Reducing Preferential Paraconsistent Reasoning to Classical Entailment
Ofer Arieli · Journal of Logic and Computation · 2003
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 through a polynomial transformation, and how preferential reasoning based on multiple-valued logic can be represented by classical circumscription-like axioms. By applying this process we provide new ways of implementing multiple-valued paraconsistent reasoning. Standard multiple-valued reasoning can thus be performed through theorem provers for classical logic, and multiple-valued preferential reasoning can be implemented using algorithms for processing circumscriptive theories (such as DLS and SCAN).