jameshales/honours-thesis

My undergraduate honours thesis, titled "Refinement Quantifiers for Logics of Belief and Knowledge".

Refinement Quantifiers for Logics of Belief and Knowledge

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This thesis was presented to the School of Computer Science and Software Engineering for the degree of Bachelor of Computer and Mathematical Sciences (First Class Honours) from the University of Western Australia in Decemer 2011.

Abstract

Modal logics are extensions of propositional logic, with which one can qualify the truth of statements with operators known as modalities. Epistemic logic is a variant of modal logic, commonly known as the logic of knowledge. Modalities in epistemic logic qualify statements by saying that a particular agent knows a statement to be true. Thus epistemic logic can be used to reason about the knowledge of a collection of agents. Doxastic logic is a similar logic, used to reason about beliefs rather than knowledge.

Informative updates are events that provide agents in modal settings with additional information. The effect of an informative update may be to give new knowledge or beliefs to the agents in the system. Informative updates in an epistemic setting can be modelled by the refinements of a Kripke model in modal logic.

Refinement quantifiers are introduced to variants of modal logic to produce refinement quantified modal logics. The refinement quantifiers are operators that quantify over the refinements of a Kripke model, and as these refinements model informative updates, this quantification can be said to be equivalent to quantifying over the informative updates that are possible in a Kripke model. Recent work by van Ditmarsch, French and Pinchinat~\cite{french2010future} has presented an axiomatisation and decidability results for the single-agent refinement quantified modal logic. We extend these results to apply to the single-agent doxastic and epistemic logics, and to the multi-agent modal and doxastic logics, by providing sound and complete axiomatisations, and decidability and expressivity results for each of these logics.

Building

Requirements:

• TeX Live 2015 or later
• LaTeXmk
• GNU Make

Simply run make.

License

This thesis is distributed under the Creative Commons Attribution Share Alike 4.0 license.