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predicate logic example
John likes all foods, apples and chicken are foods, anything that does not kill someone who eats it is a food, Bill eats peanuts and is still alive so peanuts are food, and Sue eats everything that Bill eats. This document translates statements about people and foods into logical forms using predicates and quantifiers, and then expresses them in conjunctive normal form.
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Discusses examples of predicate logic using food preferences and eating scenarios involving John, Bill, and Sue.
Illustrates the logical forms representing the food scenarios, including universal quantifications and actions related to eating.
Introduction to the Conjunctive Normal Form (CNF) related to logical expressions, following the examination of food predicates.
predicate logic example
- 1. Predicate Logic Example •John likes all kinds of food. • Apples are food. • Chicken is food. • Anything anyone eats and isn’t killed by is food. • Bill eats peanuts, and is still alive. • Sue eats everything that Bill eats.
- 2. Logical form • Johnlikes all kinds of food == ∀x food (x) ⇒ eats(John, x) • Apples are food == food(apples) • Chicken is food == food(chicken) • Anything anyone eats and isn’t killed by is food == ∀x,y eats(x,y) ∧ ¬killed(x) ⇒ food(y) • Bill eats peanuts, and is still alive == eats(Bill,Peanuts) ∧ ¬killed(Bill)(here we assume alive means not killed) • Sue eats everything that Bill eats == ∀x eats (Bill,x) ⇒ eats(Sue,x)
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