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# Otter 2013-12-02-02

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### Otter 2013-12-02-02

1. 1. OTTER 2
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. 3. Main loop of OTTER - + + + + - clash clash ++ + - Search stopped because sos empty. pick up pick up + + + + + + + - + + + - -
4. 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. 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. 6. Selfreference, contradiction and excluded middle
7. 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. 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. 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. 10. Clause Sets (節集合構成） Term rewriting Demodulators SoS (Set of Support) Detect Usable Passive Resolution
11. 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. 12. Tower of hanoi
13. 13. ハノイの塔 １ ２ ３ １ ２ ３ １ ２ ３
14. 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