TY - JOUR
T1 - Constructing Probabilistic ATMS Using Extended Incidence Calculus
AU - Liu, W.
AU - Bundy, Alan
PY - 1996/8
Y1 - 1996/8
N2 - This paper discusses the relations between extended incidence calculus and assumption-based truth maintenance systems (ATMSs). We first prove that managing labels for statements (nodes) in an ATMS is equivalent to producing incidence sets of these statements in extended incidence calculus. We then demonstrate that the justification set for a node is functionally equivalent to the implication relation set for the same node in extended incidence calculus. As a consequence, extended incidence calculus can provide justifications for an ATMS, because implication relation sets are discovered by the system automatically. We also show that extended incidence calculus provides a theoretical basis for constructing a probabilistic ATMS by associating proper probability distributions on assumptions. In this way, we can not only produce labels for all nodes in the system, but also calculate the probability of any of such nodes in it. The nogood environments can also be obtained automatically. Therefore, extended incidence calculus and the ATMS are equivalent in carrying out inferences at both the symbolic level and the numerical level. This extends a result due to Laskey and Lehner.
AB - This paper discusses the relations between extended incidence calculus and assumption-based truth maintenance systems (ATMSs). We first prove that managing labels for statements (nodes) in an ATMS is equivalent to producing incidence sets of these statements in extended incidence calculus. We then demonstrate that the justification set for a node is functionally equivalent to the implication relation set for the same node in extended incidence calculus. As a consequence, extended incidence calculus can provide justifications for an ATMS, because implication relation sets are discovered by the system automatically. We also show that extended incidence calculus provides a theoretical basis for constructing a probabilistic ATMS by associating proper probability distributions on assumptions. In this way, we can not only produce labels for all nodes in the system, but also calculate the probability of any of such nodes in it. The nogood environments can also be obtained automatically. Therefore, extended incidence calculus and the ATMS are equivalent in carrying out inferences at both the symbolic level and the numerical level. This extends a result due to Laskey and Lehner.
KW - Incidence Calculus
KW - probabilistic reasoning
KW - assumption based truth maintenance systems
U2 - 10.1016/0888-613X(96)00031-X
DO - 10.1016/0888-613X(96)00031-X
M3 - Article
VL - 15
JO - International Journal of Approximate Reasoning
T2 - International Journal of Approximate Reasoning
JF - International Journal of Approximate Reasoning
SN - 0888-613X
IS - 2
ER -