**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, constructed by extending classical logic through generalized quantifiers calledmodulated logics. We give an uniform treatment of modulated logics, obtaining some general results in model theory. Besides carefully reviewing themodulated quantifiersLogic of Ultrafiltersand theLogic of Most, two new monotonic logical systems are introduced here: theLogic of Manyand theLogic of Ubiquity, which formalize inductive assertions of the kindmanyandalmost everywherethrough new modulated quantifiers and, respectively. Although the notion ofmostcan 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 ofandupper closed sets. 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.pseudo-topologies

Source: CLE

Posted by Tony Marmo
at 00:01 GMT

Updated: Thursday, 3 March 2005 08:01 GMT