Other recent publications (not available here)

Books

Journal papers

    1. H. Barringer, D. Brough, M. Fisher, A. Hunter, R. Owens, D. Gabbay, G. Gough, I. Hodkinson, P. McBrien, M. Reynolds, Languages, meta-languages and MetateM - a discussion paper.

      2. J. IGPL 4 (no. 2) 1996, 255-272.
    2. Ian Hodkinson. Finite H-dimension does not imply expressive completeness.

      3. J. Philosophical Logic 23 (1994) 535-573.
      A conjecture of Gabbay (1981) states that any class of flows of time having the property known as finite H-dimension admits a finite set of expressively complete one-dimensional temporal connectives. Here we show that the class of `circular' structures refutes the generalisation of this conjecture to Kripke frames. We then construct from this class, by a general method, a new class of irreflexive transitive flows of time that refutes the original conjecture.
      Our paper includes full descriptions of a method for establishing finite H-dimension for a class of structures and of the technique for extending finite H-dimension to other classes, and an introduction surveying the area of expressive completeness.
    3. Wilfrid Hodges, Ian Hodkinson, Daniel Lascar, Saharon Shelah. The small index property for omega-stable omega-categorical structures and for the random graph.

      4. J. London Math. Soc. 48 (1993) 204-218.
      We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any $\omega$-stable $\omega$-categorical structure, and (ii) the random graph has the small index property. We also show that the automorphism group of such a structure is not the union of a countable chain of proper subgroups.
    4. Ian Hodkinson, Saharon Shelah. A construction of many uncountable rings using SFP domains and Aronszajn trees.

      5. Proc. London Math. Soc. 67 (1993) 449-492.
    5. David M. Evans, Wilfrid Hodges, I. M. Hodkinson, Automorphisms of bounded abelian groups, Forum Math 3 (1991), 523?541.
    6. D. M. Gabbay, I. M. Hodkinson, An axiomatisation of the temporal logic with Until and Since over the real numbers, J. Logic Computat. 1 (1990) 229?259.
    7. Wilfrid Hodges, I. M. Hodkinson, Dugald Macpherson, Omega-categoricity, relative categoricity and coordinatisation, Ann. Pure Appl. Logic 46 (1990) 169?199.
    8. I. M. Hodkinson, H. D. Macpherson, Relational structures determined by their finite induced substructures, J. Symbolic Logic 53 (1988) 222?230.

Refereed conference proceedings

  1. Dov Gabbay and Ian Hodkinson, Temporal logic in the context of databases, in: Logic and Reality: Essays on the legacy of Arthur Prior, ed. B. J. Copeland, Clarendon Press, Oxford, 1996, ISBN 0-19-824060-0, pp 69-87.
  2. I. M. Hodkinson. Expressive completeness of Until and Since over dedekind complete linear time.

    3. In: Modal logic and process algebra, ed. A. Ponse, M. de Rijke, Y. Venema, CSLI Lecture Notes 53, 1995, ISBN 1-881526-95-X, pp. 171-185.
    We prove the theorem of Kamp that the temporal connectives Until and Since are expressively complete over the class of all dedekind complete flows of time. We use an argument of Gabbay, Pnueli, Shelah, and Stavi, but presented in terms of games.
  3. D. M. Gabbay, I. M. Hodkinson, M. A. Reynolds. Temporal expressive completeness in the presence of gaps.

    4. In: Logic Colloquium 90, ed. J. Oikkonen, J. Väänänen, Springer Lecture Notes in Logic 2, 1993, ISBN 3-540-57094-2, pp. 89-121.
    It is known that the temporal connectives Until and Since are expressively complete for Dedekind Complete flows of time but that the Stavi connectives are needed to achieve expressive completeness for general linear time which may have 'gaps' in it. We present a full proof of this result.
    We introduce some new unary connectives which, along with Until and Since are expressively complete for general linear time. We axiomatize the new connectives over general linear time, define a notion of complexity on gaps and show that Until and Since are themselves expressively complete for flows of time with only isolated gaps. We also introduce new unary connectives which are less expressive than the Stavi connectives but are, nevertheless, expressively complete for flows of time whose gaps are of only certain restricted types. In this connection we briefly discuss scattered flows of time.

Unrefereed conference proceedings

  1. I. M. Hodkinson, A construction of many uncountable rings, in: Proc. 3rd Easter conference on Model Theory, Gross Köris, DDR, April 8?13 1985, pp. 134?142.
  2. D. M. Gabbay, I. M. Hodkinson, A. Hunter, RDL: an executable temporal logic for the specification and design of real-time systems, In Proceedings IEE Workshop on Temporal Reasoning, 1990.
  3. D. M. Gabbay, I. Hodkinson, A. Hunter, Using the temporal logic RDL for design specifications. In: Concurrency: Theory, Language and Architecture, Lecture Notes in Computer Science, Springer-Verlag, 1991.
  4. I. M. Hodkinson, The finite base property for some cylindric-relativized algebras, abstract, Proc. RELMICS97, Hammamet, 1997, to appear.

Technical reports, lecture notes, etc

  1. Ian Hodkinson, Lecture notes in computability, algorithms and complexity, Dept. of Computing, Imperial College, 1990, 160pp.
  2. Robin Hirsch, Ian Hodkinson, Retrieving points from intervals, research report, 1990.
  3. Ian Hodkinson, Lecture notes on the irreflexivity rule, manuscript, 1991.
  4. Ian Hodkinson, Lecture notes on automata theory and monadic second order logic, technical report, Dept. of Computing, Imperial College, 1993.
  5. Ian Hodkinson, Elimination of fixpoint operators in the temporal logic YF, technical report 90/21, Dept. of Computing, Imperial College, 1993.
  6. Ian Hodkinson, Expressive completeness in temporal logic, notes for Colchester ESSLLI workshop, 1993.
  7. Ian Hodkinson, ESSLLI 95 advanced course in temporal logic, Barcelona, 1995.
  8. Ian Hodkinson, Complexity theory — space complexity classes, technical report, Cadernos de Matemática CM/D-08, Department of Mathematics, University of Aveiro, 1996.
  9. Ian Hodkinson, Aspects of relativised semantics in logic, technical report, Cadernos de Matemática CM/I-37, Department of Mathematics, University of Aveiro, 1998.