Predicate logic is the logical system in which the atomic propositional letters of propositional logic are analyzed in terms of combinations of predicates and individual terms. The basic expressions are predicates and individual constants and variables instead of propositions.
Sentence (i) would be translated in propositional logic with a mere p (for proposition).
(i) John walks
In predicate logic, we analyze John as an individual constant j, representing an entity or individual, and walks as a predicate constant W, representing a property that is attributed to the individual. Translation of (i) into predicate logic would result in the proposition W(j), which is an atomic formula in predicate logic. The individual variables allow formulas to be quantified (into) by means of the existential quantifier and the universal quantifier.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.