Sentence examples for probability implication from inspiring English sources

We use (for html compatibility) "⊃" for Reichenbach's standard material implication and "⊇" for his probability implication, where "⊇p" is a probability implication with probability p. 3.

Reichenbach there introduces the notion of a "probability implication" with 10 axiom schemes on propositional variables involving both material implication and a new 2-place probability implication connective.

Reichenbach's probability implication is also a generalization of a deductive concept, but the concept generalized belongs first to an object language of events and their properties.

Revised, probability implication later became a foundational notion of Reichenbach's theory of probability and the central concept of his approach to inductive logic.

Interpretation is difficult, since Reichenbach both asserts that the probability of the consequent in a probability implication can be between 0 and 1 inclusive (1925d, 1978, vol. II, p. 89), but then disallows a probability implication because the consequent has probability 0 (p. 92).

The axioms do not guarantee that a probability implication, a ⊇ b[2], is the conditional probability of b given a, or even that the consequents of a collection of probability implications with a as antecedent satisfy the axioms of finite probability.

Reichenbach has an idiosyncratic notation for probability implications.

The formal rules of probability logic assure that probability implications conform to the laws of conditional probability and allow inferences integrating probability implications into deductive logic, including higher-order quantifiers over the subscripted variables.

Reichenbach's probability logic is a conservative extension of classical first-order logic to include rules for probability implications.

First-level probabilities involve infinite sequences; the ordered sets referred to by the predicates of probability implications.

If a protocol from a participant contained both Probability and Implication for a certain cause variable, only Implications was counted.