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Robert Goldblatt [58]Robert I. Goldblatt [2]
  1.  11
    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.  13
    [Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
  4.  19
    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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  5.  32
    Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
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  6.  48
    Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
  7.  2
    Quantifiers, propositions and identity: admissible semantics for quantified modal and substructural logics.Robert Goldblatt - 2011 - New York: Cambridge University Press.
    Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of (...)
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  8.  25
    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.  14
    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.  23
    Axiomatising the Logic of Computer Programming.Robert Goldblatt - 1985 - Journal of Symbolic Logic 50 (3):854-855.
  11.  38
    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.
  12.  13
    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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  13.  16
    The McKinsey axiom is not canonical.Robert Goldblatt - 1991 - Journal of Symbolic Logic 56 (2):554-562.
  14.  18
    Orthogonality and Spacetime Geometry.Robert Goldblatt - 1990 - Philosophy of Science 57 (2):335-336.
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  15.  27
    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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  16.  11
    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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  17.  7
    Orthomodularity is not elementary.Robert Goldblatt - 1984 - Journal of Symbolic Logic 49 (2):401-404.
  18.  35
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Mathematical Logic Quarterly 27 (31‐35):495-529.
  19.  35
    Grothendieck Topology as Geometric Modality.Robert I. Goldblatt - 1981 - Mathematical Logic Quarterly 27 (31-35):495-529.
  20.  9
    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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  21.  95
    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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  22.  16
    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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  23.  21
    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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  24.  4
    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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  25.  21
    A General Semantics for Quantified Modal Logic.Robert Goldblatt & Edwin D. Mares - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. 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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  26.  28
    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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  27.  20
    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.  9
    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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  29.  18
    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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  30.  32
    On canonical modal logics that are not elementarily determined.Robert Goldblatt, Ian Hodkinson & Yde Venema - 2003 - Logique Et Analyse 181:77-101.
  31.  11
    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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  32.  11
    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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  33.  9
    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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  34.  13
    A Kripke-Joyal Semantics for Noncommutative Logic in Quantales.Robert Goldblatt - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 209-225.
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  35.  10
    A Kripke-Joyal Semantics for Noncommutative Logic in Quantales.Robert Goldblatt - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 209-225.
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  36.  10
    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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  37. Mereocompactness and Duality for Mereotopological Spaces.Matt Grice & Robert Goldblatt - 2016 - In Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics. Cham, Switzerland: Springer.
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  38.  3
    Strong completeness of a first-order temporal logic for real time.Robert Goldblatt - forthcoming - Review of Symbolic Logic:1-16.
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  39.  13
    Quasi-modal equivalence of canonical structures.Robert Goldblatt - 2001 - Journal of Symbolic Logic 66 (2):497-508.
    A first-order sentence is quasi-modal if its class of models is closed under the modal validity preserving constructions of disjoint unions, inner substructures and bounded epimorphic images. It is shown that all members of the proper class of canonical structures of a modal logic Λ have the same quasi-modal first-order theory Ψ Λ . The models of this theory determine a modal logic Λ e which is the largest sublogic of Λ to be determined by an elementary class. The canonical (...)
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  40.  16
    A General Semantic for Quantified Modal Logic.Robert Goldblatt & Edwin D. Mares - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 227-246.
    In "An Alternative Semantics for Quantified Relevant Logic" (JSL 71 (2006)) we developed a semantics for quantified relevant logic that uses general frames. In this paper, we adapt that model theory to treat quantified modal logics, giving a complete semantics to the quantified extensions, both with and without the Barcan formula, of every proposi- tional modal logic S. If S is canonical our models are based on propositional frames that validate S. We employ frames in which not every set of (...)
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  41.  22
    Relativised quantification: Some canonical varieties of sequence-set algebras.Hajnal Andréka, Robert Goldblatt & István Németi - 1998 - Journal of Symbolic Logic 63 (1):163-184.
  42. Relativised Quantification: Some Canonical Varieties of Sequence-Set Algebras.Hajnal Andreka, Robert Goldblatt & Istvan Nemeti - 1998 - Journal of Symbolic Logic 63 (1):163-184.
     
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  43.  5
    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.
  44.  7
    Canonicity in Power and Modal Logics of Finite Achronal Width.Robert Goldblatt & Ian Hodkinson - forthcoming - Review of Symbolic Logic:1-31.
    We develop a method for showing that various modal logics that are valid in their countably generated canonical Kripke frames must also be valid in their uncountably generated ones. This is applied to many systems, including the logics of finite width, and a broader class of multimodal logics of ‘finite achronal width’ that are introduced here.
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  45.  15
    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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  46.  9
    Equational Logic of Polynominal Coalgerbras.Robert Goldblatt - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 149-184.
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  47.  4
    Equational Logic of Polynominal Coalgerbras.Robert Goldblatt - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 149-184.
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  48.  14
    First-order spacetime geometry.Robert Goldblatt - 1989 - In Jens Erik Fenstad, Ivan Timofeevich Frolov & Risto Hilpinen (eds.), Logic, methodology, and philosophy of science VIII: proceedings of the Eighth International Congress of Logic, Methodology, and Philosophy of Science, Moscow, 1987. New York, NY, U.S.A.: Sole distributors for the U.S.A. and Canada, Elsevier Science.
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  49.  9
    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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  50.  19
    “Locally-at” as a Topological Quantifier-Former.Robert Goldblatt - 1981 - In Uwe Mönnich (ed.), Aspects of Philosophical Logic: Some Logical Forays Into Central Notions of Linguistics and Philosophy. Dordrecht, Netherland: Dordrecht. pp. 119--127.
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