G52PAS 2011-2012 Answer to the exercise on FOL Express the following sentences in first-order logic Summary: G52PAS 2011-2012 Answer to the exercise on FOL Express the following sentences in first-order logic: 1. A friend of a friend is a friend. (Use a binary predicate Friend.) 2. An enemy's enemy is a friend. (Use binary predicates Friend and Enemy.) 3. If two people are friends, then they are not enemies. (Use binary predicates Friend and Enemy.) 4. Any two people are either enemies or friends. (Use binary predicates Friend and Enemy.) 5. John has a friend. (Use a binary predicate Friend and constant J for John.) 6. John has at least two friends. (Use a binary predicate Friend, constant J for John, and equality=.) 7. John has exactly two friends, and everyone else is an enemy. (Use binary predicates Friend and Enemy, constant J for John, and equality=.) Answer I used Friend(x, y) for `y is a friend of x' and also for `x and y are friends'. May be the latter is better expressed as Friend(x, y) Friend(y, x)', but I wanted to keep the formulas shorter. (Same for enemies.) 1. A friend of a friend is a friend. xyz(Friend(x, y) Friend(y, z) Friend(x, z)) Collections: Computer Technologies and Information Sciences