Horn clause - Wikipedia
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming, formal specification, universal algebra and model theory. Horn clauses are named for the logician Alfred Horn, who first pointed out their significance in 1951.[1] A Horn clause is a disjunctive clause (a disjunction of literal
List of fallacies - Wikipedia
A fallacy is the use of invalid or otherwise faulty reasoning in the construction of an argument. All forms of human communication can contain fallacies. Because of their variety, fallacies are challenging to classify. They can be classified by their structure (formal fallacies) or content (informal fallacies). Informal fallacies, the larger group, may then be subdivided into categories such as im
Argumentum ad populum - Wikipedia
appeal to (common) belief[3][4] appeal to popularity[5][6] appeal to the majority[7] appeal to the masses[8] argument from consensus[9] authority of the many[9][10] bandwagon fallacy[6][11] common belief fallacy[3][4] democratic fallacy[12] mob appeal[citation needed] truth by association[13] consensus gentium (Latin for 'agreement of the people')[11] Argumentum ad populum is a type of informal fa
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Algorithm that Solves 3-SAT in Polynomial Time
The question of whether the complexity class P is equal to the complexity class NP has been a seemingly intractable problem for over 4 decades. It has been clear that if an algorithm existed that would solve the problems in the NP class in polynomial time then P would equal NP. However, no one has yet been able to create that algorithm or to successfully prove that such an algorithm cannot exist.
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ゲーデルã®ä¸å®Œå…¨æ€§å®šç† - Wikipedia
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æ•°å¦ã®å“²å¦ - Wikipedia
出典ã¯åˆ—挙ã™ã‚‹ã ã‘ã§ãªãã€è„šæ³¨ãªã©ã‚’用ã„ã¦ã©ã®è¨˜è¿°ã®æƒ…å ±æºã§ã‚ã‚‹ã‹ã‚’明記ã—ã¦ãã ã•ã„。 記事ã®ä¿¡é ¼æ€§å‘上ã«ã”å”力をãŠé¡˜ã„ã„ãŸã—ã¾ã™ã€‚（2008å¹´2月） æ•°å¦ã®å“²å¦ï¼ˆã™ã†ãŒãã®ã¦ã¤ãŒãã€è‹±: philosophy of mathematics）ã¯ã€å“²å¦ï¼ˆç§‘å¦å“²å¦ï¼‰ã®ä¸€åˆ†é‡Žã§ã€æ•°å¦ã‚’æ¡ä»¶ä»˜ã‘ã¦ã„る哲å¦çš„å‰æや哲å¦çš„基礎ã€ãã—ã¦æ•°å¦ã®å“²å¦çš„æ„å‘³ã‚’ç ”ç©¶ã™ã‚‹ã‚‚ã®ã§ã‚る。 æ•°ç†å“²å¦ï¼ˆã™ã†ã‚Šã¦ã¤ãŒãã€è‹±: mathematical philosophy）ã¨ã„ã†ç”¨èªžãŒã€ã—ã°ã—ã°ã€Œæ•°å¦ã®å“²å¦ã€ã¨åŒç¾©èªžã¨ã—ã¦ä½¿ã‚れる[1]。ã—ã‹ã—ãªãŒã‚‰ã€ã€Œæ•°ç†å“²å¦ã€ã¯ã€åˆ¥ã®æ„味を少ãªãã¨ã‚‚二ã¤æŒã£ã¦ã„る。一ã¤ã¯ã€ä¾‹ãˆã°ã‚¹ã‚³ãƒ©å¦ã®ç¥žå¦è€…ã®ä»•äº‹ã‚„ライプニッツやスピノザã®ä½“ç³»ãŒç›®æ¨™ã«ã—ã¦ã„ãŸã‚ˆã†ãªã€ç¾Žå¦ã€å€«ç†å¦ã€è«–ç†å¦ã€å½¢è€Œä¸Šå¦ã€ç¥žå¦ã¨ã„ã£ãŸå“²å¦çš„主題をã€ãã®ä¸»å¼µã™ã‚‹ã¨ã“ã‚ã§ã¯ã€ã‚ˆã‚Šæ£ç¢ºã‹ã¤åŽ³å¯†ãªå½¢ã¸ã¨å½¢å¼åŒ–ã™ã‚‹ãƒ—ãƒã‚¸ã‚§ã‚¯ãƒˆã‚’æ„味
Essential Incompleteness of Arithmetic Verified by Coq
Abstract A constructive proof of the Gödel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural
Mizar - Wikipedia
自動証明検証システムMizar（ミザーã€ãƒŸã‚¶ãƒ¼ãƒ«ï¼‰ã¯ã€ã¾ã£ãŸã厳密ã«å½¢å¼çš„ãªå½¢ã§æ•°å¦çš„ãªå®šç¾©ã‚„証明を記述ã™ã‚‹ãŸã‚ã®ãƒ‡ãƒ¼ã‚¿è¨˜è¿°è¨€èªžï¼ˆMizar-言語）ã€å®Ÿéš›ã«ãã®è¨€èªžã§è¨˜è¿°ã•ã‚ŒãŸè¨¼æ˜Žã®å†…容を検証ã™ã‚‹ã“ã¨ãŒã§ãる計算機プãƒã‚°ãƒ©ãƒ （証明検証プãƒã‚°ãƒ©ãƒ ）ã€ãƒ—ãƒã‚°ãƒ©ãƒ ã‹ã‚‰å‚ç…§ã—ã¦æ–°ãŸãªè¨¼æ˜Žã®éš›ã«åˆ©ç”¨å¯èƒ½ãªå®šç¾©ã¨è¨¼æ˜Žæ¸ˆã¿ã®å®šç†ã‹ã‚‰ãªã‚‹ãƒ©ã‚¤ãƒ–ラリ (MML) ã®ä¸‰è€…ã‹ã‚‰æ§‹æˆã•ã‚Œã‚‹ã€‚ Mizar ã¨åŒæ§˜ã®ç›®çš„ã‚’æŒã¤ãƒ—ãƒã‚¸ã‚§ã‚¯ãƒˆã«ã€ãƒãƒãƒ¼ãƒˆãƒ»ãƒœã‚¤ãƒ¤ãƒ¼ã®QEDプãƒã‚¸ã‚§ã‚¯ãƒˆãŒã‚る。 概è¦[編集] システムã®é–‹ç™ºã¯1973å¹´ã«ã‚¢ãƒ³ã‚¸ã‚§ã‚¤ãƒ»ãƒˆãƒªãƒ–レッツã«ã‚ˆã£ã¦å§‹ã‚られã€ã‚·ã‚¹ãƒ†ãƒ ã®ä¿å®ˆã‚’ãƒãƒ¼ãƒ©ãƒ³ãƒ‰ã®ãƒ“アリストーク大å¦ï¼ˆè‹±èªžç‰ˆï¼‰ã€ã‚«ãƒŠãƒ€ã®ã‚¢ãƒ«ãƒãƒ¼ã‚¿å¤§å¦ã€æ—¥æœ¬ã®ä¿¡å·žå¤§å¦ã§è¡Œã£ã¦ã„る。 Mizar-言語ã§è¨˜ã•ã‚ŒãŸè¨¼æ˜Žæ–‡ï¼ˆä»¥ä¸‹ã€Mizar-論文）ã¯æ™®é€šã®ASCIIコードã§æ›¸ã‹ã‚Œã¦ã„る。Mizar-言語ã¯ã€æ•°å¦ã®é€šå¸¸ã®è¨€è‘‰é£
Jean Gallier's Home Page for logic book
Logic for Computer Science: Foundations of Automatic Theorem Proving Second Edition A corrected version of the original Wiley edition (pp. 511, 1986), published by Dover, June 2015. DOVER EDITION (June 2015) By downloading these files you are agreeing to the following conditions of use: Copyright 2015 by Jean Gallier. This material may be reproduced for any educational purpose, multiple copies may
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Books and tutorials/Mathematics - HaskellWiki
anarchy proof -
http://www.tom.sfc.keio.ac.jp/~sakai/d/?date=20060427
LoTREC | Generic Tableau Prover
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