Gabbay's separation theorem

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Any temporal logic formula can be rewritten in an equivalent "past → future" form

In mathematical logic and computer science, Gabbay's separation theorem, named after Dov Gabbay, states that any arbitrary temporal logic formula can be rewritten in a logically equivalent "past → future" form. I.e. the future becomes what must be satisfied. This form can be used as execution rules; a MetateM program is a set of such rules.

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References

Fisher, Michael David; Gabbay, Dov M.; Vila, Lluis (2005), Handbook of Temporal Reasoning in Artificial Intelligence, Foundations of Artificial Intelligence, vol. 1, Elsevier, p. 150, ISBN 9780080533360. 9780080533360 ↩
Kowalski, Robert A.; Sadri, Fariba (1996), "Towards a Unified Agent Architecture That Combines Rationality with Reactivity", Logic in Databases: International Workshop LID '96, San Miniato, Italy, July 1ÔÇô2, 1996, Proceedings, Lecture Notes in Computer Science, vol. 1154, Springer-Verlag, pp. 137–149, doi:10.1007/BFb0031739, ISBN 978-3-540-61814-0. 978-3-540-61814-0 ↩