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74.419 Artificial Intelligence Tableaux for Modal Logic

74.419 Artificial Intelligence Tableaux for Modal Logic. Reference: Graham Priest, An Introduction to Non-Classical Logic , Cambridge University Press, 2001. Tableaux. Start with negated formula. When decomposing formulas: write sub-formulas underneath for -connection.

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74.419 Artificial Intelligence Tableaux for Modal Logic

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  1. 74.419 Artificial IntelligenceTableaux for Modal Logic Reference:Graham Priest, An Introduction to Non-Classical Logic, Cambridge University Press, 2001

  2. Tableaux • Start with negated formula. • When decomposing formulas: • write sub-formulas underneath for -connection. • split into two branches for -connection. • Resolve formula with modal operators: • add new world number • ◊ - new formula is valid for (at least) one follow state •  - new formula is valid for all follow states • As soon as two atomic propositions P, P appear on a branch, this branch can be closed. • If all branches are closed, the theorem is proven. (Its negation always leads to a contradiction; it is not satisfiable.)

  3. j, iRj j, iRj Tableau Proof of ((AB)  AB) ((AB)  AB),0 (AB),0 (AB),0 AB,0 A,jB,j A,j A,j B,j B,j  

  4. Example of a Tableau Proof ((A  B) (B  C)) (A C),0 ((A  B) (B  C)),0 ((A C)),0 (A  B), 0 (B  C),0 ...

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