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Given a knowledge base and a proposition alpha we can check if our knowledge base entails alpha using a model checking algorithm that functions as such : we generate a set of all the possible models ,and if for each model where our knowledge base is true alpha is also true we can conclude that our knowledge base entails alpha. What would happen if our knowledge base contains contradictry propositions ?

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If your knowledge base contains contradictory propositions, then everything can be derived from that. See, e.g., https://en.wikipedia.org/wiki/Principle_of_explosion.

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