## Irreducible Statements and Bases for Finite–Dimensional Logical Spaces

#### Authors :

*Gennaro Auletta*(University of Cassino)

#### Abstract :

Logic can be shown to be a branch of the combinatorial calculus. In this way we can build logical spaces on the basis of a Boolean algebra. This allows us to pick up a finite number of irreducible atomic variables for each n–dimensional space. These variables have a characteristic binary ID being the neg–reversal of themselves. A theorem is proved showing that their number must be finite. Moreover, a second theorem gives us the algorithm for building sets of generators of the space. Finally, the algorithm for computing how many alternative bases there are for any n–dimensional logical space is provided.

#### Keywords :

Logical space; reversal operator; neg–reversal operator; atomic variable; spanning sets

#### Topic :

Mathematics and applied mathematicsPublication date : 2015-12-01