Specialisation calculus and communication

Abstract

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): ( A 1 ∧ A 2 ∧ … ∧ A n → P, V), ( A 1, V ′) ≒ ( A 2 ∧ … ∧ A n → P, V ″), 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.