The University of Queensland

Research Interests

• Areas of research
  In general, my research has been in logic and its relations with neighbouring disciplines. Most recent Currently, I am working mainly on relevance-sensitive truth-trees, and in some topics in the history of logic concerning Boole, Frege, and Orlov. In recent years I have also returned to topics that had for a long time been on shelves at the back of my mind. These include Gödel's 'master argument' for his first incompleteness theorem, and a semantic study of intelim rules for classical connectives. Logic of uncertain reasoning In this area, my research has followed three main lines. One was directed to clarifying the logical patterns to be found in qualitative uncertain reasoning, commonly known as nonmonotonic inference. Another established the basic relationships between nonmonotonic inference and belief revision. More recently, I have investigated the relations between qualitative and probabilistic approaches to uncertain reasoning, the concept of a lossy inference rule, and conditional probability in the light of qualitative belief change. Logic of belief change Perhaps the most frequently cited work is the creation of the so-called AGM account of the logic of belief change, with Carlos Alchourrón and Peter Gärdenfors. This was done in a variety of converging forms: postulational, in terms of partial meet operations, relations of epistemic entrenchment, and safe contraction, with also a paper reviewing the ways in which the logics of belief change and uncertain reasoning have led to new ways of doing logic. More recent papers in this area, with George Kourousias, examine the question of relevance in belief change in the light of the finest splitting theorem. Logic of norms and normative systems In the logic of norms (also known as deontic logic), earlier publications analyse the Hohfeld classification of rights relationships and its application to real-life rights claims (particularly collective rights). More recent work reconstructs the logic of norms in accord with the philosophical position that norms lack truth values, developing into a general theory of input/output logics as a framework for conditional directives and permissions. Other areas of logic Some of my work does not fall squarely into any of the above categories. One paper separates combinatorial from decision-theoretic components in Arrow's impossibility theorem and the closely related Blair/Bordes/Kelly/Suzumura theorem in the theory of collective preference, providing a particularly elegant proof of those results. Another articulates the fascinating concept of logical friendliness, studying its implicit manifestations in the literature of the last hundred and fifty years, as well as its properties. A third formulates the concept of parallel interpolation and continues Parikh's analysis of splitting in classical propositional logic. Early work in modal logic Early work focussed largely on modal logic. Perhaps the most cited contribution in this area was the adaptation, in my1965 D.Phil. thesis and a following publication, of the maximal consistent set method, then well-known in classical propositional and predicate logic (Lindenbaum, Henkin), to serve as a tool for establishing completeness results in modal and other non-classical logics, where it is now a standard procedure. Also often mentioned is the discovery of the first simple and natural propositional logic lacking the finite model property; and formulation of a generalised notion of relational model for modal logic, bringing the relational account into harmony with the algebraic one. Another item, quite ignored at the time of its publication in 1971 but often cited in recent years, proves the first (and still the main) embedding theorem for modal logics.