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14 predcalc

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Unformatted text preview: Discussion #14 Predicate Calculus Discussion #14 Chapter 2, Section 1 1/20 Topics • • • • • Predicates Variables and instantiation Quantifiers Logical expressions Bound and free variables Discussion #14 Chapter 2, Section 1 2/20 Calculus • What does calculus mean? – – Comes from the word “stone” Implies a process of calculating – – – – – Differential calculus Integral calculus Relational calculus Propositional calculus Predicate calculus • Lots of calculus studies … • Predicate calculus is a generalization of propositional calculus. Discussion #14 Chapter 2, Section 1 3/20 Predicate Calculus • Predicate calculus is also called Predicate Logic or First­Order Logic • Predicate calculus contains all the components of propositional calculus. • In addition, predicate calculus has predicates, a universe of discorse (UofD), terms, and quantifiers. Discussion #14 Chapter 2, Section 1 4/20 Predicates • A predicate is a statement that is either true or false and has zero or more arguments. • A predicate has a name followed by a list of arguments enclosed in parentheses and is called an atomic formula. Examples: Jane is the mother of Mary isMother(Jane, Mary) M(j, m) • Atomic formulas can be combined by logical connectives. Example: isMother(Jane,Mary) ⇒ ¬isMother(Mary,Jane) Examples: Jane is the mother of Mary = T • If all arguments of a predicate are individual constants, the resulting atomic formula must either be true or false. isMother(Jane, Mary) = T isMother(Mary, Jane) = F • The number and order of predicate arguments is significant. • The number of elements in the predicate list is called the arity of the predicate. Discussion #14 Chapter 2, Section 1 5/20 UofD, Terms, Quantifiers • The Universe of Discorse (UofD) is a set of values. – The UofD...
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