Resource-Bounded Paraconsistent Inference

In this paper, a new framework for reasoning from inconsistent propositional belief bases is presented. A family of resource-bounded paraconsistent inference relations is introduced. Such inference relations are based on S-3 entailment, an inference relation logically weaker than the classical one and parametrized by a set S of propositional variables. The computational complexity of our relations is identified, and their logical properties are analyzed. Among the strong features of our framework is the fact that tractability is ensured each time |S| is bounded and a limited amount of knowledge is taken into account within the belief base. Furthermore, binary connectives ∧, ∨ behave in a classical manner. Finally, our framework is general enough to encompass several paraconsistent multi-valued logics (including S-3, J3 and its restrictions), the standard coherence-based approach to inconsistency handling (based on the selection of consistent subbases) and some signed systems for paraconsistent reasoning as specific cases.

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