19. The non-transitory, computer-readable medium of claim 11 , wherein non-standardly entailment comprises using a resolution-based selection function to determine, from the inconsistent knowledge base, a subset that standardly entails the but formula, wherein the resolution-based selection function is defined as follows: rs( , Φ, 0)=Ø rs( , Φ, 1)={φεK|Φ and φ directly resolvably relevant} rs( , Φ, k)=rs(K, Φ, k)∪{φεK|Φ and φ directly resolvably k-relevant with respect to rs(K, Φ, k−1)}, for k>1.
19. The non-transitory, computer-readable medium of claim 11 , wherein non-standardly entailment comprises using a resolution-based selection function to determine, from the inconsistent knowledge base, a subset that standardly entails the but formula, wherein the resolution-based selection function is defined as follows: rs( , Φ, 0)=Ø rs( , Φ, 1)={φεK|Φ and φ directly resolvably relevant} rs( , Φ, k)=rs(K, Φ, k)∪{φεK|Φ and φ directly resolvably k-relevant with respect to rs(K, Φ, k−1)}, for k>1. 20. The non-transitory, computer-readable medium of claim 19 , wherein the using the resolution-based selection function comprises: setting an initial subset and the step value; using the resolution-based selection function and the step value to add formulas from the inconsistent knowledge base to the subset, the subset extending the initial consistent subset; determining if the subset is consistent; when the subset is not consistent: removing one or more formulas from the subset to make the consistent subset consistent; determining if the subset classically entails the original formula, wherein: the inconsistent knowledge base non-standardly entails the original formula when the subset standardly entails the original formula; the inconsistent knowledge base does not non-standardly entail the original formula when the subset does not standardly entail the original formula; when the subset is consistent: determining if the subset is a superset of the initial subset, wherein the inconsistent knowledge base does not non-standardly entail the original formula when the subset is not a superset of the initial subset; when the subset is a superset of the initial subset: determining if the subset standardly entails the original formula, wherein the inconsistent knowledge base does non-standardly entails the original formula when the subset standardly entails the original formula; when the subset does not standardly entail the original formula: setting the subset as the initial consistent subset, incrementing the step value, and repeating above steps starting from the using the resolution-based selection function and the step value.