A General Framework for Reasoning On Inconsistency by Maria Vanina Martinez, Visit Amazon's Cristian Molinaro

By Maria Vanina Martinez, Visit Amazon's Cristian Molinaro Page, search results, Learn about Author Central, Cristian Molinaro, , V.S. Subrahmanian, Leila Amgoud

This SpringerBrief proposes a normal framework for reasoning approximately inconsistency in a large choice of logics, together with inconsistency solution equipment that experience now not but been studied. The proposed framework permits clients to specify personal tastes on how one can unravel inconsistency whilst there are a number of how one can accomplish that. This empowers clients to solve inconsistency in info leveraging either their precise wisdom of the information in addition to their program wishes. The short exhibits that the framework is well-suited to deal with inconsistency in different logics, and gives algorithms to compute most well-liked suggestions. eventually, the short exhibits that the framework not just captures numerous current works, but in addition helps reasoning approximately inconsistency in different logics for which no such equipment exist today.

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The UNI principle corresponds to our universal inference mechanism and it is the same as in Benferhat et al. (1993). According to the EXI principle, a formula ψ is inferred from a knowledge base K if ψ is classically inferred from at least one preferred subbase of K . According to the ARG principle, a formula ψ is inferred from a knowledge base K if ψ is classically inferred from at least one preferred subbase and no preferred subbase classically entails ¬ψ . The last two entailment principles are not valid inference mechanisms in our framework, since the set of EXI (resp.

S is a preferred subbase of K if and only if there exists a strict total order ψ1 , . . , ψn of K respecting < such that S = Sn with S0 = 0/ Si = Si−1 ∪ {ψi } i f Si−1 ∪ {ψi } is consistent Si−1 otherwise P2 (K ) denotes the set of preferred subbases of K . 1≤i≤n 5 Link with Existing Approaches 37 In addition, the second generalization can be easily expressed in our framework. 5. Consider a knowledge base K and let W⊆ be the adopted weakening mechanism. t. O1 = CN(K1 ). 3. 5. Then, • ∀S ∈ P2 (K ), ∃O ∈ Opt (K ) such that O = CN(S).

Xn ) and Y = (Y1 ∪ . . ∪Yn ) two consistent subbases of K , where Xi = X ∩ Ki and Yi = Y ∩ Ki . We define: • Best-out preference: let a(Z) = min{i | ∃ψ ∈ Ki − Z} for a consistent subbase Z of K , with the convention min 0/ = n + 1. t. t. t. t. 1 ≤ j < i, |X j | = |Y j |. Let us consider the best-out preference and let amax(K ) = max{i | K1 ∪ . . ∪ Ki is consistent}. If amax(K ) = k, then the best-out preferred consistent subbases of K are exactly the consistent subbase of K which contain (K1 ∪ .

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