equational love

# equational

## Definitions

• adj. Of, pertaining to, or constructed using equations

### from The Century Dictionary and Cyclopedia

• In machinery, equalizing; adjusting: equivalent to differential as applied to gearing and the like.
• Operating with equations: as, equational logic.

## Etymologies

Sorry, no etymologies found.

## Examples

• The longer he considered them, the faster he was able to gather useful information: gaps in time, how missing components from his inbuilt equational field could be compensated for; he was, in other words, able to think abstractly.

Anders: A Brief History

• Thus his calculus of relations became the study of a certain equational theory which he noted had the same relation to the study of all binary relations on sets as the equational theory of Boolean algebra had to the study of all subsets of sets.

• By carrying out this analysis in the special setting of an algebra of predicates (or equivalently, in an algebra of classes) Jevons played an important role in the development of modern equational logic.

• The first volume concerned the equational logic of classes, the main result being Boole's Elimination Theorem of 1854.

• In the 1940s, Tarski joined in this development of equational logic; the subject progressed rapidly from the 1950s till the present time.

• Some elements of equational logic that we now take for granted required a considerable number of years for Jevons to resolve:

• His omission of a symbol for equality made it impossible to develop an equational algebra of logic.

• Monk (1964) proved that, unlike the calculus of classes, there is no finite equational basis for the calculus of binary relations.

• As mentioned earlier, Boole gave inadequate sets of equational axioms for his system, originally starting with the two laws due to Gregory plus his idempotent law; these were accompanied by De Morgan's inference rule that one could carry out the same operation