An approach to applying clausal resolution, a proof method well suited to mechanisation, to temporal logics has been developed by Fisher. The method involves translation to a normal form, classical style resolution within states, and temporal resolution between states. Not only has it been shown to be correct but as it consists of only one temporal resolution rule, it is particularly suitable as the basis of an automated temporal resolution theorem prover. As the application of the temporal resolution rule is the most costly part of the method, it is on this area that we focus. Detailed algorithms for a breadth-first search approach to the application of this rule are presented.
Correctness is shown and complexity given.
Analysis of the behaviour of the algorithms is carried out and we explain why this approach is an improvement to others suggested. Emphasis is put on the temporal and explanatory aspects of causal reasoning. We introduce a formal framework enabling to define the notion of voluntary cause in a way allowing for an effective retrieval of causes in a given situation. An example is presented, extension to first-order is briefly discussed, and our approach is compared to related works. In recent years, several constraint-based temporal reasoning frameworks have been proposed.