Topic: PARACONSISTENCY
Modulated Logics and Uncertain Reasoning
By Walter Carnielli & Maria Claudia C. Gracio
This paper studies a family of monotonic extensions of first-order logic which we call modulated logics, constructed by extending classical logic through generalized quantifiers called modulated quantifiers. We give an uniform treatment of modulated logics, obtaining some general results in model theory. Besides carefully reviewing the Logic of Ultrafilters and the Logic of Most, two new monotonic logical systems are introduced here: the Logic of Many and the Logic of Ubiquity, which formalize inductive assertions of the kind many and almost everywhere through new modulated quantifiers and, respectively. Although the notion of most can be captured by means of a modulated quantifier semantically interpreted by cardinal measure on sets of evidences, it is proven that this system, although sound, cannot be complete if checked against the intended model. This justifies the interest on a purely qualitative approach to this kind of quantification, what is guaranteed by interpreting the modulated quantifiers, respectively, as families of upper closed sets and pseudo-topologies. Modulated logics can be used to provide alternative foundations for fuzzy concepts and fuzzy reasoning, for reasoning on social choice theory, and for gaining a new regard on certain problems in philosophy of science.
Source: CLE
Posted by Tony Marmo
at 00:01 GMT
Updated: Thursday, 3 March 2005 08:01 GMT
