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Ph.D. ThesesFurthering the Continuous-change Event Calculus: Providing for Efficient Description of Additive Effects and an Automated Reasoner
By Ankesh Khandelwal
Event Calculus is a first-order logic based formalism for representing and reasoning about actions and their effects. It allows for descriptions of continuous-changes using arbitrary systems of ordinary differential equations. In this thesis, we extend the Event Calculus formalism for general, concise, and elaboration tolerant descriptions of additive effects. The extended Event Calculus uses aggregate expressions in first-order logic, for which the existing nonmonotonic reasoning techniques are insufficient to perform closed-world reasoning. Therefore, we define a new nonmonotonic reasoning technique for first-order logic with aggregates and use it for closed-world reasoning in the extended Event Calculus. Finally, we devise a method for constructing models for given, numerical, and finite Event Calculus domain descriptions, given an initial state and narratives of external actions. The method involves separation of logic reasoning from solving of equations for model construction, which allows for the use of off-the-shelf logic reasoners and equation solvers to implement a model builder for the Event Calculus. We also discuss a prototypical implementation of the model builder. The results of this thesis may encourage the use of logic formalisms/systems for descriptions of dynamical systems -- some simple examples include flow of water through multiple tanks, result of applying forces on multiple blocks, etc. -- with quantitative descriptions of continuous-changes. Additive effects are very common in concurrent systems, and the extended Event Calculus allows for general, concise and elaboration tolerant descriptions of them, which among other things makes the descriptions amicable to sharing, reuse, and modular development. The prototypical model-builder for the continuous-change Event Calculus formalism broadens its scope beyond theory, positioning it for use in practice.
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Research
