Title :
On functions defined on free Boolean algebras
Author :
Rosenberg, Ivo ; Simovici, Dan A. ; Jaroszewicz, Szymon
Author_Institution :
Univ. de Montreal, Que., Canada
Abstract :
We characterize measures on free Boolean algebras and we examine the relationships that exists between measures and binary tables in relational databases. It is shown that these measures are completely defined by their values on positive conjunctions and an algorithm that leads to the construction of measures starting from its values on a positive conjunction is also given, including a formula that allows the evaluation of measures for arbitrary polynomials. Finally, we study pairs of measures generated by ternary tables, i.e. by tables that contain missing or unknown values
Keywords :
Boolean algebra; Boolean functions; database theory; polynomials; relational databases; binary tables; free Boolean algebras; functions; measures; missing values; polynomials; positive conjunctions; relational databases; ternary tables; unknown values; Boolean algebra; Computer science; Cost accounting; Data mining; Logic; Particle measurements; Polynomials; Query processing; Relational databases;
Conference_Titel :
Multiple-Valued Logic, 2002. ISMVL 2002. Proceedings 32nd IEEE International Symposium on
Conference_Location :
Boston, MA
Print_ISBN :
0-7695-1462-6
DOI :
10.1109/ISMVL.2002.1011089
