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ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

SYNTAX OF PROPOSITIONAL CALCULUS. ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]. Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information Technology Institute of Applied Computer Systems Department of Systems Theory and Design

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ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

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  1. SYNTAX OF PROPOSITIONAL CALCULUS ARTIFICIAL INTELLIGENCE[INTELLIGENT AGENTS PARADIGM] Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information Technology Institute of Applied Computer Systems Department of Systems Theory and Design E-mail: Janis.Grundspenkis@rtu.lv

  2. Syntax of Propositional Calculus Symbols • The propositional symbols: P, Q, R, S, T, ... • Truth symbols: True, False • Connectives: , , , , 

  3. Syntax of Propositional Calculus Symbols (continued) Propositional symbols denote propositions, or statements about the world that may be either true or false. Propositions are denoted by uppercase letters.

  4. Syntax of Propositional Calculus Sentences • Every propositional symbol and truth symbol is a sentence • The negation of a sentence is a sentence • The conjunction, or AND, of two sentences is a sentence

  5. Syntax of Propositional Calculus Sentences (continued) • The disjunction, or OR, of two sentences is a sentence • The implication of one sentence for another is a sentence • The equivalence of two sentences is a sentence

  6. conjuncts Syntax of Propositional Calculus Sentences (continued) Examples • False, Q, True and S are sentences • False and R are sentences • P  Q  S  W is a sentence

  7. disjuncts conclusion (consequent) premise (antecedent) Syntax of Propositional Calculus Sentences (continued) • P  Q  S  W is a sentence • P  Q is a sentence • P  R  W is a sentence

  8. Syntax of Propositional Calculus Sentences (continued) Legal sentences are also called well-formed formulas (WFF). The symbols ( ) and [ ] are used to group symbols into sub-expressions and to control their order of evaluation and meaning. For example, (P  Q)  S is quite different from P  (Q  S)

  9. Syntax of Propositional Calculus Sentences (continued) The symbols ( ) and [ ] help to take into account the binding strength   and    For example, P  Q  S means (P  Q)  S P  Q  S  R means ((P  Q)  S)  R

  10.     R R P Q P Q Syntax of Propositional Calculus Sentences (continued) Question: Is P  Q  R  P  Q  Ra well-formed formula? Solution: P, Q and R are propositions andthus sentences P  Q, the conjunction of two sentences, is a sentence

  11.     R R P Q P Q Syntax of Propositional Calculus Sentences (continued) P  Q  R, the implication of asentence for another,is a sentence P and Q, the negations ofsentences, are sentences P  Q, the disjunction of two sentences, is a sentence

  12.     R R P Q P Q Syntax of Propositional Calculus Sentences (continued) P  Q  R, the disjunction of two sentences, is a sentence P  Q  R  P  Q  R, the equivalence of two sentences, is a sentence This is the original sentence, which has been constructed through a series of applications of legal rules and is therefore well formed.

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