Abstract
Let K be a propositional formula and let ϕ be a query, the propositional inference problem K |= ϕ is a Co-NP-complete problem for propositional formulas without restrictions. We show the existence of polynomial-time cases for some fragments of propositional formulas K and ϕ that are different from the already known case of Horn formulas. For example, in the case that K is a formula in the fragment Krom or Horn or Monotone, then K |= ϕ can be decided in polynomial-time for any CNF ϕ. Given two conjunctive normal forms (CNF’s) K and ϕ, when K ̸|= ϕ, our proposal builds a minimal set of independent clauses S. The falsifying assignments of S are exactly the subset of models of K, which are not models for ϕ. In this way, the CNF S could extend the initial formula K in such a way that repair the inference, it is (S ∪ K) |= ϕ is held.
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