Inference in conditional probability logic
Abstract
An important field of probability logic is the investigation of inference rules that propagate
point probabilities or, more generally, interval probabilities from premises to conclusions.
Conditional probability logic (CPL) interprets the common sense expressions of the
form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material
implication. An inference rule is probabilistically informative if the coherent probability
interval of its conclusion is not necessarily equal to the unit interval [0, 1]. Not all logically
valid inference rules are probabilistically informative and vice versa. The relationship
between logically valid and probabilistically informative inference rules is discussed and
illustrated by examples such as the modus ponens or the affirming the consequent.
We propose a method to evaluate the strength of CPL inference