A Konolige bridge between default logic and autoepistemic logic
Martijn Pennings
Abstract:
Default Logic and Autoepistemic Logic are two forms of nonmonotonic
logic originating from the works of Reiter in 1980 and Moore in 1985,
respectively. Konolige showed that via a translation from defaults to
modal formulas default logic can be expressed in autoepistemic
logic. However, no translation has been found that relates the
originally used semantics for default logic (extensions) precisely to
the originally used semantics for autoepistemic logic (expansions).
In a series of papers, Denecker, Marek and Truszczy´nski revealed a
uniform semantics for default logic and autoepistemic logic, which we
will explain. They defined several operators on the lattices of
possible world structures relating to various semantics for default
logic and autoepistemic logic. This way they defined four connected
semantics for each of the two logics, among those the two semantics of
extensions and expansions. Hence, they revealed the connection
between the two semantics (using the Konolige translation from
defaults to modal formulas), but also the difference.
We will also examine a form of prioritized versions of default logic
and autoepistemic logic inspired by Rintanen, in which preference
structures on defaults or formulas relate to preference structures on
extensions or expansion. We will explain how the Konolige translation
can be used to relate the prioritized version of default logic to the
prioritized version of autoepistemic logic. i