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CST 329 - Week 3

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This was our third week in CST 329 - Reasoning with Logic. Chapter 6 - Conditional Derivations Conditional Derivation or Subproof:  Subproofs allow us to prove conclusions when we would otherwise not be able to do so with a inference rule. When making a subproof we assume that the initial premise is true. Once the subproof is done we cannot use it other than to show the associated conclusion.   Proof with a subproof for  (Φ→Ψ)     Invalid proof using a subproof. In line 7 it references line 3, leading to a invalid argument.      Proof with a subproof using conjunctions   Proof with multiple subproofs    Theorem: A sentence that can be proved without premises.   Proof for a theorem/tautology   Chapter 7 - "Or" v:  The symbol for "Or". So  (Φ or Ψ) would be written as  (Φ v Ψ). Two sentences linked by an "Or" is called a disjunction, and each sentence is a disjunct. Disjunctions are an "inclusive or".  ...
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CST 329 - Week 2

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This was our second week in CST 329 - Reasoning with Logic. Chapter 4 - Proofs Inference Rules:  Formulas for creating valid arguments. After writing an inference rule, we can add another to continue the argument. Inference rules are made to always be valid arguments, so adding an inference rule correctly should never lead to an invalid argument.    Modus Ponens   Direct Proof:  Assuming that each line in an argument is numbered, we justify an argument by stating which inference rule was used with which lines to conclude it. Inference rules can be used for any previous lines in the argument, including lines inferred by an inference rule.   Direct Proof for Modus Ponens   Fitch Bar: As seen in the image above, an argument is written to the right of a vertical bar, with a horizontal bar separating the premises and conclusion. Named after logician Frederic Fitch.   Modus Tollens     Double Negation   Repeat Chapter 5 - "And" ^:  T...
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CST 329 - Week 1

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This was our first week in CST 329 - Reasoning and Logic. Our textbook for this class is A Concise Introduction to Logic , which is available for free. Chapter 1: Developing a Precise Language Propositional Logic:  Meaning the logic of sentences. Sometimes also called "sentential logic" or "sentential calculus". In propositional logic the smallest independent parts of a language are sentences. Declarative Sentence:  A sentence that describes the world and can be either true or false. An example would be "It rained in Central Park on June 26, 2015". A declarative sentence cannot be ambigous, for example "Tom is kind of tall" is too vague to be declarative (how can we tell if Tom is tall?).   Bivalence:  Also called the principle of non-contradiction. The belief that there are two truth values (true and false) and that they exlude each other, meaning that something must either be true or false, and cannot be both or neither.   Primitives:  Somethin...
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