mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

and

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

, Gabbay's separation theorem, named after

Dov Gabbay Dov M. Gabbay (, ; born October 26, 1945) is an Israeli logician. He is Augustus De Morgan Professor Emeritus of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London. Work Gabbay has autho ...

, states that any arbitrary

temporal logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

formula can be rewritten in a

logically equivalent In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on ...

"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..

References

Artificial intelligence Theorems Temporal logic {{Comp-sci-stub