# Avoiding Logical Omniscience by Default - An Investigation into Autoepistemic Logic (Levesque, 1990)

- Matthias Unterhuber,
*University of Düsseldorf and University of Salzburg*

## Abstract

In cognitive science epistemic logic is often used to describe
reasoning with knowledge. Standard systems of epistemic logic suffer from the
fact that they presuppose perfect and flawless reasoning (i.e. logical
omniscience). Deviation from this ideal (e.g. logical ignorance) cannot be
described by standard epistemic systems adequately. The majority of approaches to
this problem weakens the logical principles of standard epistemic logic. However,
by doing this we lose the system’s capacity to describe agents’
positive reasoning capacities. A new way out of this predicament is the use of
default logic. Levesque’s (1990) All I Know Logic – a non-standard
default logic – is specifically designed to model ignorance by agents.
However, my discussion of defaults in this system shows: (1) Levesque’s
system needs to be weakened to account for logical ignorance, or, alternatively,
(2) we may avoid logical omniscience by describing the logical principles as
defaults in a non-monotonic conditional logic.

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