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In this paper, we describe an abstract framework and axioms under which exact local computation of marginals is possible. The primitive objects of the framework are variables and valuations. The primitive operators of the framework are combination and marginalization. These operate on valuations. We state three axioms for these operators and we derive the… (More)

- Glenn Shafer
- 1996

Probability and causality must live together because both involve contingency. When I assign a probability to a coin's falling heads, I am saying that how it will fall is contingent. When I say the wind caused a tree to topple, I am saying that the wind and the toppling were contingent. The tree might have remained standing had the wind been less severe.… (More)

- Glenn Shafer
- UAI
- 1985

This article gives an algorithm for the exact implementation of Demp-ster's rule in the case of hierarchical evidence. This algorithm is computationally efficient, and it makes the approximation suggested by Gordon and Shortliffe unnecessary. The algorithm itself is simple, but its derivation depends on a detailed understanding of the interaction of… (More)

In this paper, we propose a logic of action and causality. The most important part of our contribution is a semantics that integrates action, temporal structure, and probability. The semantics is based on a mathematical structure called an event space. This space is inhabited by situations or instantaneous events with binary relations over them. The… (More)