# Lect10 - Homework 2A due today Homework 2B due Tuesday(9/28...

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Homework 2A due today Homework 2B due Tuesday (9/28) 1

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More on Soundness and Completeness of inference procedures 2
I Inference Procedure Database (axiom set) 1 , 2 , 3 ,… Derived theorems Inference Procedure: choose one or more inference rules choose conventional (derive the goal directly) or refutational (add negated goal, derive contradiction) (if ambiguous we will assume conventional) Intrinsic properties of I (soundness and completeness) force important relations between and { i } Derivation requires an inference procedure Entailment does NOT 3

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Completeness An inference procedure is complete iff for any database (axiom set), any sentence entailed by the database can be derived from the database using the inference procedure. It may not be possible for an inference procedure to derive a sentence even though the sentence is entailed by the database. Such an inference procedure is incomplete . Given a database, a complete inference procedure must derive everything entailed by it (including all tautologies). 4
An inference procedure is sound iff for any database (axiom set) every sentence derivable from the database using the inference procedure is entailed by the database. Some inference procedure may derive statements that do not follow logically from the database. Such an inference procedure is unsound . Given a database, a sound inference procedure must only derive statements that are entailed by it (that logically follow from it). 5

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## This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Fall '08 term at University of Illinois, Urbana Champaign.

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Lect10 - Homework 2A due today Homework 2B due Tuesday(9/28...

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