CISC 204 Lecture Notes - Lecture 6: Logical Consequence, Sequent, Propositional Calculus
25 Sep 2017
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This class is about meta-logic, which means that we are reasoning about a logical system. The object of study is the entire axiomatic system of propositional logic that is presented in the text. We will address item (1) with a de nition, allowing us to relate syntax and semantics. Item (2) is known as soundness or correctness. As we saw in the last class, the truth of a propositional formula can be determined using truth tables. We wish to show that the proof rules are correct , by which we mean that valid sequents preserve truth. This correctness comes from computing a truth table, which is a semantic model. For this class and the next class, we will use a common abbreviation that is not in the text. We will use the capital greek symbol to represent a set of formulas. For our purposes, we can say that has n formulas or that a set of formulas.
