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In his efforts to generalize the syllogism, De Morgan replaced the copula "is" with a general binary relation in the second paper of the series dating from 1850.
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By allowing different binary relations in the two premises of a syllogism, he was led to introduce the composition of the two binary relations to express the conclusion of the syllogism.
Prior, in his address to a conference in Wellington in 1954, seems to have been the first to use the binary relation in an explicitly tense-modal context.
(k-step relation) Let Δ I be the nonempty universe set, S a binary relation in Δ I, and k a natural number.
Inspired mainly by Peirce's work, Schröder examined the algebra of logic for binary relations in Vol. III of his Vorlesungen über die Algebra der Logik.
Since it is difficult to investigate all network structure comprehensively for large number of genes by conventional Bayesian networks, we established an original evaluation formula we named "score value" focusing on the binary relations included in the network structure.
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.
We introduce a binary relation over the set of HSPs to reflect the order in which exons or their parts follow.
We study relationships between preference change in the binary relation framework and belief change in the belief revision theory.
For example, if R is a binary
Each role in the set (N_mathsf{R }={r,ldotsts }) is interpreted as a binary relation on the domain.
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