Object-Oriented First-Order Logic

This paper describes a novel logic that extends First-Order Logic (FOL) to create counterparts of the Object-Oriented paradigm. We call it Object-Oriented First-Order Logic (OOFOL). FOL provides richness of representation, but is unwieldy in modeling large, complex tasks. On the other hand, the Object-Oriented paradigm has been successful at treating large, complex tasks in both software and knowledge engineering.In OOFOL, objects are theories that are connected via interface vocabularies to other objects, classes are used to provide a reusable logical template, and inheritance is used to adapt classes to specialized tasks. We show that such a logic can be given simple semantics using FOL. A variant of the logic that allows links between the objects to be unidirectional is also examined. This variant is called Directed Object-Oriented First-Order Logic (Directed OOFOL). We show that such a system can be given semantics using Circumscription. Our new tools facilitate the object-oriented design of theories. We demonstrate this through a few applications taken from model-based reasoning, theories of action and cognitive robotics. These examples also demonstrate the use of the object-oriented methodology and tools for the construction of first-order theories. We conclude with proposed inference algorithms for these logics