I was the Principal Investigator in an Arché research project, funded by the Arts and Humanities Research Council (AHRC) on the Foundations of Logical Consequence. This project started in January 2009 and concluded in June 2012. There were two associated project seminars, the Foundations of Logic Consequence Seminar and the Arché Logic Group. The project opened with a Workshop on ‘Proof-theoretical and model-theoretical semantics’ on 12-13 January 2009. Multi-media broadcasts of some of the sessions are now available at the new Arché Projects website. We held further Workshops, on The Logic of Denial in October 2009, and on Propositions, Context and Consequence in March 2010, a Conference on the Foundations of Logical Consequence in June 2010, and a Mini-course on 'Logic or Logics?' followed by a Workshop on the same theme at the end of September 2010. There was a further Workshop on Paradox and Logical Revision in early April 2011, another on 'The Epistemology of Logic' on 29-30 October, and another on 'Indefinite Extensibility and Logical Paradoxes' on 2-4 December 2011. The final Conference on the Foundations of Logical Consequence took place in St Andrews from 8-10 June 2012.

From the summer of 2012, I will be leading a new Arché project on Models, Modality and Meaning.

A previous project was an examination of Bradwardine’s discussion of insolubles and the Liar paradox. I prepared a new edition and English translation of Bradwardine’s Latin text from the thirteen known manuscripts. The work appeared in May 2010 as volume 10 in the series Dallas Medieval Texts and Translations published by Peeters.

I am currently preparing a new English translation with Introduction of John Buridan's Treatise on Consequences. I reviewed the existing English translation in Vivarium 25 (1987), pp. 154-7.