The language of first-order logic

Abstract

Abstract The language of first-order predicate logic is the set of all sentences constructible in accordance with the following (informal) grammar. We assume some alphabet of constant symbols some alphabet of function symbols some alphabet of variable symbols some alphabet of predicate symbols - Note-a tuple (or n-tuple) of n>O items, where n is finite, is an ordered arrangement of those items. The three items b, Y and Z can be ordered, for instance, into the tuple <b, Y, Z>. Another possible 3-tuple is <Y, b, Z>, which is treated as being distinct from the previous one. The conventional tuple delimiters < and > are replaced by ( and ) in our logic language. A function symbol which applies to n-tuples for a specified value of n is said to be an n-ary function symbol or, equivalently, to have arity n. Thus, in the example above, ‘f’ is 3-ary.