Josep Puyol-Gruart, Lluís Godo, Carles Sierra
Artificial Intelligence Research Institute (IIIA)
Spanish Scientific Research Council (CSIC)
Campus UAB. 08193 Bellaterra, Catalonia, Spain
E-mail: {puyol,godo,sierra}@iiia.csic.es
In this paper we propose a deductive calculus aiming at improving the
query/simple-answer communication behaviour of many intelligent
systems. In an uncertain reasoning context this behaviour consists of
getting certainty values for propositions as answers to
queries. Instead, with our calculus, answers to queries will become
sets of formulas: a set of propositions and a set of specialised rules
containing propositions for which the truth value is unknown in their
left part. This type of behaviour is much more informative because it
returns to users not only the answer to a query but all the relevant
information, related to the answer, necessary to, possibly, improve
the solution. To exemplify the general approach a family of
propositional rule-based languages founded on multiple-valued logics
is presented and formalised. The deductive system defined on top of
these languages is based on a Specialisation Inference Rule
(SIR): 
, where V,
V' and V'' are truth intervals. This inference rule provides a way
of generating rules containing less conditions in their premise by
eliminating the conditions for which a definitive truth value already
exists. The soundness and atom completeness of the deductive system
are proved. The implementation of this deductive calculus is based on
partial deduction techniques. Finally, an example of the application
of the specialisation calculus to a multi-agent system is
provided. : Partial Deduction, Multi-agent
System, Multiple-valued Logic.