Gabbay's separation theorem
Encyclopedia
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.
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
and computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, Gabbay's separation theorem, named after Dov Gabbay
Dov Gabbay
Dov M. Gabbay is Augustus De Morgan Professor of Logic at the Group of Logic, Language and Computation, Department of Computer Science, King's College London . He has authored over four hundred and fifty research papers and over thirty research monographs...
, states that any arbitrary temporal logic
Temporal logic
In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. In a temporal logic we can then express statements like "I am always hungry", "I will eventually be hungry", or "I will be hungry...
formula can be rewritten in a logically equivalent
Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.Syntactically, p and q are equivalent if each can be proved from the other...
"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.