Representation and Analysis of Electrical Circuits in a Deductive System

We have developed representations and analysis methods for electrical circuits in a deductive system called DUCK.** Circuits are represented as conjunctions of logical predicates. Circuit analysis is done as an iteration of proofs which determine the basic structures in the circuit. Electrical constraints for the circuit are produced from the results of the proofs. The constraints are then solved using propagation methods. 1 INTRODUCTION When an expert first looks at a circuit schematic, he tries to partition the circuit into familiar sub-circuits with known goals. He then tries to pursue the causality of electrical events through those sub-circuits to determine if and how it achieves the overall goal of the circuit. This is based on his assumption that every electronic circuit is designed as a goal oriented composition of basic circuits with known goals. Even in the analysis of an electrical circuit with an unknown goal, although we could perform a formal numerical analysis of the full circuit equations, we try to discover specific sub-structures, such as series or parallel circuits, in order to rewrite the circuit into a simpler one. In many cases we can analyze circuits without formal numerical analysis. Using a deductive system, we have implemented the process which determines these specific structures in a circuit. Circuit elements and devices are represented as logical predicates which have element names and connecting nodes as terms. A circuit is represented as a conjunction of propositions which represent each electrical element or device. The process of determining a specific structure in the object circuit is realized as a proof of a predicate bound by existential quantifiers representing the existence of the specific structure. Since the trans­ formation of a circuit into an equivalent one involves changing the axioms which represent the * present address ** DUCK is a set of LISP routines which implement a relational database similar to those found in AI language such as PLANNER and Prolog. [8] object circuit, it is executed as a meta procedure outside of the deductive system. If a specific structure is found in the object circuit, local electrical constraints for the specific structure are translated into global constraints on the object circuit using the results of the proof. The constraints are solved by means of propagation methods. [12] II REPRESENTATION OF CIRCUITS A. Predicates for elements and circuits The circuit CA12 of Figure 1 is represented as follows (1) in the DUCK …