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Default Logic

Aliases: Default Reasoning

Categories: Inference and Reasoning , Knowledge Representation

Author(s): Helen Lowe

In reasoning about incompletely specified worlds, it may be necessary to make default assumptions that lead to tentative conclusions. For example, if we know that Tweety is a bird, we may assume that Tweety can fly. If we later discover that Tweety is an ostrich, we may retract this assumption. Hence inferences based on such assumptions may need to be modified or rejected on the basis of later revelations. One way of accounting for default reasoning is through non-monotonic logic (see Non-monotonic Reasoning), which allows conclusions to be rejected when more information is added to the premises. In non-monotonic logics, the usual set of axioms used in deriving theorems is augmented by a set of default rules which serve to infer conclusions that cannot otherwise be derived. Formally, a default logic is a pair , where is a set of first-order sentences and is a set of default rules, each of which has the form:

which can be read as `from

and the inability to prove

b, infer

'. The first order sentences

and

are called the prerequisite, the justification, and the consequent of the default, respectively. The defaults can be viewed as extending the knowledge (as contained in

) that we have about the world. Any acceptable set of beliefs about that world is called an `extension'. Default theories may have none, exactly one, or many extensions.

References:

Reiter, R., A Logic for Default Reasoning Artificial Intelligence 13 (1980), 81--132, also in `Readings in non-monotonic reasoning', (Ginsberg, M.L., ed.), Morgan Kaufmann, Los Altos, CA, 1987, pp. 68--93 .

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