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A Unit Resolution-Based Approach to Tractable and Paraconsistent Reasoning

A family of unit resolution-based paraconsistent inference relations ⊢*Σ for propositional logic in the clausal case is introduced. Parameter Σ is any consistent set of clauses representing the beliefs which are intended to be exploited through full deduction, i.e., every classical consequence of Σ must be kept w.r.t. ⊢*Σ, whatever the belief base B. Contrariwise to many paraconsistent inference relations, any relation ⊢*Σ can be decided in time linear in |B| whenever Σ is of bounded size. We show that ⊢*Σ exhibits several valuable properties, including strong paraconsistency. We also show how a unit propagation algorithm can be simply turned into a decision procedure for ⊢*Σ. We finally show how the ⊢*Σ family relates to several inference relations proposed so far as approximations of classical entailment.