Selective Deduction with the Aid of the Variable-Entered Karnaugh Maps

Abstract

An important class of logical reasoning problems involves selective deduction from given hypotheses, which is deduction with the knowledge of certain information, or the lack thereof, about some of the pertinent variables. This note solves selective deduction problems via a powerful manual pictorial tool, viz., the variable-entered Karnaugh map (VEKM). The VEKM can be utilized to obtain the set of all prime implicants of the underlying function and then apply the knowledge available to select a subset thereof. Moreover, it allows a skipping of the tedious step of obtaining the complete sum in its general form by incorporating the available knowledge right from the outset. This is a time-saving short cut indeed, since no implicants are generated except those that are ultimately retained. An illustrative example serves to explain the steps of the method proposed herein and to demonstrate its superiority to the conventional method.