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Otter 2013-12-02-02
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Otter 2013-12-02-02

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  • 1. OTTER 2
  • 2. Four interactions and OTTER Gravitational interaction (weighting) + - weight_list(pick_and_purge). weight(P(rew($(0),$(0)),$(1)), 99) + + - + Strong interaction (modulation) Electromagnetic interaction (resolution) -father(x,y) | -mother(x,z) | grandmother(x,z) (a=b) | (c=d). P(a) | Q(n, f(c,g(d))).
  • 3. Main loop of OTTER - + + + + - clash clash ++ + - Search stopped because sos empty. pick up pick up + + + + + + + - + + + - -
  • 4. Hyper resolution - + + - + + + + - 1 |set(hyper_res). 2 |assign(stats_level,1). 3| 4 |list(usable). 5| -Sibling(x,y) | Brother(x,y) | Sister(x,y). 6 |end_of_list. 7| 8 |list(sos). 9| Sibling(pat, ray) | Cousin(pat, ray). 10 |end_of_list. + - + + + + -
  • 5. paramodulation 1 |set(para_into). 4 |assign(stats_level,1). 5| 6 |list(usable). 7| a1 = b1. 8| a2 = b2. 9 |end_of_list. 10 | 11 |list(sos). 12 | P(a1,a2). 13 |end_of_list. Clauses are generated according to line 7 and 8.
  • 6. Selfreference, contradiction and excluded middle
  • 7. Satisfiability problem (SAT) Cであれば、 Aである場合もあるし、 Bである場合もある。 A B C Problem is satisfiable B A C AとBは同時には 成り立たない。 AとBが導出されればそれは論 証不可能な命題! Problem is unsatisfiable
  • 8. Syntax “-A | B”: proof by contradiction B C A 3 |list(usable). 4| -Greek(x) | Person(x). 5| -Person(x) | Mortal(x). 6 |end_of_list. 8 |list(sos). 9| Greek(socrates). 10 |end_of_list. 12 |list(passive). 13 | -Mortal(socrates). 14 |end_of_list. A ⊃ B B →A There exists Ai where B∪¬A → Ф 1 [] -Greek(x)|Person(x). 2 [] -Person(x)|Mortal(x). 3 [] Greek(socrates). 4 [] -Mortal(socrates). 5 [hyper,3,1] Person(socrates). 6 [hyper,5,2] Mortal(socrates). 7 [binary,6.1,4.1] $F.
  • 9. Verification and satisfiability 常に偽 検証不可能 恒偽 恒真 常に真 充足可能 検証可能 システム稼動状態の総体 充足不可能 ある値域 で偽になるシステム
  • 10. Clause Sets (節集合構成) Term rewriting Demodulators SoS (Set of Support) Detect Usable Passive Resolution
  • 11. Syntax “A | B” (exclusive, fermi particle model) A ∩ B → empty set B∪¬A → not Ф A B C fermi particle model X a Y Z b c bose particle model X(a) | Y(b) either, exclusive X a Y c electron, proton Z c a b a X(a) or Y(b) inclusive photon
  • 12. Tower of hanoi
  • 13. ハノイの塔 1 2 3 1 2 3 1 2 3
  • 14. Tower of hanoi initial state, final state and 2^N-1 最初はすべての円盤が左端の杭に小さいも のが上になるように順に積み重ねられてい る。 初期状態 Board_and_Poll([1,2,3,4,5], [5], [5]). 最終地点 Board_and_Poll([5], [1,2,3,4,5], [5]). 円盤数 1 2^N-1 2^1-1 1 2 2^N-1 2^2-1 3 3 2^N-1 2^3-1 7 4 2^N-1 2^4-1 15 5 2^N-1 2^5-1 31 6 2^N-1 2^6-1 63 7 2^N-1 2^7-1 127 64 2^N-1 2^64-1