Chapter 3 - The First-Order Logic

Abstract

This chapter focuses on the first-order logic. Any function or predicate symbol takes a specified number of arguments. If a function symbol f takes n arguments, f is called an n-place function symbol. It is noted that an individual symbol or a constant may be considered a function symbol that takes no argument. Similarly, if a predicate symbol P takes n arguments, P is called an n-place predicate symbol. A function is a mapping that maps a list of constants to a constant. For example, father is a function that maps a person named John to a person who is John's father. Therefore, father (John) represents a person, even though his name is unknown. An occurrence of a variable in a formula is bound if and only if the occurrence is within the scope of a quantifier employing the variable, or is the occurrence in that quantifier. A variable is free in a formula if at least one occurrence of it is free in the formula. A variable is bound in a formula if at least one occurrence of it is bound.