Input-Output Logics

Leendert van der Torre
Section: Logic
Level: Advanced


Input-output logics have been proposed by David Makinson and Leendert van der Torre (Journal of Philosophical Logic, 29:4, August 2000) as a generalization of several theories of deontic logic, non-monotonic reasoning and belief revision.

From a very general perspective, logic is often seen as an `inference motor', with premises as inputs and conclusions as outputs. But it may also be seen in another role, as `secretarial assistant' to some other, perhaps non-logical, transformation engine. From this point of view, the task of logic is one of preparing inputs before they go into the machine, unpacking outputs as they emerge and, less obviously, co-ordinating the two. The process as a whole is one of `logically assisted transformation', and is an inference only when the central transformation is so. This is the general perspective underlying input-output logics. It is one of `logic at work' rather than `logic in isolation'; we are not studying some kind of non-classical logic, but a way of using the classical one.

On a pre-logical level, this picture is perfectly familiar from elementary set theory. Consider any universe, not necessarily of propositions, and any relation on it. For example, the universe may be the set of humans, and the relation the parent/child relation. Given an input of a set of the universe, the output of this set under the relation may be understood simply as the set of all children of persons in the given set.

Input-output logics may be seen as investigating what happens to this basic picture when we pass to the logical level, i.e. when the universe is the set of propositions of some language, and input and output are both under the sway of the consequence operation of classical consequence. These are in a certain sense frills, but give rise to subtle and interesting behaviour.


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Leendert van der Torre
Department of Artificial Intelligence
Faculty of Sciences
Vrije Universiteit Amsterdam
De Boelelaan 1081a
1081 HV Amsterdam
The Netherlands
(+31) 20 444 7740
(+31) 20 444 7653 (fax)