On translations of temporal logic of actions into monadic second-order logic

The Temporal Logic of Action introduced by Lamport [4] for specifying the behavior of concurrent systems is compared with monadic second order logic which is accepted as an universal formalism for specifying temporal behaviors. The consequences of Lamport's decision to combine in the existential quantifier of TLA, both the standard existential quantifier and the non-logical closure under stuttering are investigated. A continuous time interpretation is provided for TLA and it is argued that this interpretation is more appropriate than the standard discrete time interpretation. Also, some decidability problems are investigated.