FORMALIZING MULTIPLE-VALUED LOGICS AS INSTITUTIONS

Many of the uncertainty management systems used in the Knowledge Based Systems technology can be considered as the set of mechanisms that a certain underlying multiple-valued logic supplies: certainty values, numeric or linguistic, would be the truth-values of that logic, a knowledge base would be a set of axioms, arid the mechanisms of uncertainty combination and propagation would be the inference rules of the deduction system. In this communication we formalize multiple-valued logics inside the institutional framework. We structure multiple-valued logics as families of institutions, each one being indexed by a class of truth-values algebras, in such a way that each morphism between truth-values algebras determines a corresponding morphism of institutions. These institution morphisms are a basic mechanism in modular Expert System languages in order to build uncertainty management systems that deal with different logics in different modules.