Let us start by illustrating most of the source languages currently
accepted by the translator.
The translation of each of them is actually based on specific transformation
rules.
Monomodal logics.
This is the basic translation of modal formulas into
relational terms originated in [11]:
,
where is
a relational variable uniquely corresponding to , for every
propositional variable ;
,
for every propositional sentence ;
,
for all propositional sentences ;
,
where
is a constant relation designating the
accessibility relation between possible worlds, for every
propositional sentence .
Latticebased modal logics.
These logics, together with their corresponding relational renderings,
are described in [14,3,9].
The Prolog translator can handle the modal constructs of

latticebased modal logics with possibility operators;

latticebased modal logics with necessity operators;

latticebased modal logics with sufficiency operators.
Logic with knowledge operator
, subject to
this translation rule:

Logic of nondeterministic information (NIL) [2, Sect. 7.2].
A multimodal logic with three modalities, representing
the relation of inclusion and similarity, proper of an information system.

Information logic (IL) [2, Sect. 7.3].
A modal logic with three modal operators corresponding
to the relations of indiscernibility, forward inclusion,
and similarity of an information system.
Intuitionistic logic.
The translation of intuitionistic logic is based on the following rules:
where is a reflexive and transitive relation.
Multimodal logic.
These logics correspond to multimodal frames consisting in
a relational system
where
is
a family of accessibility relations (enjoying closure properties
with respect to relational constructs).
Modalities are then of the form and
where
is any relational term of
.
Other modal logics.
Other modal logics currently accepted by the translator involve:
specification operators, temporal operators, Humberstone operators, sufficiency operators, etc [12].
As concerns the target language to which the translation is directed, currently
all translation are performed into the algebra of dyadic relations [16].
So, given a formula the system produces a relational equation of the
form
=.
Further target languages can be easily added by providing suitable description of
the languages in terms or rewriting rules.
For instance, at the present time, the following targets are under consideration:
Automated generation of an input file to be processed by
deduction systems for relational frameworks.
A viable possibility, among others, consists in exploiting a first order theorem prover
following the approach described in [6,7];
Translation into a first order language suitable to be processed by
existing deduction systems a la RasiowaSikorski;
Translation into the language of the theory of aggregates described in [4,1].
In this case, the result of the translation could be inputted to
a deduction system for theorybased reasoning [8];
Output in terms of L^{A}TEX commands (for both input and output formulas);