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

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 tips to get to the bottom of inconsistency while there are a number of how one can accomplish that. This empowers clients to unravel inconsistency in facts leveraging either their targeted wisdom of the information in addition to their software wishes. The short exhibits that the framework is well-suited to deal with inconsistency in numerous logics, and offers algorithms to compute most well-liked thoughts. eventually, the short indicates that the framework not just captures a number of present works, but additionally helps reasoning approximately inconsistency in different logics for which no such equipment exist today.

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Extra info for A General Framework for Reasoning On Inconsistency

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Most existing monotonic logics such as classical logic, Horn logic, probabilistic logic, temporal logic are special cases of Tarski’s definition of a logic. Thus, we develop a framework for reasoning about inconsistency in any logic that satisfies Tarski’s axioms. Second, we propose the notion of an “option” in any logic satisfying Tarski’s axioms. An option is a set of formulas in the logic that is closed and consistent – however, the end user is not forced to choose a maximal consistent subset and options need not be maximal or even subsets of the original inconsistent knowledge base.

The satisfiability of a sentence is defined analogously; entailment is defined in the expected way. , {Bp, B¬p} is a consistent knowledge base. However, {Bp, ¬Bp} is inconsistent. 6. Consider the following inconsistent knowledge base K that represents the knowledge of an agent regarding a city’s subway system: ψ1 : goingNorthTrain1 ψ2 : B goingNorthTrain1 ψ3 : goingNorthTrain1 → canGetUpTownFromStationA ψ4 : B(goingNorthTrain1 → canGetUpTownFromStationA) ψ5 : ¬(canGetUpTownFromStationA) Using a train schedule associated with train station A, we might be able to express formulas ψ1 and ψ3 .

Benferhat et al. 1993) Let K = (K1 ∪ . . ∪ Kn ) be a propositional knowledge base, X = (X1 ∪ . . ∪ 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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