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संगोष्ठी पत्र
प्रश्नपत्र:- कृ त्रत्रम बुद्धि
विषय:- Propositional Logic and Predicate Logic
मागगदर्गक
डॉ.पीयूष प्रताप ससंह  
सह  ायक प्रोफे सर
प्रस्तुतकती
अंजना ककर्नपुरी
एम. आई. एल. ई.
तृतीय छमाह  ी
अध्ययन सत्र(2017-18)
सूचना एिं भाषा असभयांत्रत्रकी के न्द्र
मह  ात्मा गांिी अंतरराष्रीय हह  ंदी विश्िविद्यालय, ििाग
Logic(तकग )
 तकग की प्रकिया को एक िैज्ञाननक अध्ययन और ननयमों और
प्रकियाओं की प्रणाली के रूप में पररभावषत ककया जा सकता ह  ै
जो तकग प्रकिया में सह  ायता करते ह  ैं।
 A logic is a mathematical notation (a language) for stating
knowledge.
 The process of knowledge is called reasoning.
 Information Logic(process) Conclusion
 Reasoning(तकग ) मानि बुद्धि की मुख्य गनतविधि में से एक
ह  ै ।
 इस गनतविधि के अंतगगत statements (कथन) को construct
,organize एिं manipulate करके नये ननष्कषग को बनाने की
प्रकिया को Logic Implementation कह  ते ह  ैं ।
 लॉजजक को दो तरह   से विभाजजत कर सकते ह  ैं :-
Logic
propositional logic predicate logic
Propostional Logic
 Propositonal logic की के िल दो ह  ी states ह  ोती ह  ैं either it is
true or it is false अथागत् यह   logic ,binary state में ह  ी कायग
करता ह  ै।
 इन states को propositions कह  ा जाता ह  ै।
 उदह  ारण :- diamond is a hard material.(true)
Rubber is a good conductor of electricitiy.(false)
 Propositions और िाक्य connectives के द्िारा जुड़े ह  ोते ह  ैं जो
इस प्रकार ह  ैं :-
 उदह  ारण :- A – it is hot.
B – it is humid.
C – it is raining.
B A - if it is humid , then it is hot.
(A&B) ~C –if it is hot and humid then it is not raining.
 Propositional Logic दो तरह   के ह  ोते ह  ैं :-
 Atomic propositional logic
 Molecular propositional logic
Predicate Logic
 इसके अंतगगत real world से सम्बंधित सभी समस्यायों का
ननिारण तथा ह  र तरह   के logic का implementation ककया जा
सकता ह  ै।
 Predicate logic को तीन मुख्य भागों में विभाजजत ककया जा
सकता ह  ै :-
 Predicates – दो atoms को एक relation में जोड़कर define
करिाने िाले को predicate कह  ते ह  ैं।
उदह  ारण :- Ram likes Car. Likes(Ram , Car)
 Term – terms predicate में argument ह  ोते ह  ैं जो इस प्रकार ह  ैं:
A constant एक टमग ह  ै और a variable भी एक टमग ह  ै।
predicate function
if (f and x1 , x2 ..........n ) then f(x1,x2,x3.......xn) is
called term .
 Quantifiers – Quantifiers एक ऐसा symbol ह  ै जो ह  मारे
लॉजजकल expression में variable के scope तथा range
को declare और identify कर सकता ह  ै ।
Quantifiers दो तरह   के ह  ोते ह  ैं :-
 Universal Quantifier
 Existential Quantifier
 Predicate logic में free और bound variables ह  ोते ह  ैं अथागत्
कु छ variable Quantifier के scope के बाह  र ह  ोते ह  ैं उन्द्ह  ें free
variable कह  ते ह  ैं तथा जो variable Quantifier के scope के
अंतगगत ह  ोते ह  ैं उन्द्ह  ें bound variable कह  ते ह  ैं ।
 ककसी भी real world problem का solution true या false में नह  ीं
ह  ो सकता अथागत् logic की binary value नह  ीं ह  ो सकती ह  ै
propositional logic के इस drawback से उभरने के सलए
predicate logic का उपयोग करते ह  ैं ।
 इसी drawback को overcome करने के सलए Artificial
intelligence में Lotif Zadeh द्िारा Fuzzy logics भी design
ककया गया ह  ै।
 सन्दर्भ सूची :-
 https://www.youtube.com/watch?v=GS3HKR6CV8E
 https://www.youtube.com/watch?v=tpDU9UXqsUo
 https://en.wikipedia.org/wiki/Propositional_calculus

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Logic

  • 1. संगोष्ठी पत्र प्रश्नपत्र:- कृ त्रत्रम बुद्धि विषय:- Propositional Logic and Predicate Logic मागगदर्गक डॉ.पीयूष प्रताप ससंह सह ायक प्रोफे सर प्रस्तुतकती अंजना ककर्नपुरी एम. आई. एल. ई. तृतीय छमाह ी अध्ययन सत्र(2017-18) सूचना एिं भाषा असभयांत्रत्रकी के न्द्र मह ात्मा गांिी अंतरराष्रीय हह ंदी विश्िविद्यालय, ििाग
  • 2. Logic(तकग )  तकग की प्रकिया को एक िैज्ञाननक अध्ययन और ननयमों और प्रकियाओं की प्रणाली के रूप में पररभावषत ककया जा सकता ह ै जो तकग प्रकिया में सह ायता करते ह ैं।  A logic is a mathematical notation (a language) for stating knowledge.  The process of knowledge is called reasoning.
  • 3.  Information Logic(process) Conclusion  Reasoning(तकग ) मानि बुद्धि की मुख्य गनतविधि में से एक ह ै ।  इस गनतविधि के अंतगगत statements (कथन) को construct ,organize एिं manipulate करके नये ननष्कषग को बनाने की प्रकिया को Logic Implementation कह ते ह ैं ।  लॉजजक को दो तरह से विभाजजत कर सकते ह ैं :- Logic propositional logic predicate logic
  • 4. Propostional Logic  Propositonal logic की के िल दो ह ी states ह ोती ह ैं either it is true or it is false अथागत् यह logic ,binary state में ह ी कायग करता ह ै।  इन states को propositions कह ा जाता ह ै।  उदह ारण :- diamond is a hard material.(true) Rubber is a good conductor of electricitiy.(false)
  • 5.  Propositions और िाक्य connectives के द्िारा जुड़े ह ोते ह ैं जो इस प्रकार ह ैं :-
  • 6.  उदह ारण :- A – it is hot. B – it is humid. C – it is raining. B A - if it is humid , then it is hot. (A&B) ~C –if it is hot and humid then it is not raining.  Propositional Logic दो तरह के ह ोते ह ैं :-  Atomic propositional logic  Molecular propositional logic
  • 7. Predicate Logic  इसके अंतगगत real world से सम्बंधित सभी समस्यायों का ननिारण तथा ह र तरह के logic का implementation ककया जा सकता ह ै।  Predicate logic को तीन मुख्य भागों में विभाजजत ककया जा सकता ह ै :-  Predicates – दो atoms को एक relation में जोड़कर define करिाने िाले को predicate कह ते ह ैं। उदह ारण :- Ram likes Car. Likes(Ram , Car)
  • 8.  Term – terms predicate में argument ह ोते ह ैं जो इस प्रकार ह ैं: A constant एक टमग ह ै और a variable भी एक टमग ह ै। predicate function if (f and x1 , x2 ..........n ) then f(x1,x2,x3.......xn) is called term .  Quantifiers – Quantifiers एक ऐसा symbol ह ै जो ह मारे लॉजजकल expression में variable के scope तथा range को declare और identify कर सकता ह ै । Quantifiers दो तरह के ह ोते ह ैं :-  Universal Quantifier  Existential Quantifier
  • 9.  Predicate logic में free और bound variables ह ोते ह ैं अथागत् कु छ variable Quantifier के scope के बाह र ह ोते ह ैं उन्द्ह ें free variable कह ते ह ैं तथा जो variable Quantifier के scope के अंतगगत ह ोते ह ैं उन्द्ह ें bound variable कह ते ह ैं ।  ककसी भी real world problem का solution true या false में नह ीं ह ो सकता अथागत् logic की binary value नह ीं ह ो सकती ह ै propositional logic के इस drawback से उभरने के सलए predicate logic का उपयोग करते ह ैं ।  इसी drawback को overcome करने के सलए Artificial intelligence में Lotif Zadeh द्िारा Fuzzy logics भी design ककया गया ह ै।
  • 10.  सन्दर्भ सूची :-  https://www.youtube.com/watch?v=GS3HKR6CV8E  https://www.youtube.com/watch?v=tpDU9UXqsUo  https://en.wikipedia.org/wiki/Propositional_calculus