TY - JOUR
T1 - Assignment Methods for Incidence Calculus
AU - McLean, R. G.
AU - Bundy, Alan
AU - Liu, W.
PY - 1995
Y1 - 1995
N2 - IIncidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds, called incidences, are associated with axioms, and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidence of formulae which are not axioms, and bounds for the probability of such a formula can then be obtained. In practice an assignment of probabilities directly to axioms may be given, and it is then necessary to find an assignment of incidence which will reproduce these probabilities. We show that this task of assigning incidences can be viewed as a tree searching problem, and two techniques for performing this research are discussed. One of these is a new proposal involving a depth first search, while the other incorporates a random element. A Prolog implementation of these methods has been developed. The two approaches are compared for efficiency and the significance of their results are discussed. Finally we discuss a new proposal for applying techniques from linear programming to incidence calculus.
AB - IIncidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds, called incidences, are associated with axioms, and probabilities are then associated with these sets. Inference rules are used to deduce bounds on the incidence of formulae which are not axioms, and bounds for the probability of such a formula can then be obtained. In practice an assignment of probabilities directly to axioms may be given, and it is then necessary to find an assignment of incidence which will reproduce these probabilities. We show that this task of assigning incidences can be viewed as a tree searching problem, and two techniques for performing this research are discussed. One of these is a new proposal involving a depth first search, while the other incorporates a random element. A Prolog implementation of these methods has been developed. The two approaches are compared for efficiency and the significance of their results are discussed. Finally we discuss a new proposal for applying techniques from linear programming to incidence calculus.
KW - Incidence calculus
KW - probabilistic reasoning
KW - incidence assignment
KW - linear programming
U2 - 10.1016/0888-613X(94)00013-S
DO - 10.1016/0888-613X(94)00013-S
M3 - Article
VL - 12
SP - 21
EP - 41
JO - International Journal of Approximate Reasoning
JF - International Journal of Approximate Reasoning
SN - 0888-613X
IS - 1
ER -