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**Coherent prevision as a linear functional without an underlying measure space: The purely arithmetic structure of logical relations among conditional quantities.**
*(English)*
Zbl 0859.68104

Coletti, Giulianella (ed.) et al., Mathematical models for handling partial knowledge in artificial intelligence. Selected papers from a workshop, Sicily, Italy, June 19-25, 1994. New York, NY: Plenum Press. 101-111 (1995).

Summary: Our focus is on the structure of conditional quantities and conditional prevision assertions which are crucial to implementing the fundamental theorem of prevision as an “inference engine”, foreseen in principle and constructed in simple forms for more than a century. I argue that conditional quantities do entail a minimal logical structure as required by the principle of coherency. But attempts to identify a more extensive structure of a logic of conditional events via many-valued logical functions are misdirected. The equivalent roles of arithmetic and of many-valued logics in generating a function space of object quantities are made apparent.

For the entire collection see [Zbl 0845.00054].

For the entire collection see [Zbl 0845.00054].