Abstract
The paper proposes a causal network based on a multi-valued logic and inferencing on the network. The network is called Multi-valued Logic Network (MVL network), and is expressed as a directed acyclic graph as is probabilistic network. It describes a structure of causal relations among propositions or events; each node expresses a proposition with a logical variable that takes a truth value in [0,1], and each arc does an implication with a truth value. This paper deals with a problem to propagate truth intervals to all nodes, when those of some nodes called "determined nodes" are given. The truth interval expresses a constraint on truth of the corresponding node. When the nodes are considered to be events, the truth value could be interpreted as intensity of occurrence.First, this paper discusses and defines the propagation of truth interval using causal inference based on Lukasiewicz Infinite-valued logic. Then, it shows that the network can be devided into several subnetworks at determined nodes. The generated subnetworks are classified into two groups; one is singly connected networks and the other is multiply connected networks. The paper goes into details about propagation of truth interval for the two types of subnetworks. Finally, it shows the whole algorithm of propagation and a numerical example.
