Transcription of Inference Rules and Proof Methods - Engineering
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Inference Rules and Proof Methods - Engineering
IntroRules of InferenceProof MethodsInference Rules and Proof MethodsLucia MouraWinter 2010 CSI2101 Discrete Structures Winter 2010: Rules of Inferences and Proof MethodsLucia MouraIntroRules of InferenceProof MethodsIntroductionRules of Inference and Formal ProofsProofs in mathematics are valid arguments that establish the truth ofmathematical a sequence of statements that end with a argument isvalidif the conclusion (final statement) follows fromthe truth of the preceding statements (premises). Rules of Inference are templates for building valid will study Rules of inferences for compound propositions, for quantifiedstatements, and then see how to combine will be the main ingredients needed informal Discrete Structures Winter 2010: Rules of Inferences and Proof MethodsLucia MouraIntroRules of InferenceProof MethodsIntroductionProof Methods and Informal ProofsAfter studying how to writeformal proofsusing Rules of Inference forpredicate logic and quantified statements, we will move useful theorems usingformal proofswould result in long andtedious proofs, where every single logical step must be used for human consumption (rather than for automated derivationsby the computer) are usuallyinformal pro
or previously proven statements (antecedents) to yield a new true statement (the consequent). A formal proof demonstrates that if the premises are true, then the conclusion is true. Note that the word formal here is not a synomym of rigorous. A formal proof is based simply on symbol manipulation (no need of thinking, just apply rules).
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