Completing symbolic rule bases using betweenness and analogical proportion

© Springer Japan 2014. Classical deduction is limited as a tool for reasoning about logical domain theories, in its ability to make sense of situations that are not explicitly covered. Humans on the other hand are remarkably adept at speculation about new situations, by drawing analogies or by relying on knowledge of similar situations. In this chapter, we are interested in formalising this process to develop a form of commonsense reasoning about incomplete rule bases. More precisely, we discuss two methods which can be used to derive plausible rules from a given set of propositional rules and a set of analogical proportions. The first method is based on the view that whenever the antecedents of four rules are in an analogical proportion, their consequences are likely to be in an analogical proportion as well. It often produces useful results, although it may be too adventurous for some applications. The second method is more cautious and makes explicit the assumptions under which it produces sound conclusions. Finally, we show how the second method may be further refined, in such a way that we recover the first method as a special case