Event, Property, and Hierarchy in Order-Sorted Logic

Knowledge representation in logics, even in the order-sorted logic that includes a sort hierarchy, tends to lose the conciseness and the nuances of natural language. If we could construct a logic that includes both predicates and terms as classes in the hierarchies, it would be very useful for connecting general knowledge to specic knowledge. Although there are actually logics that are equipped with such a predicate hierarchy, they are built by logical implication and they cause the problem of predicate unication between dierent argument structures. In this paper, we present a logic language with a class hierarchy of predicates, where in the unication of predicates we devise a mechanism for deriving superordinate predicates in the hierarchy and for quantifying supplementary arguments. The arguments are quan-tied dierently, depending on whether a predicate is interpreted as an occurrence of an event or a universal property. T h us, we include the distinction between events and properties in predicates and present a logic language that can exibly relate predicates with dierent argument structures. We formalize the logic language both by s y n tax and semantics, and develop the inference system.