Sentence examples for binary relations on the from inspiring English sources

The function · I maps atomic concepts to subsets of Δ I and role names to binary relations on the domain Δ I.

All trees depend on a set of extant genomes, which are disjoint sets of genes plus binary relations on these sets of genes called 'adjacencies'adjacencies

Thus the formula defines a binary relation on the integers, namely the set of pairs of integers that satisfy it.

Each role in the set (N_mathsf{R }={r,ldotsts }) is interpreted as a binary relation on the domain.

An equational theory as a set of pairs of terms amounts to a binary relation on the set of all terms.

It can be shown that a binary relation on the set of terms is an equational theory if and only if it is a substitutive congruence.

In our main theorems, we employ a binary relation on the metric space that does not have to be either a partial order nor a transitive relation.

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe.

In our main theorems, we employ a binary relation on the metric space, which does not have to be a partial order.

For example, a binary relation on the universe {1,…,m} can be represented by a word w11 … w1m#…#wmm … wherewhere the relation holds of (i, j) iff wij = 1.

For another example, we can (using choice) say that the universe of discourse is infinite by saying that there is a transitive relation on the universe such that every element bears the relation to something, but not to itself: ∃R[∀x ∀y ∀z(Rxy & Ryz → Rxz) & ∀x[¬Rxx & ∃y Rxy] Here the second-order quantifier "∃R" expresses the existence of some binary relation on the universe.