Towards the minimum set of primitive relations in temporal logic (Q1101103)

The paper deals with the problem of minimalization of primitive relations between intervals in interval-based temporal logic. Deductions by looking up a transitivity table are preferred to the general-purpose deductions by the authors. A new concept of time inversion mapping is introduced as a tool of primitive relation reduction. There are thirteen possible relations between two intervals. It is shown that a set of eight primitive relations plus the time inversion mapping is as powerful as the set of thirteen primitive relations. In a time reasoning system with thirteen primitive relations there are 169 deduction rules, contained in the transitivity table. Using the time inversion mapping the number of deduction rules can be reduced to 74 plus a formula characterizing deductions in a time reasoning system in terms of the time-inversion mapping.