This paper describes a language called £N whose structure mirrors that of natural language. £N is characterized by absence of variables and individual constants. Singular predicates assume the role of both individual constants and free variables. The role of bound variables is played by predicate functors called "selection operators." Like natural languages, £N is implicitly many-sorted. £N does not have an identity relation. Its expressive power lies between the predicate calculus without identity and the predicate calculus with identity. The loss in expressiveness relative to the predicate calculus with identity however is not significant. Deduction in £N is intended to parallel reasoning in natural language, and therefore is termed "surface reasoning." In contrast to deduction in a disparate underlying logic such as clausal form, each step of a proof in £N has a direct counterpart in the surface language. A sound and complete axiomatization is given. Derived rules, corresponding to monotonicity and conservativity of quantifiers and to unification and resolution in conventional logic, are presented. Several problems are worked to illustrate reasoning in £N.
Purdy, William C., "A Logic for Natural Language" (1990). Electrical Engineering and Computer Science Technical Reports. 64.