In this chapter, we consider the question of whether there is a proof for every valid formula of DC, i.e. whether the proof system of DC is complete. When using DC formulas in specifications, we want ∫S to be the integral of a Boolean-valued function. Therefore, to show the completeness of DC, it must be shown that the axioms DCA1 — DCA6, together with the rules IR1 and IR2 and the axioms and rules of IL, are enough to ensure that temporal variables of the form ∫S are definable by integrals.
KeywordsClosed Interval Open Interval Proof System Relative Completeness Finite Partition
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