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Profile: Roni Hirsch (Tel Aviv University)
Profile: Robbie Hirsch (Princeton University)
  1. Step by Step-Building Representations in Algebraic Logic.Robin Hirsch & Ian Hodkinson - 1997 - 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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  2. On Modal Logics Between K × K × K and $S5 \Times S5 \Times S5$.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - 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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  3. Relation Algebra Reducts of Cylindric Algebras and an Application to Proof Theory.Robin Hirsch, Ian Hodkinson & Roger D. Maddux - 2002 - 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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  4.  43
    Maudlin's Mathematical Maneuver: A Case Study in the Metaphysical Implications of Mathematical Representations.Robert J. Hirsch - 2015 - Philosophy and Phenomenological Research 93 (3).
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  5.  10
    Maudlin's Mathematical Maneuver: A Case Study in the Metaphysical Implications of Mathematical Representations.Robert J. Hirsch - 2017 - Philosophy and Phenomenological Research 94 (1):170-210.
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  6.  20
    Provability with Finitely Many Variables.Robin Hirsch, Ian Hodkinson & Roger D. Maddux - 2002 - 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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  7. On Modal Logics Between K × K × K and S5 × S5 × S.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
  8.  17
    Complete Representations in Algebraic Logic.Robin Hirsch & Ian Hodkinson - 1997 - 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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  9.  4
    Relation Algebras with N-Dimensional Relational Bases.Robin Hirsch & Ian Hodkinson - 2000 - Annals of Pure and Applied Logic 101 (2-3):227-274.
    We study relation algebras with n-dimensional relational bases in the sense of Maddux. Fix n with 3nω. Write Bn for the class of non-associative algebras with an n-dimensional relational basis, and RAn for the variety generated by Bn. We define a notion of relativised representation for algebras in RAn, and use it to give an explicit equational axiomatisation of RAn, and to reprove Maddux's result that RAn is canonical. We show that the algebras in Bn are precisely those that have (...))
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  10.  8
    Strongly Representable Atom Structures of Cylindric Algebras.Robin Hirsch & Ian Hodkinson - 2009 - 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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  11.  3
    Relation Algebras From Cylindric Algebras, II.Robin Hirsch & Ian Hodkinson - 2001 - Annals of Pure and Applied Logic 112 (2-3):267-297.
    We prove, for each 4⩽ n ω , that S Ra CA n+1 cannot be defined, using only finitely many first-order axioms, relative to S Ra CA n . The construction also shows that for 5⩽n S Ra CA n is not finitely axiomatisable over RA n , and that for 3⩽m S Nr m CA n+1 is not finitely axiomatisable over S Nr m CA n . In consequence, for a certain standard n -variable first-order proof system ⊢ m (...)
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  12.  1
    Relation Algebras From Cylindric Algebras, I.Robin Hirsch & Ian Hodkinson - 2001 - Annals of Pure and Applied Logic 112 (2-3):225-266.
    We characterise the class S Ra CA n of subalgebras of relation algebra reducts of n -dimensional cylindric algebras by the notion of a ‘hyperbasis’, analogous to the cylindric basis of Maddux, and by representations. We outline a game–theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of S Ra CA n.
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  13.  12
    How Informed is Online Informed Consent?K. Varnhagen Connie, Gushta Matthew, Daniels Jason, C. Peters Tara, Parmar Neil, Law Danielle, Hirsch Rachel, Sadler Takach Bonnie & Johnson Tom - 2005 - Ethics and Behavior 15 (1):37-48.
    We examined participants' reading and recall of informed consent documents presented via paper or computer. Within each presentation medium, we presented the document as a continuous or paginated document to simulate common computer and paper presentation formats. Participants took slightly longer to read paginated and computer informed consent documents and recalled slightly more information from the paginated documents. We concluded that obtaining informed consent online is not substantially different than obtaining it via paper presentation. We also provide suggestions for improving (...)
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  14. On Modal Logics Between {$\Roman K\Times\Roman K\Times \Roman K$} and {${\Rm S}5\Times{\Rm S}5\Times{\Rm S}5$}.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
  15.  48
    A Finite Relation Algebra with Undecidable Network Satisfaction Problem.Robin Hirsch - 1999 - Logic Journal of the IGPL 7 (4):547-554.
    We define a finite relation algebra and show that the network satisfaction problem is undecidable for this algebra.
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  16.  36
    Mosaics and Step-by-Step| Remarks onA Modal Logic of Relations' by Venema & Marx.Robin Hirsch & Ian Hodkinson - 1999 - In E. Orłowska (ed.), Logic at Work. Heidelberg.
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  17.  54
    Meet-Completions and Representations of Ordered Domain Algebras.R. Hirsch & R. Egrot - forthcoming - Journal of Symbolic Logic.
  18.  64
    Reply to Commentators.Review author[S.]: Eli Hirsch - 1996 - Philosophy and Phenomenological Research 56 (1):223-234.
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  19.  37
    Peter Van Inwagen's Material Beings.Review author[S.]: Eli Hirsch - 1993 - Philosophy and Phenomenological Research 53 (3):687-691.
  20.  14
    Der Erste Kritiker Marxens.Rudolf Hirsch - 1957 - Zeitschrift für Religions- Und Geistesgeschichte 9 (3):246-257.
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  21.  4
    Axiomatising Various Classes of Relation and Cylindric Algebras.Robin Hirsch & Ian Hodkinson - 1997 - Logic Journal of the IGPL 5 (2):209-229.
    We outline a simple approach to axiomatising the class of representable relation algebras, using games. We discuss generalisations of the method to cylindric algebras, homogeneous and complete representations, and atom structures of relation algebras.
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  22.  15
    Positive Fragments of Relevance Logic and Algebras of Binary Relations.Robin Hirsch & Szabolcs Mikulás - 2010 - Review of Symbolic Logic 4 (1):81-105.
    We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
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  23. On Modal Logics Between â â à and Ë¢ Ë¢ Ë.R. Hirsch, I. Hodkinson & A. Kurucz - forthcoming - Journal of Symbolic Logic.
  24.  16
    On the Number of Variables Required for Proofs.R. Hirsch, I. Hodkinson & Roger Maddux - 2002 - Journal of Symbolic Logic 67 (1):197-213.
  25.  2
    Meet-Completions and Ordered Domain Algebras.R. Egrot & R. Hirsch - 2015 - Logic Journal of the IGPL 23 (4):584-600.
  26.  11
    Undecidability of Representability as Binary Relations.Robin Hirsch & Marcel Jackson - 2012 - Journal of Symbolic Logic 77 (4):1211-1244.
    In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.
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  27.  7
    From Points to Intervals.Robin Hirsch - 1994 - Journal of Applied Non-Classical Logics 4 (1):7-27.
  28.  4
    Weak Representations of Relation Algebras and Relational Bases.Robin Hirsch, Ian Hodkinson & Roger D. Maddux - 2011 - 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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  29.  8
    Relation Algebra Reducts of Cylindric Algebras and Complete Representations.Robin Hirsch - 2007 - Journal of Symbolic Logic 72 (2):673 - 703.
    We show, for any ordinal γ ≥ 3, that the class RaCAγ is pseudo-elementary and has a recursively enumerable elementary theory. ScK denotes the class of strong subalgebras of members of the class K. We devise games, Fⁿ (3 ≤ n ≤ ω), G, H, and show, for an atomic relation algebra A with countably many atoms, that Ǝ has a winning strategy in Fω(At(A)) ⇔ A ∈ ScRaCAω, Ǝ has a winning strategy in Fⁿ(At(A)) ⇐ A ∈ ScRaCAn, Ǝ (...)
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  30.  1
    Ordered Domain Algebras.Robin Hirsch & Szabolcs Mikulás - 2013 - Journal of Applied Logic 11 (3):266-271.
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  31.  1
    Corrigendum To:“Relation Algebra Reducts of Cylindric Algebras and Complete Representations”.R. D. Hirsch - 2013 - Journal of Symbolic Logic 78 (4):1345-1346.
  32. Complete Representations in Algebraic Logic.Robin Hirsch & Ian Hodkinson - 1997 - 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 are elementary.
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  33. Language as Reflective Experience.Richard Hirsch - 2010 - Semiotica 2010 (182):215-228.
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  34. Mosaics and Step-by-Step. Remarks on “A Modal Logic of Relations”.Robin Hirsch, Ian Hodkinson, Maarten Marx, Szabolsc Mikulás & Mark Reynolds - 1999 - In E. Orłowska (ed.), Logic at Work. Heidelberg.
     
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  35. Maudlin's Mathematical Maneuver: A Case Study in the Metaphysical Implications of Mathematical Representations.Robert J. Hirsch - 2017 - Latest Issue of Philosophy and Phenomenological Research 94 (1):170-210.
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  36. Step by Step-Building Representations in Algebraic Logic.Robin Hirsch & Ian Hodkinson - 1997 - 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 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 algebra is $\omega$-categorical. We (...)
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  37. The Neat Embedding Problem for Algebras Other Than Cylindric Algebras and for Infinite Dimensions.Robin Hirsch & Tarek Sayed Ahmed - 2014 - Journal of Symbolic Logic 79 (1):208-222.