Object-Oriented First-Order Logic

We wish to improve modeling in first-order logic (FOL) by using object-oriented tools. To this end, we describe Object-Oriented First-Order Logic (OOFOL), which is a simple extension of FOL. It does not surpass the expressive power of FOL, but it provides object-oriented tools to the knowledge engineer. 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 this logic has a simple semantics provided by FOL. A variant of the logic that allows links between the objects to be unidirectional is also examined. We call this variant 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 specialized inference algorithms for these logics.