Master's thesis, RWTH Aachen University, Aachen, 2021.
Based on weighted possible worlds semantics, Belle and Lakemeyer recently proposed the logic DS, a probabilistic extension of a modal variant of the situation calculus with a model of belief. The logic has many desirable properties like full introspection and it is able to precisely capture the beliefs of a probabilistic knowledge base in terms of the notion of only-believing. While intuitively appealing, it is unclear how to plan with such logic. The fundamental problem behind is the lack of projection reasoning mechanisms. Projection reasoning, in general, is to decide what holds after actions. Two main solutions to projection exist: regression and progression. Roughly, regression reduces a query about the future to a query about the initial state. Progression, on the other hand, changes the initial state according to the effects of actions and then checks whether the formula holds in the updated state. In this thesis we study projection by progression in the logic DS. It is known the progression of a categorical knowledge base w.r.t. a noise-free action corresponds to what is only known after that action. We show how to progress a type of probabilistic knowledge base by the notion of only-believing after actions.
@thesis{ qihui_msthesis,
title    = {Reasoning about Belief by Progression},
author   = {Qihui, Feng},
year     = {2021},
school   = {RWTH Aachen University},
type     = {mathesis},
keywords = {knowledge representation, progression of belief},
abstract={
Based on weighted possible worlds semantics, Belle and Lakemeyer recently proposed the logic DS, a probabilistic extension of a modal variant of the situation
calculus with a model of belief. The logic has many desirable properties like full
introspection and it is able to precisely capture the beliefs of a probabilistic knowledge base in terms of the notion of only-believing. While intuitively appealing, it
is unclear how to plan with such logic. The fundamental problem behind is the lack
of projection reasoning mechanisms.
Projection reasoning, in general, is to decide what holds after actions. Two
main solutions to projection exist: regression and progression. Roughly, regression
reduces a query about the future to a query about the initial state. Progression,
on the other hand, changes the initial state according to the effects of actions and
then checks whether the formula holds in the updated state. In this thesis we
study projection by progression in the logic DS. It is known the progression of a
categorical knowledge base w.r.t. a noise-free action corresponds to what is only known after that action. We show how to progress a type of probabilistic knowledge
base by the notion of only-believing after actions.
}
}