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Ian Hodkinson [36]I. Hodkinson [10]I. M. Hodkinson [2]Im Hodkinson [1]
  1. R. Hirsch, I. Hodkinson & A. Kurucz (forthcoming). On Modal Logics Between â â à and Ë¢ Ë¢ Ë. Journal of Symbolic Logic.
     
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  2. I. Hodkinson, F. Wolter & M. Zakharyaschev (forthcoming). Fragments of Rst-Order Temporal Logics. Annals of Pure and Applied Logic.
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  3. Jannis Bulian & Ian Hodkinson (2013). Bare Canonicity of Representable Cylindric and Polyadic Algebras. Annals of Pure and Applied Logic 164 (9):884-906.
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  4. Johan Benthem, Nick Bezhanishvili & Ian Hodkinson (2012). Sahlqvist Correspondence for Modal Mu-Calculus. Studia Logica 100 (1-2):31-60.
    We define analogues of modal Sahlqvist formulas for the modal mu-calculus, and prove a correspondence theorem for them.
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  5. Ian Hodkinson (2012). J. Väänänen, Models and Games. Bulletin of Symbolic Logic 18 (3):406.
     
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  6. Ian Hodkinson & Szabolcs Mikulás (2012). On Canonicity and Completions of Weakly Representable Relation Algebras. Journal of Symbolic Logic 77 (1):245-262.
    We show that the variety of weakly representable relation algebras is neither canonical nor closed under Monk completions.
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  7. Johan van Benthem, Nick Bezhanishvili & Ian Hodkinson (2012). Sahlqvist Correspondence for Modal Mu-Calculus. Studia Logica 100 (1):31-60.
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  8. Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2011). Weak Representations of Relation Algebras and Relational Bases. Journal of Symbolic Logic 76 (3):870 - 882.
    It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RA n and wRRA contains the other.
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  9. Ian Hodkinson (2011). Johan van Benthem Nick Bezhanishvili. Studia Logica 97:1-32.
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  10. Ian Hodkinson (2010). The Bounded Fragment and Hybrid Logic with Polyadic Modalities. Review of Symbolic Logic 3 (2):279-286.
    We show that the bounded fragment of first-order logic and the hybrid language with and operators are equally expressive even with polyadic modalities, but that their fragments are equally expressive only for unary modalities.
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  11. Ian Hodkinson & Hicham Tahiri (2010). A Bisimulation Characterization Theorem for Hybrid Logic with the Current-State Binder. Review of Symbolic Logic 3 (2):247-261.
    We prove that every first-order formula that is invariant under quasi-injective bisimulations is equivalent to a formula of the hybrid logic . Our proof uses a variation of the usual unravelling technique. We also briefly survey related results, and show in a standard way that it is undecidable whether a first-order formula is invariant under quasi-injective bisimulations.
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  12. Robin Hirsch & Ian Hodkinson (2009). Strongly Representable Atom Structures of Cylindric Algebras. Journal of Symbolic Logic 74 (3):811-828.
    A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n >3, the class of all strongly representable n-dimensional cylindric algebra atom structures is not closed under ultraproducts and is therefore not elementary. Our proof is based on the following construction. From an arbitrary (...)
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  13. Ian Hodkinson & Altaf Hussain (2008). The Modal Logic of Affine Planes is Not Finitely Axiomatisable. Journal of Symbolic Logic 73 (3):940-952.
    We consider a modal language for affine planes, with two sorts of formulas (for points and lines) and three modal boxes. To evaluate formulas, we regard an affine plane as a Kripke frame with two sorts (points and lines) and three modal accessibility relations, namely the point-line and line-point incidence relations and the parallelism relation between lines. We show that the modal logic of affine planes in this language is not finitely axiomatisable.
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  14. Ian Hodkinson (2006). Complexity of Monodic Guarded Fragments Over Linear and Real Time. Annals of Pure and Applied Logic 138 (1):94-125.
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  15. Ian Hodkinson (2006). Hybrid Formulas and Elementarily Generated Modal Logics. Notre Dame Journal of Formal Logic 47 (4):443-478.
    We characterize the modal logics of elementary classes of Kripke frames as precisely those modal logics that are axiomatized by modal axioms synthesized in a certain effective way from "quasi-positive" sentences of hybrid logic. These are pure positive hybrid sentences with arbitrary existential and relativized universal quantification over nominals. The proof has three steps. The first step is to use the known result that the modal logic of any elementary class of Kripke frames is also the modal logic of the (...)
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  16. I. Hodkinson (2005). G. Mints and R. Muskens (Editors), Games, Logic, and Constructive Sets. Bulletin of Symbolic Logic 11 (3).
     
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  17. Ian Hodkinson (2005). Games, Logic, and Constructive Sets, Edited by Mints G. And Muskens R., CSLI Lecture Notes, Vol. 161. CSLI Publications, Stanford, CA, 2003, Xii+ 128 Pp. [REVIEW] Bulletin of Symbolic Logic 11 (3):439-442.
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  18. G. Mints, R. Muskens & Ian Hodkinson (2005). REVIEWS-Games, Logic, and Constructive Sets. Bulletin of Symbolic Logic 11 (3):439-441.
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  19. Nick Bezhanishvili & Ian Hodkinson (2004). All Normal Extensions of S5-Squared Are Finitely Axiomatizable. Studia Logica 78 (3):443 - 457.
    We prove that every normal extension of the bi-modal system S52 is finitely axiomatizable and that every proper normal extension has NP-complete satisfiability problem.
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  20. Robert Goldblatt, Ian Hodkinson & Yde Venema (2004). Erdős Graphs Resolve Fine's Canonicity Problem. Bulletin of Symbolic Logic 10 (2):186-208.
    We show that there exist 2 ℵ 0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation results of (...)
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  21. Ian Hodkinson (2004). Nick Bezhanishvili. Studia Logica 78:443-457.
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  22. Robert Goldblatt, Ian Hodkinson & Yde Venema (2003). On Canonical Modal Logics That Are Not Elementarily Determined. Logique Et Analyse 181:77-101.
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  23. R. Hirsh, I. Hodkinson & Roger D. Maddux (2003). REVIEWS-Relation Algebras by Games. Bulletin of Symbolic Logic 9 (4):515-519.
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  24. Ian Hodkinson & Martin Otto (2003). Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures. Bulletin of Symbolic Logic 9 (3):387-405.
    We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms (...)
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  25. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between K × K × K and S5 × S5 × S. Journal of Symbolic Logic 67 (1):221-234.
  26. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between K × K × K and $S5 \Times S5 \Times S5$. Journal of Symbolic Logic 67 (1):221 - 234.
    We prove that every n-modal logic between K n and S5 n is undecidable, whenever n ≥ 3. We also show that each of these logics is non- finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov-Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a (...)
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  27. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between {$\Roman K\Times\Roman K\Times \Roman K$} and {${\Rm S}5\Times{\Rm S}5\Times{\Rm S}5$}. Journal of Symbolic Logic 67 (1):221-234.
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  28. R. Hirsch, I. Hodkinson & Roger Maddux (2002). On the Number of Variables Required for Proofs. Journal of Symbolic Logic 67 (1):197-213.
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  29. Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2002). Provability with Finitely Many Variables. Bulletin of Symbolic Logic 8 (3):348-379.
    For every finite n ≥ 4 there is a logically valid sentence φ n with the following properties: φ n contains only 3 variables (each of which occurs many times); φ n contains exactly one nonlogical binary relation symbol (no function symbols, no constants, and no equality symbol): φ n has a proof in first-order logic with equality that contains exactly n variables, but no proof containing only n - 1 variables. This result was first proved using the machinery of (...)
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  30. Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2002). Relation Algebra Reducts of Cylindric Algebras and an Application to Proof Theory. Journal of Symbolic Logic 67 (1):197-213.
    We confirm a conjecture, about neat embeddings of cylindric algebras, made in 1969 by J. D. Monk, and a later conjecture by Maddux about relation algebras obtained from cylindric algebras. These results in algebraic logic have the following consequence for predicate logic: for every finite cardinal α ≥ 3 there is a logically valid sentence X, in a first-order language L with equality and exactly one nonlogical binary relation symbol E, such that X contains only 3 variables (each of which (...)
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  31. Ian Hodkinson (2002). Loosely Guarded Fragment of First-Order Logic has the Finite Model Property. Studia Logica 70 (2):205 - 240.
    We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.
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  32. Ian Hodkinson (2002). Monodic Packed Fragment with Equality is Decidable. Studia Logica 72 (2):185-197.
    We prove decidability of satisfiability of sentences of the monodic packed fragment of first-order temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. We also prove decidability over models with finite domains, over flows of time including the real order.
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  33. Robin Hirsch & Ian Hodkinson (2001). Relation Algebras From Cylindric Algebras, I. Annals of Pure and Applied Logic 112 (2-3):225-266.
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  34. Robin Hirsch & Ian Hodkinson (2001). Relation Algebras From Cylindric Algebras, II. Annals of Pure and Applied Logic 112 (2-3):267-297.
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  35. Robin Hirsch & Ian Hodkinson (2000). Relation Algebras with -Dimensional Relational Bases. Annals of Pure and Applied Logic 101 (2-3):227-274.
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  36. Ian Hodkinson, Frank Wolter & Michael Zakharyaschev (2000). Decidable Fragments of First-Order Temporal Logics. Annals of Pure and Applied Logic 106 (1-3):85-134.
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  37. H. Andréka, I. Hodkinson & I. Németi (1999). Finite Algebras of Relations Are Representable on Finite Sets. Journal of Symbolic Logic 64 (1):243-267.
    Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have the `finite base property' and have decidable universal theories, and that any finite algebra in each class is representable on a finite set.
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  38. Robin Hirsch & Ian Hodkinson (1999). Mosaics and Step-by-Step| Remarks onA Modal Logic of Relations' by Venema & Marx. In. In E. Orłowska (ed.), Logic at Work. Heidelberg.
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  39. Robin Hirsch, Ian Hodkinson, Maarten Marx, Szabolsc Mikulás & Mark Reynolds (1999). Mosaics and Step-by-Step. Remarks on “A Modal Logic of Relations”. In E. Orłowska (ed.), Logic at Work. Heidelberg.
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  40. Robin Hirsch & Ian Hodkinson (1997). Complete Representations in Algebraic Logic. Journal of Symbolic Logic 62 (3):816-847.
    A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.
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  41. Robin Hirsch & Ian Hodkinson (1997). Step by Step-Building Representations in Algebraic Logic. Journal of Symbolic Logic 62 (1):225-279.
    We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finite relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an (...)
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  42. I. Hodkinson, R. Kaye, I. Korec, F. Maurin, H. Mildenberger & F. O. Wagner (1997). Friedman, Sy D. And VeliCkovit, B., Al-Definability. Annals of Pure and Applied Logic 89:277.
     
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  43. Ian Hodkinson (1997). Atom Structures of Cylindric Algebras and Relation Algebras. Annals of Pure and Applied Logic 89 (2):117-148.
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  44. Ian Hodkinson (1997). L. Csirmaz, D. Gabbay, M. De Rijke, Eds., Logic Colloquium '92, Studies in Logic Language, and Information. Journal of Logic, Language and Information 6 (4):453-457.
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  45. Ian Hodkinson & András Simon (1997). The K-Variable Property is Stronger Than H-Dimension K. Journal of Philosophical Logic 26 (1):81-101.
    We study the notion of H-dimension and the formally stronger k-variable property, as considered by Gabbay, Immerman and Kozen. We exhibit a class of flows of time that has H-dimension 3, and admits a finite expressively complete set of onedimensional temporal connectives, but does not have the k-variable property for any finite k.
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  46. Ian Hodkinson (1994). Finite H-Dimension Does Not Imply Expressive Completeness. Journal of Philosophical Logic 23 (5):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 (...)
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  47. W. Hodges, Im Hodkinson & D. Macpherson (1990). EVANS, DM, and HEWITT, PR, Counterexamples to a Con-Jecture on Relative Categoricity GOODMAN, ND, Topological Models of Epistemic Set Theory HEWITT, PR, See EVANS, DM. Annals of Pure and Applied Logic 46:299.
     
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  48. Wilfrid Hodges, I. M. Hodkinson & Dugald Macpherson (1990). Omega-Categoricity, Relative Categoricity and Coordinatisation. Annals of Pure and Applied Logic 46 (2):169-199.
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  49. I. M. Hodkinson & H. D. Macpherson (1988). Relational Structures Determined by Their Finite Induced Substructures. Journal of Symbolic Logic 53 (1):222-230.
    A countably infinite relational structure M is called absolutely ubiquitous if the following holds: whenever N is a countably infinite structure, and M and N have the same isomorphism types of finite induced substructures, there is an isomorphism from M to N. Here a characterisation is given of absolutely ubiquitous structures over languages with finitely many relation symbols. A corresponding result is proved for uncountable structures.
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