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Abstract:
Normal modal logics can be defined axiomatically as Hilbert systems, or
semantically in terms of Kripke's possible
worlds and accessibility relations. Unfortunately there are Hilbert axioms
which do not have corresponding
first-order properties for the accessibility relation. For these logics the
standard semantics-based theorem proving
techniques, in particular, the relational translation into first-order
predicate logic, do not work.
There is an alternative translation, the so-called functional translation, in
which the accessibility relations are
replaced by certain terms which intuitively can be seen as functions mapping
worlds to accessible worlds. In this
paper we show that from a certain point of view this functional language is
more expressive than the relational
language, and that certain second-order frame properties can be mapped to
first-order formulae expressed in the
functional language. Moreover, we show how these formulae can be computed
automatically from the Hilbert
axioms. This extends the applicability of the functional translation method.
