The definition of concepts is a central problem in commonsense reasoning. Many themes in nonmonotonic reasoning concern implicit and explicit definability. implicit definability in nonmonotonic logic is always relative to the context-the current theory of the world. We show that fixed point equations provide a generalization of explicit definability, which correctly captures the relativized context. Theories expressed within this logical framework provide implicit definitions of concepts.
... er, it is possible to derive these fixed points entirely within the logic. B. Shults and BJ. Kuipers, Proving properties of continuous systems: qualitative simulation and temporal logic We demonstrate an automated method for proving temporal logic statements about solutions to ordinary differential equations (ODES), even in the face of an incomplete specification of the ODE. The method combines an implemented, on-the-fly, model checking algorithm for statements in the temporal logic CTL* with the output of the qualitative simulation algorithm QSIM. Based on the QSIM Guaranteed Coverage Theorem, we prove that for certain CTL* statements, @, if @J is true for the temporal structure produced by QSIM, then a corresponding temporal statement, @', holds for the solution of any ODE consistent with the qualitative differential equation (QDE) that QSIM used to generate the temporal structure. J. Rickel and B. Porter, Automated modeling of complex systems to answer prediction questions A question about the behavior of a complex, physical system can be answered by simulating the systemthe challenge is building a model of the system that is appropriate for answering the question. If the model omits relevant aspects of the system, the predicted behavior may be wrong. If, on the other hand, the model includes many aspects that are irrelevant to the question, it may be difhcult to simulate and explain. The leading approach to automated modeling, "compositional modeling", constructs a simplest adequate model for a question from building blocks ("model fragments") that are designed by knowledge engineers. This paper presents a new compositional modeling algorithm that constructs models from simpler building blocks -the individual influences among system variables -and addresses important modeling issues that previous programs left to the knowledge engineer. In the most rigorous test of a modeling algorithm to date, we implemented our algorithm, applied it to a large knowledge base for plant physiology, and asked a domain expert to evaluate the models it produced. Blsevier Science B.V.