Epistemic Modelling and Protocol Dynamics
Yanjing Wang
Abstract:
In Part I, we introduce logics for specifying epistemic protocols
including their goals and their dynamics. Chapter 3 departures from
the existing discussions about protocols in the field of Dynamic
Epistemic Logic by introducing a logic which can specify both the
epistemic protocols and their goals within the language. We formalize
the verification problem of epistemic protocols under the assumption
of meta knowledge about the intended goal. The subtlety of this
verification problem is discussed in theory and examples. In Chapter
4, we address the question: “How can people get to know a protocol?”
For this, we develop logics which are convenient for reasoning about
knowledge change and protocol change. With various protocol-changing
operators we can handle the dynamics of protocols and formalize how
actions acquire new meanings as a result of protocol change. We show
that all the three logics we introduced can be translated back to
Propositional Dynamic Logic (PDL) on standard Kripke models, thus the
techniques of modelling and model checking we develop in the other
parts of the dissertation can be applied to these logics.
In Part II we address the issue of epistemic modelling, in order to
study model checking for the logics introduced in Part I. In Chapter 5
we propose new composition operations on static and event models with
arbitrary vocabularies, aiming at a compositional method for
generating initial epistemic models. We prove decomposition theorems
w.r.t. our new operator and demonstrate the use of our methods by
various examples. Chapter 6 reports results on counting the number of
different models given a finite set of initial assumptions. Restricted
to image-finite models, we show that if a modal µ-calculus formula has
an infinite model modulo bisimulation then it has 2^aleph-zero (the
cardinality of the continuum) different models modulo bisimulation. On
the other hand, if it does not have any infinite models modulo
bisimulation then all its models can be represented in a normal form.
Part III introduces abstraction techniques that are particularly
useful on making the model checking more efficient. A 3-valued
semantics for Public Announcement Logic is defined and studied in
Chapter 7 to facilitate abstractions of models. We define a relation
with vocabulary and agent mappings between concrete models and their
abstractions, thus making it possible to also abstract the signatures
of models. We then give a logical characterization of this abstraction
relation thus showing it is safe to check properties on the abstract
model instead of the original concrete model. Chapter 8 studies the
PDL on so-called accelerated Kripke models where the transitions in
the models are labelled by regular expressions in order to obtain
informative abstractions. By making use of a technique of regular
expression rewriting, we analyse the complexity of the model checking
and satisfiability problems of this logic and give a complete
axiomatization.
In Part IV (Chapter 9) we survey the epistemic approaches to security
protocol verification. We summarize the most important techniques in
the Epistemic Temporal Logic and Dynamic Epistemic Logic approaches to
security protocol verification, and compare these two approaches in
term of convenience. We argue that some security properties can only
be faithfully formalized by temporal logic with knowledge operators,
but are not expressible by standard temporal logic. However, we need
to pay some cost in model checking complexity, in exchange to the
expressiveness we gain.