Some Thoughts on Theorem Proving

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Presentation transcript:

Some Thoughts on Theorem Proving 2002. 02. 08 In-hee Lee

Problems About Theorem Proving Method Resolvent may contain redundant literals. Resolvent may contain both positive and negative literal. Form of goal: single literal/multiple literals © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

1. Redundant Literal Problem Redundant literal can be resolved with different clause. Can cause logical problem. No problem! Choose only the shortest. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

© 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/ 1. Example C ~B ~C ~C B C ~A ~A A C ~B ~C ~C B C ~A A © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

2. Conflict Literal Problem If one clause contains both positive and negative literal of one variable, it becomes TRUE. Should not involve in proof process any more. But in our implementation, it can. No problem! Choose only the shortest. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

© 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/ 2. Example ~C ~B ~C ~A C B C A ~C ~A C A © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

3. One/Multiple Literal Goal Problem Single literal goal What we considered so far. Multiple literal goal Reduce to single literal goal © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/

© 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/ Still Got A Problem… Determining length of proof. If all formulars are not necessary. If some formulars are used more than once. The length of final product is not the sum of given sequences. Finding shortest will make it. If goal literal is used more than once. Doesn’t form one single strand. © 2001, SNU BioIntelligence Lab, http://bi.snu.ac.kr/