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Probabilistic argumentation is an alternative to causal modeling withBayesian networks. Probabilistic argumentation structures (PAS) are defined onfamilies of compatible frames (f.c.f). This is a generalization of the usualmultivariate models based on families of variables. The crucial relation ofconditional independence between frames of a f.c.f is introduced and shown toform a quasi-separoid, a weakening of the well-known structure of a separoid.It is shown that PAS generate probability potentials on the frames of thef.c.f. The operations of aggregating different PAS and of transport of a PASfrom one frame to another induce an algebraic structure on the family ofpotentials on the f.c.f, an algebraic structure which is similar to valuationalgebras related to Bayesian networks, but more general. As a consequence thewell-known local computation architectures of Bayesian networks for inferenceapply also for the potentials on f.c.f. Conditioning and conditionals can bedefined for potentials and it is shown that these concepts satisfy similarproperties as conditional probability distributions. Finally a max/prod algebrabetween potentials is defined and applied to find most probable configurationsfor a factorization of potentials.

Probabilistic Argumentation and Information Algebras of Probability Potentials on Families of Compatible Frames