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This SpringerBrief proposes a basic framework for reasoning approximately inconsistency in a wide selection of logics, together with inconsistency solution tools that experience now not but been studied. The proposed framework permits clients to specify personal tastes on tips to unravel inconsistency while there are a number of how one can achieve this. This empowers clients to unravel inconsistency in facts leveraging either their targeted wisdom of the information in addition to their program wishes. The short indicates that the framework is well-suited to address inconsistency in different logics, and offers algorithms to compute hottest thoughts. ultimately, the short indicates that the framework not just captures numerous current works, but additionally helps reasoning approximately inconsistency in numerous logics for which no such tools exist today.

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A General Framework for Reasoning On Inconsistency

This SpringerBrief proposes a common framework for reasoning approximately inconsistency in a wide selection of logics, together with inconsistency solution equipment that experience no longer but been studied. The proposed framework permits clients to specify personal tastes on how you can get to the bottom of inconsistency whilst there are a number of how you can achieve this.

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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 ∪ . . ∪ Kk ); we denote them by Pbo (K ).

Consider the following set S = K1 ∪ K2 ∪ x∈True {xT : [1, 1], ← xT ∧ xF : [1, 1]} ∪ x∈False {xF : [1, 1], ← xT ∧ xF : [1, 1]} It is easy to see that S is a maximal consistent subset of K ∗ , and thus O = CN(S) is a preferred option for K ∗ . It can be easily verified that u : [1, 1] ∈ O. 3 Propositional Linear Temporal Logic Temporal logic has been extensively used for reasoning about programs and their executions. It has achieved a significant role in the formal specification and verification of concurrent and distributed systems (Pnueli 1977).

Suppose that the preferred options are those that modify a minimum number of formulas. 4 Finally, suppose that the preference relation is expressed as before but, in addition, we would like to change the degree of truth as little as possible. 4, ψ1 , ψ2 }) We refer to fuzzy knowledge bases whose formulas are built from propositional Horn formulas as Horn fuzzy knowledge bases. The following theorem states that even for this restricted subset of fuzzy logic, the problem of deciding whether a formula is a universal consequence of a knowledge base is coNP-hard.

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