In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.

00We look at denotational semantics, using sets and functions, the substitution lemma and equational theory.

00It is proved using a direct axiomatization of Kleisli categories of equational lifting monads.

00Our framework allows equational reasoning of non-deterministic functions, even tho it is possible to specify non-determinism.

00- (i.) The statement of problems in equational form should precede the solution of equations.

00In quantitative judgments we may think x = y, or, as Boolero oses x = v Ã‚° p p y = - Ã‚° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.

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