Marcel L.J. Van de Vel

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries.

Features are unary operators used to build record-like expressions. The resulting term algebras are encountered in linguistic computation and knowledge representation. We present a general description of feature logic and of a slightly restricted version, called record logic. It is shown that every first-order theory can be faithfully interpreted in a record logic with various additional axioms. This fact is used elsewhere [15] to extend a result of Tarski and Givant [14] on expressing first order theories in relation algebra.