First - Order  Predicate  Logic

 

.......... ¹®ÀåÀÇ Á־ °³º° °³Ã¼ (individual object) ÀÏ ¶§ ÀÏÂ÷ ¼ú¾î³í¸®(first order predicate logic) À» »ç¿ëÇÑ´Ù°í ÇÑ´Ù. ¿¹¸¦µé¸é "Socrates is  mortal (¼ÒÅ©¶óÅ×½º´Â Á״´Ù)" °ú °°Àº °æ¿ìÀÌ´Ù. ¹Ý¸é¿¡  Á־ ¶Ç´Ù¸¥ ¼ú¾î·Î ±¸¼ºµÇ¾î ÀÖÀ» ¶§ ¿ì¸®´Â second order logic ¶Ç´Â higher order logicÀ» »ç¿ëÇÑ´Ù°í ¸»ÇÑ´Ù. ¿¹µéµé¸é "Being mortal is tragic (Á״´ٴ °ÍÀº ºñ±ØÀÌ´Ù)" ¿¡¼­ Being mortal °ú °°Àº °æ¿ìÀÌ´Ù ................

¼ú¾î³í¸® (Predicate Logic) ¿¡¼­ Á¤·®ÀÚ (Quantifier) °¡ º¯¼ö¿¡¸¸ Àû¿ëµÇ°í, ¼ú¾î³ª ÇÔ¼ö¿¡ ´ëÇؼ­´Â Çã¿ëÇÏÁö ¾Ê´Â °æ¿ì À̸¦ ÀÏÂ÷ ¼ú¾î°è»ê(First Order Predicate Calculus)À̶ó°í ÇÑ´Ù. ¿¹¸¦ µé¾î (¢£x) P(x) °°Àº °æ¿ìÀÌ´Ù. ¹Ý¸é¿¡ (¢£P) P(x) ¹®ÀåÀº ¼ú¾îºÎÈ£ P ¿¡ Á¤·®ÀÚ°¡ Àû¿ëµÇ¹Ç·Î ÀÏÂ÷ ¼ú¾î°è»ê¿¡¼­´Â Çã¿ëµÇÁö ¾Ê´Â ¹®ÀåÀÌ´Ù. ´ëºÎºÐÀÇ ¸ðµç ³í¸®ÀûÀΠǥÇöÀº ÀÏÂ÷ ¼ú¾î°è»êÀ¸·Î ¸ðµÎ ³ªÅ¸³¾ ¼ö ÀÖÀ¸¹Ç·Î, PROLOG¿Í °°Àº ÀΰøÁö´É ¾ð¾îµéÀº ÀÏÂ÷ ¼ú¾î°è»ê¿¡ ±Ù°ÅÇÏ°í ÀÖ´Ù.

... ÀÏÂ÷¼ú¾î³í¸®´Â "°Å±â¿¡ .... ÇÑ ¹°Ã¼°¡ ÀÖ´Ù" ¶óµç°¡ "¸ðµç ¹°Ã¼¿¡ ´ëÇØ ±×°ÍÀº ... ÇÑ °æ¿ìÀÌ´Ù" ¿Í °°Àº Á¤·®È­µÈ ¹®ÀåÀ» Çü½ÄÈ­ÇÏ´Â ±âÈ£³í¸®Çп¡¼­ÀÇ ÇÑ ÀÌ·ÐÀÌ´Ù. ¹Ý¸é¿¡ higher-order logic ¶ó°í ÇÏ´Â °ÍÀº "°Å±â¿¡ .... ÇÑ ¹°Ã¼ÀÇ ÁýÇÕÀÌ ÀÖ´Ù" ¶óµç°¡ "¸ðµç ¼ºÁú¿¡ ´ëÇØ ±×°ÍÀº .... ÇÑ °æ¿ìÀÌ´Ù" ¸¦ Çã¿ëÇÏ´Â °ÍÀ¸·Î½á ÀÏÂ÷¼ú¾î³í¸®¿¡¼­´Â ±×°ÍÀÌ Çã¿ëµÇÁö ¾Ê´Â´Ù.

±×·³¿¡µµ ºÒ±¸ÇÏ°í, ÀÏÂ÷¼ú¾î³í¸®´Â ÁýÇÕÀÌ·Ð ÀüºÎ¿Í °ÅÀÇ ¸ðµç ¼öÇÐÀ» Çü½ÄÈ­Çϱ⿡ ÃæºÐÇÒ Á¤µµ·Î °­·ÂÇÏ´Ù. ±×°ÍÀº ¼öÇÐÀÇ ±âÃÊ°¡ µÇ´Â ÀüÅëÀûÀÎ ³í¸® ÀÌ·ÐÀÌ´Ù. ±×°ÍÀº ¸íÁ¦·Ð (sentential logic) º¸´Ù´Â ´õ °­ÇÑ ÀÌ·ÐÀÌÁö¸¸, »ê¼ú (arithmetic), ÁýÇÕÀÌ·Ð, second-order logic º¸´Ù´Â ¾àÇÑ ÀÌ·ÐÀÌ´Ù.

´Ù¸¥ ³í¸® À̷аú °°ÀÌ ÀÏÂ÷¼ú¾î³í¸®´Â ´ÙÀ½°ú °°Àº °ÍÀ¸·Î ±¸¼ºµÈ´Ù.

µÎ°¡Áö À¯ÇüÀÇ °ø¸®°¡ ÀÖ´Ù : Á¤·®È­µÈ ¹®ÀåÀ» Æ÷ÇÔÇÏ´Â ÀûÀýÇÑ Ã߷п¡ °üÇÑ ÀÏ¹Ý Áø¸®Ä¡¸¦ Æ÷ÇÔÇÏ´Â ³í¸®Àû °ø¸® (logical axioms which embody the general truths about proper reasoning involving quantified statements) ¿Í, ÁýÇÕÀ̷п¡¼­ ÁýÇÕÀ» ¹¦»çÇÏ´Â instance axiom À̳ª »ê¼ú¿¡¼­ ¼ö¸¦ ¹¦»çÇÏ´Â °ø¸®¿Í °°ÀÌ, Áï½Ã ´ë»ó¹°À» ¹¦»çÇÏ´Â °ø¸®°¡ ±×°ÍÀÌ´Ù.

First-order calculus ¿¡¼­ Ãß·Ð ±ÔÄ¢ÀÇ ÁýÇÕÀÌ À¯ÇÑÇÑ ¹Ý¸é¿¡, °ø¸®ÀÇ ÁýÇÕÀº ¹«ÇÑ ÀÏ ¼ö ÀÖ´Ù. ±×·¯³ª ÁÖ¾îÁø well-formed formula ¿¡ ´ëÇØ ±×°ÍÀÌ °ø¸®ÀÎÁö ¾Æ´ÑÁö¸¦ °áÁ¤ÇÒ ¼ö ÀÖ´Â ÀÏ¹Ý ¾Ë°í¸®ÁòÀÌ ÀÖÀ» ÇÊ¿ä°¡ ÀÖ´Ù. ´õ±¸³ª, ÁÖ¾îÁø Ãß·Ð ±ÔÄ¢ÀÇ ÀÀ¿ëÀÌ Á¤È®ÇÑÁö ¾Æ´ÑÁö¸¦ °áÁ¤ÇÒ ¼ö ÀÖ´Â ¾Ë°í¸®ÁòÀÌ ¶ÇÇÑ ÀÖ¾î¾ß ÇÑ´Ù. .... Wikipedia : First-order logic

term :

Prolog   ³í¸® (Logic)   ¿¬°á»ç (Connective)   ¼ú¾î³í¸® (Predicate Logic)   ±âÈ£ ³í¸®ÇÐ (Symbolic Logic)   Ãß·Ð (Reasoning)   Ãß·Ð ±ÔÄ¢ (Inference Rule)   Á¤·®ÀÚ (Quantifier)   ÀÏÂ÷³í¸® (First-order Predicate Calculus)   Àü¹®°¡½Ã½ºÅÛ (Expert System)   ³í¸®½Ä(wff)   °ø¸® (Axiom)

site :

Wikipedia : First-order logic