Conditional probability and defeasible inference
Building on work of \textit{B. C. van Fraassen} [``Fine-grained opinion, probability, and the logic of full belief'', J. Philos. Log. 24, 349--377 (1995; Zbl 0825.03015)], the authors show how the qualitative concept of a rational consequence relation (i.e. a preferential consequence satisfying the condition of rational monotony) may be characterized in terms of nonstandard probability functions (specifically, two-place functions \(p(x,a)\) into the real interval, satisfying the multiplicative condition and whose projections formed by fixing \(a\) are either standard Kolmogorov probability functions or equal to the function with constant value 1). They show that each of their probabilistically generated inference relations is rational, and that for finite languages the converse holds.
scientific article; zbMATH DE number 5004555
scientific article