Reasoning About Sensing Actions and Reactivity

Abstract

This thesis focuses on the problem of reasoning about sensing actions and the relationship between action theory and reactive control. The first approach to reasoning about sensing actions is due to Moore1. He used the possible world semantics to represent knowledge and treated the accessible relation between world models as a fluent. Later, Hass proposed another way of formulating sensing actions using first order logic. Moore’s formulation was then adapted to reasoning about sensing actions in situation calculus by Scherl and Levesque. In 1997, Lobo, Taylor, and Mendez extended the language , a high-level action description language of Gelfond and Lifschitz, to allow sensing actions and called the new language K . Lobo et al. defined the semantics of K , which will be denoted by LTM hereafter, by situation transition functions, which are extensions of the state transition functions of . Baral and Son proposed different approximations for the semantics of K , denoted by a 2. However, it was not clear whether there is a situation calculus counterpart of K , as Kartha proved for , or not. Another question was to prove the soundness of a with respect to LTM . We will present a new approach to reasoning about sensing actions in K , in which transition functions are defined over knowledge states (or k-states). A k-state is a pair s Σ where s is a state and Σ is a set of states. Intuitively, s represents the real state of the world and Σ represents the possible states of the world in which an agent thinks it may be in. We denote the new semantics by K and prove that Kartha’s results can be extended to domains with sensing actions. More importantly, we prove the soundness of the different approximations of K , a, with respect to K and LTM. To compute K , we translate domain descriptions in K into extended logic programs where the answer set semantics of the latter coincides with K . It is also expected that our formalism corresponds to POMDP (Partial Observable Markov Decision Process), a well-known statistical approach to reasoning about sensing actions. Theories of actions can be used to model deliberate agents which achieve their goals by repeatedly (a) making observa-