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Abstract:
In this paper we present a translation principle, called the
\emph{axiomatic translation}, for reducing propositional modal logics
with background theories, including
triangular properties such as transitivity, Euclideanness and
functionality, to decidable logics.
The goal of the axiomatic translation principle is to
find simplified theories, which
capture the inference problems in the original theory, but in a way
that is more amenable to automation and easier to deal with by existing
theorem provers.
The principle of the axiomatic translation is conceptually very simple
and can be largely automated.
Soundness is automatic under reasonable assumptions, and termination of
ordered resolution is easily achieved, but
the non-trivial part of the approach is proving completeness.
