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 tools that experience no longer but been studied. The proposed framework permits clients to specify personal tastes on easy methods to get to the bottom of inconsistency while there are a number of how you can achieve this. This empowers clients to solve inconsistency in info leveraging either their designated wisdom of the knowledge in addition to their software wishes. The short exhibits that the framework is well-suited to deal with inconsistency in numerous logics, and gives algorithms to compute hottest concepts. eventually, the short exhibits that the framework not just captures a number of latest works, but additionally helps reasoning approximately inconsistency in different logics for which no such equipment exist today.
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O = CN(KS ). t. sc(O ) < sc(O). t. O = CN(KS ). Since the objective function of LP(K ) corresponds to sc, then S does not minimize the objective function, which is a contradiction. 2. Suppose that O ∈ Opt P (K , WP ). t. O = CN(KS ). Suppose by contradiction that S is not a solution of LP(K ). This means that it does not minimize the objective function. Then, there is a solution S of LP(K ) which has a lower value of the objective function. As shown before, O = CN(KS ) is an option and has a score lower than O, which is a contradiction.
1. Let T = (Arg(K ), Ru ) be an AS over the base K . • ∀E ∈ Ext(T ), ∃O ∈ Opt (K ) such that O = CN( • ∀O ∈ Opt (K ), ∃E ∈ Ext(T ) such that O = CN( Supp(a)). Supp(a)). a∈E a∈E Proof. Straightforward. 1 An AS is finite iff each argument is attacked by a finite number of arguments. It is infinite otherwise. Chapter 6 Conclusions Past works on reasoning about inconsistency in AI have suffered from multiple flaws: (i) they apply to one logic at a time and are often invented for one logic after another.
3. 5. Then, • ∀S ∈ P2 (K ), ∃O ∈ Opt (K ) such that O = CN(S). • ∀O ∈ Opt (K ), ∃S ∈ P2 (K ) such that O = CN(S). Proof. Straightforward. Brewka (1989) provides a weak and strong notion of provability for both the generalizations described above. t. ψ ∈ CN(S); ψ is strongly provable from K iff for every preferred subbase S of K we have ψ ∈ CN(S). 8), whereas the former is not a valid inference mechanism, since the set of weakly provable formulas might be inconsistent. Observe that Brewka’s approach is committed to a specific logic, weakening mechanism and preference criterion, whereas our framework is applicable to different logics and gives the flexibility to choose the weakening mechanism and the preference relation that the end-user believes more suitable for his purposes.
A General Framework for Reasoning On Inconsistency by Maria Vanina Martinez, Visit Amazon's Cristian Molinaro Page, search results, Learn about Author Central, Cristian Molinaro, , V.S. Subrahmanian, Leila Amgoud