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CW 304
O. Arieli and M. Denecker
Circumscriptive approaches to paraconsistent reasoning
Abstract
We introduce a general method for paraconsistent reasoning in the context of classical logic. A standard technique for paraconsistent reasoning on inconsistent classical theories is by shifting to multiple-valued logics. We show how these multiple-valued theories can be ``shifted back'' to two-valued classical theories, and how preferential reasoning based on multiple-valued logic can be represented by classical circumscription-like axioms. By applying this process we manage to overcome the shortcoming of classical logic in properly handling inconsistent data, and provide new ways of implementing multiple-valued paraconsistent reasoning through theorem provers for classical logic. Standard multiple-valued reasoning can thus be incorporated with specialized methods for compiling circumscriptive theories, and multiple-valued preferential reasoning can be implemented using algorithms for processing second-order formulae (such as DLS and SCAN).
report.pdf / mailto: O. Arieli