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#
Input-Output Logics

**
Leendert
van der Torre
**

Section: Logic

Level: Advanced

## Description

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.

## Materials

lecture notes

## Lecturers

Leendert van der Torre

Department of Artificial Intelligence

Faculty of Sciences

Vrije Universiteit Amsterdam

De Boelelaan 1081a

1081 HV Amsterdam

The Netherlands

torre@cs.vu.nl

(+31) 20 444 7740

(+31) 20 444 7653 (fax)

http://www.cs.vu.nl/~torre/