Ildikó Sain COMPUTER SCIENCE TEMPORAL LOGICS NEED THEIR CLOCKS

We use first-order temporal logic (FTL) with modalities ©, [F ], and U denoting “nexttime”, “always-in-the-future”, and “until” respectively. Given a first-order similarity type or language L, the usual predicate etc. symbols of L are considered to be rigid, i.e. their meanings do not change in time. Similarly, individual variables xi (i ∈ ω) are rigid. To this we add an infinity yi (i ∈ ω) of flexible constants. That is, the meaning of yi is allowed to change in time. Other authors, see e.g. Abadi [1]-[4], add flexible predicates too, but we will not need them here though we will mention them occasionally. Our theorems remain true even if we allow flexible predicateand function symbols, as it will be very easy to see. Fm(FTL) denotes the set of all FTL-formulas (of some fixed similarity type L) defined above.