A formal theory for reasoning about action, knowledge and time

Abstract

Aiming at achieving a proper regulation of their behavior in real-world environments, participating agents need to reason not only about the specifications of the environment they inhabit, but also about their own knowledge concerning its current state by exploiting information acquired at run-time. Considering the highly dynamic nature of most complex domains, the study of knowledge evolution over time is a critical aspect. In this thesis, we develop a unified formal theory of action, knowledge and time using the language of the Event Calculus and automate the process of reasoning about a wide range of commonsense phenomena. Traditionally, epistemic reasoning has been structured around the highly expressive but computationally expensive "possible worlds" specifications. Recent theories adopt alternative representations for knowledge, dismissing the accessibility relation of possible worlds and promising more efficient reasoning in classes of restricted expressiveness. The framework we propose combines the full expressive power of the possible worlds semantics with the benefits of alternative approaches, building on a proper handling of a type of causal dependencies that emerge among partially known world aspects. We investigate the properties of these so called hidden causal dependencies and develop a provably sound and complete axiomatization that is independent of the underlying formalism. We show correctness properties by studying the correlation of the theory with an epistemic formalism that implements the standard definition for knowledge, based on a recently proposed branching version of the Event Calculus. Furthermore, we investigate a number of different extensions of the basic axiomatization augmenting the mental state of intelligent agents with essential cognitive skills, such as the ability to remember and forget, to reason about physical actions, to handle complex ramifications in partially observable domains, and others. We demonstrate the potential of the theory by modeling complex benchmark problems proposed in relevant literature, as well as scenarios that emerge in the highly demanding nascent field of Ambient Intelligence. Finally, we also describe the design of a reasoner that can accommodate both epistemic and online reasoning and present a way to implement the framework using logic programming languages