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 proofs, where steps are combinedor skipped, axioms or Rules of Inference are not explicitly second part of these slides will cover Methods for writing Discrete Structures Winter 2010: Rules of Inferences and Proof MethodsLucia
Formal Proofs: using rules of inference to build arguments De nition A formal proof of a conclusion q given hypotheses p 1;p 2;:::;p n is a sequence of steps, each of which applies some inference rule to hypotheses or previously proven statements (antecedents) to yield a new true statement (the consequent).
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