We present a proof procedure that is complete for first-order logic, but which can also be used when searching for finite models. The procedure uses a normal form which is based on geometric formulas. For this reason we call the procedure geometric resolution. We expect that the procedure can be used as an efficient proof search procedure for firstorder logic. In addition, the procedure can be ...

Three universal approximation formulas given by so called disjunctive, conjunctive and additive normal forms are recalled. Properties and relations between all three formulas are studied. The quality of approximation is shown and the role of genetic algorithms in the field of fuzzy approximation is explained.

This paper introduces an incremental algorithm for learning a Boolean function from examples. The functions are constructed in the disjunctive normal form (DNF) or the conjunctive normal form (CNF) and emphasis is placed in inferring functions with as few clauses as possible. This incremental algorithm can be combined with any existing algorithm that infers a Boolean function from examples. In ...

We mean by a normal form a finite set of ordered pairs of subsets of a fixed set that fulfils two conditions: elements of it consist of disjoint sets and elements of it are incomparable w.r.t. inclusion. The underlying set corresponds to a set of propositional variables but is arbitrary. The correspodents to a normal form of a formula, e.g. a disjunctive normal form, is as follows. The normal f...

reference electrode (3). The ionized calcium concentration of sequential retentates prepared by ultrafiltration of a human control serum increased with increasing protein concentration in a way consistent with Donnan theory (4, 5) when the analyzers’ standard reference-electrode liquid junctionswere used; however, the ionized calcium in the same retentates declined slightly with increasing prot...