  In this paper we present a theorem proving methodology for a restricted but
significant fragment of the conditional language made up of (boolean
combinations of) conditional statements with unnested antecedents. The method
is based on the possible world semantics for conditional logics. The KEM label
formalism, designed to account for the semantics of normal modal logics, is
easily adapted to the semantics of conditional logics by simply indexing labels
with formulas. The inference rules are provided by the propositional system KE+
- a tableau-like analytic proof system devised to be used both as a refutation
and a direct method of proof - enlarged with suitable elimination rules for the
conditional connective. The theorem proving methodology we are going to present
can be viewed as a first step towards developing an appropriate algorithmic
framework for several conditional logics for (defeasible) conditional
obligation.
