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 basic framework for reasoning approximately inconsistency in a wide selection of logics, together with inconsistency solution tools that experience no longer but been studied. The proposed framework permits clients to specify personal tastes on the right way to unravel inconsistency whilst there are a number of how one can accomplish that. This empowers clients to unravel inconsistency in facts leveraging either their designated wisdom of the information in addition to their software wishes. The short exhibits that the framework is well-suited to address inconsistency in numerous logics, and offers algorithms to compute most popular strategies. eventually, the short exhibits that the framework not just captures a number of present works, but in addition helps reasoning approximately inconsistency in different logics for which no such equipment exist today.

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Cn be an instance of 3-DNF VALIDITY, where the Ci ’s are conjunctions containing exactly three literals, and X is the set of propositional variables appearing in φ . We derive from φ a Horn temporal knowledge base K ∗ as follows. Given a literal of the form x (resp. ¬x), with x ∈ X, we denote with p( ) the propositional variable xT (resp. xF ). Let K1 = {u ∨ ¬p( 1) ∨ ¬p( 2 ) ∨ ¬p( 3 ) : 1 | 1∧ 2∧ 3 is a con junction o f φ } and K2 = {u ∨ ¬xT ∨ ¬xF : 1| x ∈ X} Given a variable x ∈ X, let Kx = { xT : 1, xF : 1, ¬xT ∨ ¬xF : 1} Finally, K ∗ = K1 ∪ K2 ∪ Kx x∈X The derived instance of our problem is (K ∗ , u : 1).

At each step, the set of formulas that can be believed from a set of justifications can be computed in time O(n ∗ m) where n is the number of justifications used in that step and m is the number of formulas in the theory. Priority-based management of inconsistent knowledge bases has been addressed also in Benferhat et al. (1993) (see also Cayrol and Lagasquie-Schiex 1995). Specifically, propositional knowledge bases are considered and a knowledge base K is 38 5 Link with Existing Approaches supposed to be stratified into strata K1 , .

How the system is supposed to behave. Suppose now that there is a monitoring system which reports data regarding the system’s behavior and, for instance, the following formula is added to the knowledge base: ψ3 received ∧ ¬processed ∧ processed 28 4 Handling Inconsistency in Monotonic Logics The inclusion of ψ3 makes the knowledge base inconsistent, since the monitoring system is reporting that a request was received and was not processed at the next moment in time, but two moments afterwards.

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