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Logic as algebra

spencermortensen.com · 829 words · saved by 1 readers

In classical propositional logic, proofs are often made using the rules of inference, or using the tableaux and resolution methods. However, there is another way to construct proofs: one that treats logic as algebra. The algebraic method treats logic like high school algebra, where the values are limited to {0,1} instead of C, and the operators are the boolean operators. Constructing a proof amounts to solving a system of equations. Let’s start with an example. Given a set of premises, we’ll construct a proof without using any of the traditional methods of proving theorems. Instead, we’ll construct the proof algebraically. Example 1. Given the premises ¬P, Q⊃P, and Q∨R, can we infer R? First, we’ll express the premises algebraically: Here we use lowercase letters to represent the variables: If P is a propositional variable, then p is the corresponding algebraic variable, and if Q⊃P is a propositional statement, then q⊃p=1 is the corresponding algebraic equation. The premises give us a

Logic as algebra In classical propositional logic, proofs are often made using the rules of inference , or using the tableaux and resolution methods. However, there is another way to construct proofs: one that treats logic as algebra. The algebraic method treats logic like high school algebra, where the values are limited to instead of , and the operators are the boolean operators. Constructing a proof amounts to solving a system of equations. Algebraic proofs Let’s start with an example. Given a set of premises, we’ll construct a proof without using any of the traditional methods of proving t

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