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Rules of Inference
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Universal Instantiation
From , infer for a particular . Example: All birds can fly. Tweety is a bird. Therefore, Tweety can fly.
Simplification
From , infer . Example: The ball is red and round. Therefore, the ball is red.
Disjunctive Syllogism
If and are given, then we can infer . Example: It is either raining or snowing. It is not raining. Therefore, it is snowing.
Existential Generalization
From for a particular , infer . Example: Tweety can fly. Therefore, there exists a bird that can fly.
Hypothetical Syllogism
If and are given, then we can infer . Example: If it rains, the picnic will be canceled. If the picnic is canceled, we will watch a movie. Therefore, if it rains, we will watch a movie.
Modus Tollens
If and are given, then we can infer . Example: If it is raining, then the ground is wet. The ground is not wet. Therefore, it is not raining.
Resolution
From and , infer . Example: It will rain or snow today. It will not rain or it will be cold. Therefore, it will snow or be cold.
Modus Ponens
If and are given, then we can infer . Example: If it is raining, then the ground is wet. It is raining. Therefore, the ground is wet.
Addition
From proposition , we can infer , for any proposition . Example: It is raining. Therefore, it is raining or I am hungry.
Conjunction
From and , infer . Example: The ball is red. The ball is round. Therefore, the ball is red and round.
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