Paraconsistent Reasoning via Quantified Boolean Formulas, I: Axiomatising Signed Systems [chapter]

Philippe Besnard, Torsten Schaub, Hans Tompits, Stefan Woltran
2002 Lecture Notes in Computer Science  
Through minimal-model semantics, three-valued logics provide an interesting formalism for capturing reasoning from inconsistent information. However, the resulting paraconsistent logics lack so far a uniform implementation platform. Here, we address this and specifically provide a translation of two such paraconsistent logics into the language of quantified Boolean formulas (QBFs). These formulas can then be evaluated by off-the-shelf QBF solvers. In this way, we benefit from the following
more » ... tages: First, our approach allows us to harness the performance of existing QBF solvers. Second, different paraconsistent logics can be compared with in a unified setting via the translations used. We alternatively provide a translation of these two paraconsistent logics into quantified Boolean formulas representing circumscription, the well-known system for logical minimization. All this forms a case study inasmuch as the other existing minimization-based many-valued paraconsistent logics can be dealt with in a similar fashion.
doi:10.1007/3-540-45757-7_27 fatcat:6pkp2w3r6zflri6spnmee7wv5i