A set of postulates for Boolean algebra

A Set of Independent Axioms for Boolean Algebra

1. Introduction IT is well known that there are a number of sets of axioms for Boolean algebra. In this paper, I give a set of five independent axioms using conditioned disjunction as the ternary operation which is postulated. The ternary operation is most naturally defined on the set 2 n —this is done in §2. The theorem is stated in §3 together with a slight generalization of this result; the ...

Single Axioms for Boolean Algebra

Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction technique...

On Forgetting Postulates in Answer Set Programming

Forgetting is an important mechanism for logicbased agent systems. A recent interest has been in the desirable properties of forgetting in answer set programming (ASP) and their impact on the design of forgetting operators. It is known that some subsets of these properties are incompatible, i.e., they cannot be satisfied at the same time. In this paper, we are interested in the question on the ...

On the Triple Jump of the Set of Atoms of a Boolean Algebra

We prove the following result about the degree spectrum of the atom relation on a computable Boolean algebra. Let C be a computable Boolean algebra with infinitely many atoms and a be the Turing degree of the atom relation of C. If d is a c.e. degree such that a′′′ ≤T d′′′, then there is a computable copy of C where the atom relation has degree d. In particular, for every high3 c.e. degree d, a...

Ternary Boolean Algebra