Annual Boole Lecture was established and is sponsored by the Boole Centre for Research in Informatics, the Cork Constraint Computation Centre, the Department of Computer Science, and the School of Mathematics, Applied Mathematics and Statistics at University College Cork. The series is named in honour of George Boole, the first professor of Mathematics at UCC, whose seminal work on logic in...

The Annual Boole Lecture was established and is sponsored by the Boole Centre for Research in Informatics, the Cork Constraint Computation Centre, the Department of Computer Science, and the School of Mathematics, Applied Mathematics and Statistics at University College Cork. The series is named in honour of George Boole, the first professor of Mathematics at UCC, whose seminal work on logic in...