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 advantages: 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.
CITATION STYLE
Besnard, P., Schaub, T., Tompits, H., & Woltran, S. (2003). Paraconsistent reasoning via quantified boolean formulas, II: Circumscribing inconsistent theories. In Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) (Vol. 2711, pp. 528–539). Springer Verlag. https://doi.org/10.1007/978-3-540-45062-7_43
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