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Predicate Calculus Discussion #14 Chapter 2, Section 1 1/20 Topics
Variables and instantiation
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
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
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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- Winter '12
- Sue, Jim, Tim, Ann, Zed