• Corpus ID: 252567986

Satisfiability degrees for BCK-algebras

@inproceedings{Evans2022SatisfiabilityDF,
  title={Satisfiability degrees for BCK-algebras},
  author={C. Matthew Evans},
  year={2022}
}
. We investigate the satisfiability degree of some equations in finite BCK-algebras; that is, given a finite BCK-algebra and an equation in the lan- guage of BCK-algebras, what is the probability that elements chosen uniformly randomly with replacement satisfy that equation? Specifically we consider the equations for the excluded middle, double negation, commutativity, positive implicativity, and implicativity. We give a suffi- cient condition for an equation to have a finite satisfiability gap among… 

Figures and Tables from this paper

References

SHOWING 1-10 OF 17 REFERENCES

Degree of Satisfiability in Heyting Algebras

Given some finite structure M and property p, it is natural to study the degree of satisfiability of p in M; i.e. to ask: what is the probability that uniformly randomly chosen elements in M satisfy

Degree of satisfiability of some special equations

A well-known theorem of Gustafson states that in a non-Abelian group the degree of satisfiability of $xy=yx$, i.e. the probability that two uniformly randomly chosen group elements $x,y$ obey the

A Survey on the Estimation of Commutativity in Finite Groups

Abstract. Let G be a finite group and let C = {(x, y) ∈ G × G ∣ xy = yx}. Then Pr(G) = ∣C∣/∣G∣ is the probability that two elements of G, chosen randomly with replacement, commute. This probability

On commuting probability of finite rings

Gaps in probabilities of satisfying some commutator-like identities

We show that there is a positive constant δ < 1 such that the probability of satisfying either the 2-Engel identity [ X 1 , X 2 , X 2 ] = 1 or the metabelian identity [[ X 1 , X 2 ], [ X 3 , X 4 ]] =

ON COMMUTATIVITY OF FINITE RINGS

Properties of external direct product of two rings are based on properties of component rings. These results are used to construct special types of rings. Any ring which is a cyclic additive group is

On BCK algebras

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two presentations, dual to each other. We cla...

Finite rings with many commuting pairs of elements

We investigate the set of values attained by Pr(R), the probability that a random pair of elements in a nite ring R commute. A key tool is a new notion of isoclinism for rings, and an associated

Algebraic Foundations Of Many Valued Reasoning

Al algebraic foundations of many valued reasoning is universally compatible with any devices to read and an online access to it is set as public so you can get it instantly.

Contrasting the commuting probabilities of groups and rings

We contrast the set of commuting probabilities of all finite rings with the set of commuting probabilities of all finite groups.