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Introduction to Logic
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Tools for Thought
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As with Propositional Logic, we can demonstrate logical entailment in Relational Logic by writing proofs. As with Propositional Logic, it is possible to show that a set of Relational Logic premises logically entails a Relational Logic conclusion if and only if there is a finite proof of the conclusion from the premises. Moreover, it is possible to find such proofs in a finite time.
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The Fitch system for Relational Logic is an extension of the Fitch system for Propositional Logic. In addition to the logical rules of inference we have already seen, there are a few new rules of inference (described in the next section) - rules of inference for universally quantified sentences, rules of inference for existentially quantified sentences, and a new type of rule called Domain Closure.
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Note that the Fitch system described here works only for premises and conclusions that are closed sentences. This is not a significant limitation, since every open sentence is logically equivalent to a closed sentence in which the free variables have been universally quantified.
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