A consistency-recovering system for inference engines

Abstract

A good inference engine must be expected to deal effectively with contradictions arising from uncertain, incomplete and contradictory information.

Systems based on classiscal logics obviously cannot cope with that.

Usual non-monotonic logics. on the other hand, have some particularyly undesirable features: they don't tend toward stabilization, in the sense that their picture of the world can change any moment in any point; they don't learn from experience, that is never draw conclusions about the reliability of the source or the state of the subject under examination; they cannot sensibly have a fixed "action point", that is a point of belief at which actions are taken, even if a sequence of degrees of belief is present; finally, to have a logical model, they must have infinitely increasing levels of belief, which is very unnatural. All this brings about several absurd responses.

We outline here a system which, while being non-classical, has none of the features above. Its model is based on a many-valued extension of the Kripke model for intuitionistic logic. The main idea is that if contradictions are discovered with a certain frequency, the system tries to identify the source, context, or both, responsible, and the then decreases the appropriate reliabilities. This action is balanced by an opposite set of functions which increases such reliability if no contradictions are discovered and not enough "believe knowledge" has been produced.

The problem of having a finited number of degrees of belief, and a fixed point of action, is tackled by defining a meta-model, inside which the object models can collapse and be reconstructed when contradictions are discovered at the top truth value. This corresponds to expressing a (human) decision about formal logic in the formalism itself.

In the end we briefly present some more features, interesting but not essential.