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Robert Goldblatt [57]Robert I. Goldblatt [2]
  1.  2
    Logics of Time and Computation.Robert Goldblatt - 1992 - CSLI Publications.
    Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic of henceforth, next, and until, and to the propositional dynamic logic of regular programs.
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  2. Logics of Time and Computation.Robert Goldblatt - 1990 - Studia Logica 49 (2):284-286.
     
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  3.  7
    Mathematics of Modality.Robert Goldblatt - 1993 - Center for the Study of Language and Information Publications.
    Modal logic is the study of modalities - expressions that qualify assertions about the truth of statements - like the ordinary language phrases necessarily, possibly, it is known/believed/ought to be, etc., and computationally or mathematically motivated expressions like provably, at the next state, or after the computation terminates. The study of modalities dates from antiquity, but has been most actively pursued in the last three decades, since the introduction of the methods of Kripke semantics, and now impacts on a wide (...)
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  4.  8
    [Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
  5.  49
    Quantifiers, Propositions and Identity: Admissible Semantics for Quantified Modal and Substructural Logics.Robert Goldblatt - 2011 - Cambridge University Press.
    Machine generated contents note: Introduction and overview; 1. Logics with actualist quantifiers; 2. The Barcan formulas; 3. The existence predicate; 4. Propositional functions and predicate substitution; 5. Identity; 6. Cover semantics for relevant logic; References; Index.
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  6.  25
    Mathematical Modal Logic: A View of its Evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
  7.  21
    Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
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  8.  60
    An Alternative Semantics for Quantified Relevant Logic.Edwin D. Mares & Robert Goldblatt - 2006 - Journal of Symbolic Logic 71 (1):163-187.
    The quantified relevant logic RQ is given a new semantics in which a formula for all xA is true when there is some true proposition that implies all x-instantiations of A. Formulae are modelled as functions from variable-assignments to propositions, where a proposition is a set of worlds in a relevant model structure. A completeness proof is given for a basic quantificational system QR from which RQ is obtained by adding the axiom EC of 'extensional confinement': for all x(A V (...)
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  9.  86
    Diodorean Modality in Minkowski Spacetime.Robert Goldblatt - 1980 - Studia Logica 39 (2-3):219 - 236.
    The Diodorean interpretation of modality reads the operator as it is now and always will be the case that. In this paper time is modelled by the four-dimensional Minkowskian geometry that forms the basis of Einstein's special theory of relativity, with event y coming after event x just in case a signal can be sent from x to y at a speed at most that of the speed of light (so that y is in the causal future of x).It is (...)
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  10.  18
    The Finite Model Property for Logics with the Tangle Modality.Robert Goldblatt & Ian Hodkinson - 2018 - Studia Logica 106 (1):131-166.
    The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness (...)
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  11.  11
    Axiomatising the Logic of Computer Programming.Robert Goldblatt - 1985 - Journal of Symbolic Logic 50 (3):854-855.
  12. Persistence and Atomic Generation for Varieties of Boolean Algebras with Operators.Robert Goldblatt - 2001 - Studia Logica 68 (2):155-171.
    A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V.This paper explores relationships between these "persistence" properties and questions of whether V is generated by its complex algebras or its atomic members, or is closed under canonical embedding algebras or completions. It also develops a (...)
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  13.  82
    An Admissible Semantics for Propositionally Quantified Relevant Logics.Robert Goldblatt & Michael Kane - 2010 - Journal of Philosophical Logic 39 (1):73-100.
    The Routley-Meyer relational semantics for relevant logics is extended to give a sound and complete model theory for many propositionally quantified relevant logics (and some non-relevant ones). This involves a restriction on which sets of worlds are admissible as propositions, and an interpretation of propositional quantification that makes ∀ pA true when there is some true admissible proposition that entails all p -instantiations of A . It is also shown that without the admissibility qualification many of the systems considered are (...)
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  14.  57
    The McKinsey Axiom is Not Canonical.Robert Goldblatt - 1991 - Journal of Symbolic Logic 56 (2):554-562.
  15.  28
    Spatial Logic of Tangled Closure Operators and Modal Mu-Calculus.Robert Goldblatt & Ian Hodkinson - 2017 - Annals of Pure and Applied Logic 168 (5):1032-1090.
  16.  14
    Orthogonality and Spacetime Geometry.Robert Goldblatt - 1990 - Philosophy of Science 57 (2):335-336.
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  17.  42
    The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2012 - Journal of Philosophical Logic (1):1-20.
    Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...)
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  18.  5
    The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2014 - Journal of Philosophical Logic 43 (1):133-152.
    Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...)
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  19.  41
    Orthomodularity is Not Elementary.Robert Goldblatt - 1984 - Journal of Symbolic Logic 49 (2):401-404.
  20.  13
    The McKinsey–Lemmon Logic is Barely Canonical.Robert Goldblatt & Ian Hodkinson - 2007 - Australasian Journal of Logic 5:1-19.
    We study a canonical modal logic introduced by Lemmon, and axiomatised by an infinite sequence of axioms generalising McKinsey’s formula. We prove that the class of all frames for this logic is not closed under elementary equivalence, and so is non-elementary. We also show that any axiomatisation of the logic involves infinitely many non-canonical formulas.
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  21.  66
    An Abstract Setting for Henkin Proofs.Robert Goldblatt - 1984 - Topoi 3 (1):37-41.
    A general result is proved about the existence of maximally consistent theories satisfying prescribed closure conditions. The principle is then used to give streamlined proofs of completeness and omitting-types theorems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory respects a certain class of inference rules.
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  22.  22
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Mathematical Logic Quarterly 27 (31‐35):495-529.
  23.  59
    Parallel Action: Concurrent Dynamic Logic with Independent Modalities.Robert Goldblatt - 1992 - Studia Logica 51 (3-4):551 - 578.
    Regular dynamic logic is extended by the program construct, meaning and executed in parallel. In a semantics due to Peleg, each command is interpreted as a set of pairs (s,T), withT being the set of states reachable froms by a single execution of, possibly involving several processes acting in parallel. The modalities ] are given the interpretations>A is true ats iff there existsT withsRT andA true throughoutT, and.
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  24.  27
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (31-35):495-529.
  25.  70
    Conservativity of Heyting Implication Over Relevant Quantification.Robert Goldblatt - 2009 - Review of Symbolic Logic 2 (2):310-341.
    It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The conservative presence (...)
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  26.  41
    On the Role of the Baire Category Theorem and Dependent Choice in the Foundations of Logic.Robert Goldblatt - 1985 - Journal of Symbolic Logic 50 (2):412-422.
    The Principle of Dependent Choice is shown to be equivalent to: the Baire Category Theorem for Čech-complete spaces (or for complete metric spaces); the existence theorem for generic sets of forcing conditions; and a proof-theoretic principle that abstracts the "Henkin method" of proving deductive completeness of logical systems. The Rasiowa-Sikorski Lemma is shown to be equivalent to the conjunction of the Ultrafilter Theorem and the Baire Category Theorem for compact Hausdorff spaces.
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  27.  29
    Erdős Graphs Resolve Fine's Canonicity Problem.Robert Goldblatt, Ian Hodkinson & Yde Venema - 2004 - 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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  28.  59
    Monadic Bounded Algebras.Galym Akishev & Robert Goldblatt - 2010 - Studia Logica 96 (1):1 - 40.
    We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA's is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that can be seen as an algebraic counterpart to semantic completeness for monadic free logic. The analysis involves the representation of (...)
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  29.  28
    An Algebraic Study of Well-Foundedness.Robert Goldblatt - 1985 - Studia Logica 44 (4):423 - 437.
    A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. These algebras, however, (...)
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  30.  6
    The Tangled Derivative Logic of the Real Line and Zero-Dimensional Space.Robert Goldblatt & Ian Hodkinson - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 342-361.
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  31.  24
    On Canonical Modal Logics That Are Not Elementarily Determined.Robert Goldblatt, Ian Hodkinson & Yde Venema - 2003 - Logique Et Analyse 181:77-101.
  32.  3
    A General Semantics for Quantified Modal Logic.Robert Goldblatt & Edwin D. Mares - 2006 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. Stanford: CSLI Publications. pp. 227-246.
    This paper uses an "admissible set semantics" to treat quantification in quantified modal logics. The truth condition for the universal quantifier states that a universally quantified statement (x)A(x) is true at a world w if and only if there is some proposition true at that world that entails every instance of A(x). It is shown that, for any canonical propositional modal logic the corresponding admissible set semantics characterises the quantified version of that modal logic.
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  33.  6
    A Kripke-Joyal Semantics for Noncommutative Logic in Quantales.Robert Goldblatt - 2006 - In Guido Governatori, Ian Hodkinson & Yde Venema (eds.), Advances in Modal Logic, Volume 6. CSLI Publications. pp. 209-225.
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  34. Mereocompactness and Duality for Mereotopological Spaces.Matt Grice & Robert Goldblatt - 2016 - In Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics. Springer.
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  35.  7
    Final Coalgebras and the Hennessy–Milner Property.Robert Goldblatt - 2006 - Annals of Pure and Applied Logic 138 (1):77-93.
    The existence of a final coalgebra is equivalent to the existence of a formal logic with a set of formulas that has the Hennessy–Milner property of distinguishing coalgebraic states up to bisimilarity. This applies to coalgebras of any functor on the category of sets for which the bisimilarity relation is transitive. There are cases of functors that do have logics with the Hennessy–Milner property, but the only such logics have a proper class of formulas. The main theorem gives a representation (...)
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  36.  1
    A Kripke-Joyal Semantics for Noncommutative Logic in Quantales.Robert Goldblatt - 2006 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 209-225.
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  37.  59
    Functional Monadic Bounded Algebras.Robert Goldblatt - 2010 - Studia Logica 96 (1):41 - 48.
    The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion of (...)
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  38.  42
    Maps and Monads for Modal Frames.Robert Goldblatt - 2006 - Studia Logica 83 (1-3):309-331.
    The category-theoretic nature of general frames for modal logic is explored. A new notion of "modal map" between frames is defined, generalizing the usual notion of bounded morphism/p-morphism. The category Fm of all frames and modal maps has reflective subcategories CHFm of compact Hausdorff frames, DFm of descriptive frames, and UEFm of ultrafilter enlargements of frames. All three subcategories are equivalent, and are dual to the category of modal algebras and their homomorphisms. An important example of a modal map that (...)
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  39.  21
    Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic.Elena Aladova, Pablo Barceló, Johan van Benthem, Gerald Berger, Katrin M. Dannert, Neil Dewar, Răzvan Diaconescu, Ivo Düntsch, Wojciech Dzik, M. Eyad Kurd-Misto, Giambattista Formica, Michèle Friend, Robert Goldblatt, Georg Gottlob, Erich Grädel, Robin Hirsch, Ian Hodkinson, Marcel Jackson, Peter Jipsen, Roger D. Maddux, J. B. Manchak, Ewa Orłowska, Andreas Pieris, Boris Plotkin, Tatjana Plotkin, Vaughan R. Pratt, Ian Pratt-Hartmann, Tarek Sayed Ahmed, James Owen Weatherall, Dag Westerståhl, James Wimberley, Krzysztof Wójtowicz & Christian Wüthrich (eds.) - 2021 - Springer Verlag.
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  40.  1
    Advances in Modal Logic, Volume 7: Papers From the Seventh Advances in Modal Logic Conference, Held in Nancy, France, September 2008.Carlos Areces & Robert Goldblatt (eds.) - 2008 - London, England: College Publications.
  41. Equational Logic of Polynominal Coalgerbras.Robert Goldblatt - 2003 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 149-184.
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  42. Modal Logics of Some Hereditarily Irresolvable Spaces.Robert Goldblatt - 2022 - In Ivo Düntsch & Edwin Mares (eds.), Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Springer Verlag. pp. 303-322.
    A topological space is hereditarilyk-irresolvable if none of its subspaces can be partitioned into k dense subsets. We use this notion to provide a topological semantics for a sequence of modal logics whose n-th member K4Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}_n$$\end{document} is characterised by validity in transitive Kripke frames of circumference at most n. We show that under the interpretation of the modality ◊\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Diamond $$\end{document} as the (...)
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  43. Modal Logics That Bound the Circumference of Transitive Frames.Robert Goldblatt - 2021 - In Elena Aladova, Pablo Barceló, Johan van Benthem, Gerald Berger, Katrin M. Dannert, Neil Dewar, Răzvan Diaconescu, Ivo Düntsch, Wojciech Dzik, M. Eyad Kurd-Misto, Giambattista Formica, Michèle Friend, Robert Goldblatt, Georg Gottlob, Erich Grädel, Robin Hirsch, Ian Hodkinson, Marcel Jackson, Peter Jipsen, Roger D. Maddux, J. B. Manchak, Ewa Orłowska, Andreas Pieris, Boris Plotkin, Tatjana Plotkin, Vaughan R. Pratt, Ian Pratt-Hartmann, Tarek Sayed Ahmed, James Owen Weatherall, Dag Westerståhl, James Wimberley, Krzysztof Wójtowicz & Christian Wüthrich (eds.), Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic. Springer Verlag. pp. 233-265.
    For each natural number n we study the modal logic determined by the class of transitive Kripke frames in which there are no cycles of length greater than n and no strictly ascending chains. The case n=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=0$$\end{document} is the Gödel-Löb provability logic. Each logic is axiomatised by adding a single axiom to K4, and is shown to have the finite model property and be decidable. We then consider a number of extensions (...)
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  44.  8
    Definable Operators on Stable Set Lattices.Robert Goldblatt - 2020 - Studia Logica 108 (6):1263-1280.
    A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose (...)
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  45.  21
    Stål Anderaa (Oslo), A Traktenbrot Inseparability Theorem for Groups. Peter Dybjer (G Öteborg), Normalization by Yoneda Embedding (Joint Work with D. Cubric and PJ Scott). Abbas Edalat (Imperial College), Dynamical Systems, Measures, Fractals, and Exact Real Number Arithmetic Via Domain Theory. [REVIEW]Anita Feferman, Solomon Feferman, Robert Goldblatt, Yuri Gurevich, Klaus Grue, Sven Ove Hansson, Lauri Hella, Robert K. Meyer & Petri Mäenpää - 1997 - Bulletin of Symbolic Logic 3 (4).
  46.  28
    Vaughan R. Pratt. Semantical Considerations on Floyd–Hoare Logic. 17th Annual Symposium on Foundations of Computer Science, Institute of Electrical and Electronics Engineers, New York1976, Pp. 109–121. - Michael J. Fischer and Richard E. Ladner. Propositional Dynamic Logic of Regular Programs. Journal of Computer and System Sciences, Vol. 18 , Pp. 194–211. - Krister Segerberg. A Completeness Theorem in the Modal Logic of Programs. Universal Algebra and Applications. Papers Presented at Stefan Banach International Mathematical Center at the Semester “Universal Algebra and Applications” Held February 15–June 9, 1978, Edited by Tadeuz Traczyk, Banach Center Publications, Vol. 9, PWN—Polish Scientific Publishers, Warsaw1982, Pp. 31–46. - Rohit Parikh. The Completeness of Propositional Dynamic Logic. Mathematical Foundations of Computer Science 1978, Proceedings, 7th Symposium, Zakopane, Poland, September 4–8, 1978, Edited by J. Winkowski, Lecture Notes in Computer Science, Vol. 64, Springe. [REVIEW]Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
  47.  7
    Strong Completeness of Modal Logics Over 0-Dimensional Metric Spaces.Robert Goldblatt & Ian Hodkinson - 2020 - Review of Symbolic Logic 13 (3):611-632.
    We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.
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  48.  16
    “Locally-at” as a Topological Quantifier-Former.Robert Goldblatt - 1981 - In U. Mönnich (ed.), Aspects of Philosophical Logic. Dordrecht. pp. 119--127.
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  49.  13
    Observational Ultraproducts of Polynomial Coalgebras.Robert Goldblatt - 2003 - Annals of Pure and Applied Logic 123 (1-3):235-290.
    Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and state-transition systems. This paper continues the study of equational logic and model theory for polynomial coalgebras begun in Goldblatt , where it was shown that Boolean combinations of equations between terms of observable type form a natural language of observable formulas for specifying properties of polynomial coalgebras, and for giving a Hennessy–Milner style logical characterisation of observational indistinguishability of (...)
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  50.  19
    Grishin Algebras and Cover Systems for Classical Bilinear Logic.Robert Goldblatt - 2011 - Studia Logica 99 (1-3):203-227.
    Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (“propositions”) of cover systems that use an orthogonality relation to interpret the negations. The variety of Grishin algebras is shown to be closed under MacNeille completion, and this is applied to embed an arbitrary Grishin algebra into the algebra of all propositions of some cover system, (...)
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