1.2.4. Logic by Translation

A specific general logical method that has gained prominence in the past few decades is that of logic by translation. By this method, one can overcome difficulties of developing results in a certain logical system by exporting the problem to another logical system where a solution is known or, for various reasons, is easier to obtain. This relies on translations/encodings between logical systems that have adequate properties both for the forward translation and for shifting the obtained result back to the source logic. Logicby-translation has had many applications in logic and computer science, many of them through institution theory. That is mostly thanks to the fact that institution theory, with its category–theoretic build where logical systems arise as categorical objects, has come up with adequate mathematical concepts of structural mapping between institutions at an abstract level [18,46]. The value of the institution–theoretic proposal to logic-by-translation [47] has been awarded internationally by the scientific community at the *2nd World Congress of Universal Logic* (Xi'an, 2007).
