Annotation-based deduction in temporal logic
This paper presents a deductive system for predicate temporal logic with induction.
Representing temporal operators by first-order expressions enables temporal deduction to use the already developed techniques of first-order deduction. But when translating from temporal logic to first-order logic is done indiscriminately, the ensuing quantifications and comparisons of time expressions encumber formulas, hindering deduction. So in the deductive system presented here, translation occurs more carefully, via reification rules. These rules paraphrase selected temporal formulas as nontemporal first-order formulas with time annotations. This time reification process suppresses quantifications (the process is analogous to quantifier skolemization) and uses addition instead of complicated combinations of comparisons. Some ordering conditions on arithmetic expressions can arise, but such are handled automatically by a special-purpose unification algorithm plus a decision procedure for Presburger arithmetic.
This deductive system is relatively complete.
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