Deduction with uncertain conditionals (revised & simplified, with examples)

Section 1 of this paper provides an introduction to this new “algebra of conditionals”, addresses various plausibility tests for such an algebra, provides a Venn diagram disproving a supposed counter-example, and answers various other objections raised in the literature about the efficacy of this algebraic extension of logic and conditional probability. Section 2 greatly simplifies the calculation of the implications of a set of conditional propositions or conditional events. These results depend on defining a deductive relation for conditionals (actually two have been found) with the property that the conjunction of two conditionals implies each of its components. That seemingly innocuous property assures that the deductively closed set implied by a finite set of n conditionals with respect to the deductive relation is implied by the single conditional formed by conjoining all n of them. The results are illustrated by solving several examples of deduction with several uncertain conditionals.