Conditional beliefs in action

摘要

Humans rarely have sound or even complete knowledge about their environment.Instead, we usually picture different contingencies what the world could belike. For example, we might believe that a specific box is presumably empty, andthat otherwise it most plausibly contains a gift. On the grounds of(conditional) beliefs like this we act. Sometimes we perceive new informationthat refutes some of these contingencies; then we revise our beliefsappropriately. To a human, all this is natural and mundane.For a machine to do the same, it needs a formal representation and understandingof conditional belief and actions and perception. In this thesis we develop aformalization and semantics of these concepts in one coherent logical languageand investigate their interaction. The main contributions are as follows. First we introduce a method to express that a set of conditional beliefs is allthat is believed. This captures the idea that a (conditional) knowledge basecovers the agent's beliefs to their full extent. We refer to this concept asonly-believing, as it generalizes Levesque's only-knowing to conditionalbeliefs. It can also be considered a semantic version of Pearl's meta-logicalSystem~Z.Then we investigate the belief projection problem, which refers to determiningwhat is believed after a number of actions have occurred. Solving the beliefprojection problem is essential to reason about beliefs in dynamic systems, likea robot for example. We propose two solutions in the framework of Reiter'ssituation calculus. Namely, we extend the well-known concepts of queryregression and knowledge base progression to conditional beliefs.Finally, as a step towards practical reasoning about beliefs and contingencies,we develop a limited-reasoning system for conditional beliefs. We complementLakemeyer and Levesque's limited first-order inference with a novel soundfirst-order consistency test. Together, these techniques enable us toapproximate the notions of conditional belief and only-believing in a way thatis sound and decidable for an important class of problems.