順序従属性とその推論について

抄録

There are many models and laws in sciences, which are qualitative in the sense that emphases are laid on rough-cut relationships among attributes of the objects of the studies rather than detailed qualitative models. Qualitative models are prevailing in social sciences such as economics and management sciences, explanation of behavior of devices, educational domains, thought experiments, and so forth. In many cases, relations among attributes are derived from those among attribute values. Functional dependency and order dependency in relational database theory are a typical example of that kind of relations. The main objective of this paper is to investigate basic logical validity, namely, soundness and completeness, of reasoning based on some qualitative models of order-dependency type : Two types of order dependency and two variants, namely, OD-I,II and TOD-I,II, are defined. Two ODs are derived from families of partial orders between attribute values, and TODs are derived from those of total orders. Inference axioms are provided for ODs, while definitions of TODs are translated, in a certain manner, into propositional logic, and thereby logical validity is proved.