PHIL 220 Study Guide - Midterm Guide: Propositional Calculus, Atomic Sentence, Sentence Clause Structure
10 Jul 2018
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In other words, a completed open branch points us to a row in the truth table of the set of sentences in which all of the sentences would be true. Consistency: a nite set of sentences in sentential logic is truth-functionally consistent if and only if the set has a truth-tree with at least one completed open branch. Inconsistency: a nite set of sentences in sentential logic is truth-functionally inconsistent if and only if the set has a closed truth-tree. Closed branch: a branch on which contradictory literals occur (we mark closed branches with an ) Open branch: a branch that is not closed. Completed open branch: an open branch on which every sentence is either a literal or has been decomposed (we check o all nonliteral sentences once they have been decomposed, and mark a completed open branch with an o) Closed truth-tree: a truth-tree on which all the branches are closed.
