A Canonical Form Algorithm Forprovingequivalence 0 F Conditionalforms

In [ 1) axioms and canonical form algorithms for proving equivalence for the theory of conditional forms are presented. These algorithms form the foundation of [2] where they are extended to enable proving the correctness of compilation. The algorithms are distinguished on the basis of whether or not strong or weak equivalence is desired. In the case of strong equivalence, an additional set of axioms was introduced. Xn this note we prove that the additional axioms were unnecessary, and that there is essentially no difference in the msthod of proof for strong and weak equivalence. We also present a simpler algorithm for proving strong equivalence. case x is a pf and a general variable’ others&z. This value is determined for a gbf (p +x6 y) according to Table 1. Two gbrs are said to be strongly equivalent (denoted by =) if they have the same value for all values of the propositional variables & them including the case of undefined propositional variables. The gbfs are weak.ly equivalent (denoted by =,,,J if they have the same values for all values of the propositional variables when these are restricted to T and ~9 There are two equivalence rules which enMe the use of equivalences to generate other equivalences. These rules hold for both weak and strong equivalences.