A Graph-Based Approach to Resolution in Temporal Logic

An approach to the mechanisation of temporal logics, based on a form of clausal resolution has been developed [Fis91, Fis93]. Temporal formulae incorporating both past-time and future-time temporal operators are converted into Separated Normal Form, and then both non-temporal and temporal resolution rules are applied. The temporal resolution rule attempts to match conditions which must be eventually satisfied with sets of formulae which together imply that the condition will never be satisfied. In this dissertation the sets of formulae which are used in the application of the temporal resolution rule are identified using graph theoretic techniques. This is achieved by first extracting formulae or combinations of formulae that could possibly stop a condition being satisfied and then using them to build a graph. Secondly any loops identified during the construction of the graph will mean that the condition can never be satisfied, and are used in the application of the temporal resolution rule thus deriving further formulae. This temporal resolution method has been combined with sub-programs performing translation to normal form and non-temporal resolution to produce an integrated resolution based temporal theorem prover. The main algorithm cycles through these three procedures until false is derived, (the original formula was unsatisfiable) or no new formulae can be generated (the original formula was satisfiable).