Research interests
My early-career research interests originate in the use of temporal logics in
system verification, but spread to cover many connected areas. These
days I am mostly interested in linguistics, specifically phonology.
Fixpoint logics
A central area of my research during the 90s and 00s was
fixpoint logics, and particularly the modal mu-calculus. These provide
a foundational logic for verification using the temporal logic
paradigm, and also have a wealth of intrinsically interesting
mathematical properties.
As a consequence of this interest, I also became interested in
fixpoints in general, which led to some forays into (mostly quite
elementary!) descriptive set theory.
I am not currently working in this area, but maintain a connection by reviewing.
True concurrency
A long-standing interest is theories and models of true
concurrency, in which causality and the independence of parallel
components are taken seriously. Currently I am working with my student
Christian Odenwald on more traditional philosophical logic approaches to
causality, and planning to bring the two approaches closer together.
Independence-friendly logic
In 00s and 10s, I was working on modal analogues of Hintikka's
Independence-Friendly Logic. This was inspired by its intuitively
obvious links with concurrency - an intuition which takes a while to
pin down! I am not at present working specifically on IF.
Natural language
I have always been interested in natural language, particularly
phonology, and since the mid 00s I have been concentrating on
this. One interest is the meta-theory of phonology: what are
(intendedly) formal theories devised by phonologists, and how can
one compare them usefully? On a more grounded level, I work on the
Khoisan language !Xoon, which has many interesting properties
which provoke reexamination of some of the basic assumptions of
traditional frameworks.
Papers and preprints
Selected publications:
These are probably the papers of most interest in my various areas.
- Poster at OCP21 on new data
for !Xoon A-raising.
- A journal paper on the use of
simulation in phonology.
- The journal paper on the
phonology of clicks in Khoisan.
- A CSL paper with a new game semantics
for dependence logic.
- A poster about the difficulty of
learning complex vowel systems.
- A preprint of a chapter on
mu-calculi in the Handbook of Modal Logic.
-
The journal version of two papers on
fixpoints and parity conditions in descriptive set theory, and a
conference paper dealing with
one of the problems raised there.
- A full version of a paper on fixpoint
extensions of independence-friendly logic, and a full paper on the complexity of such logics.
-
A paper in a Festschrift for
Gabriel Sandu
considering the use of Henkin quantification in modal logic.
- A preprint of an introduction
to modal mu-calculus, appearing as a chapter in the Handbook of
Process Algebra
-
The journal version of the original paper
establishing the strictness of the modal mu-calculus alternation
hierarchy, and a journal version of two conference papers,
simplifying the proof, and addressing the issue of Niwinski's fixpoint
algebras on trees.
Most of my papers and preprints are online,
accompanied by a short description and notes about dependencies.
Slides from talks
My talks page has the slides from some of my
seminar etc. talks. This material will be moved into the publications
page, but is currently separate.