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  1. Modal Foundations for Predicate Logic.Johan van Benthem - 1997 - Logic Journal of the IGPL 5 (2):259-286.
    The complexity of any logical modeling reflects both the intrinsic structure of a topic described and the weight of the formal tools. Some of this weight seems inherent in even the most basic logical systems. Notably, standard predicate logic is undecidable. In this paper, we investigate ‘lighter’ versions of this general purpose tool, by modally ‘deconstructing’ the usual semantics, and locating implicit choice points in its set up. The first part sets out the interest of this program and the modal (...)
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  • Dynamic Squares.Patrick Blackburn & Yde Venema - 1995 - Journal of Philosophical Logic 24 (5):469 - 523.
  • Sahlqvist's Theorem for Boolean Algebras with Operators with an Application to Cylindric Algebras.Maarten de Rijke & Yde Venema - 1995 - Studia Logica 54 (1):61-78.
    For an arbitrary similarity type of Boolean Algebras with Operators we define a class ofSahlqvist identities. Sahlqvist identities have two important properties. First, a Sahlqvist identity is valid in a complex algebra if and only if the underlying relational atom structure satisfies a first-order condition which can be effectively read off from the syntactic form of the identity. Second, and as a consequence of the first property, Sahlqvist identities arecanonical, that is, their validity is preserved under taking canonical embedding algebras. (...)
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  • The World is the Totality of Facts, Not of Things.Agustín Rayo - 2017 - Philosophical Issues 27 (1):250-278.
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  • La conscience de l'observateur: de la physique théorique à la logique mathématique.Yvon Provençal - 1977 - Dialogue 16 (2):228-244.
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  • Boolean Sentence Algebras: Isomorphism Constructions.William P. Hanf & Dale Myers - 1983 - Journal of Symbolic Logic 48 (2):329-338.
    Associated with each first-order theory is a Boolean algebra of sentences and a Boolean space of models. Homomorphisms between the sentence algebras correspond to continuous maps between the model spaces. To what do recursive homomorphisms correspond? We introduce axiomatizable maps as the appropriate dual. For these maps we prove a Cantor-Bernstein theorem. Duality and the Cantor-Bernstein theorem are used to show that the Boolean sentence algebras of any two undecidable languages or of any two functional languages are recursively isomorphic where (...)
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  • On the Number of Generators of Cylindric Algebras.H. Andréka & I. Németi - 1985 - Journal of Symbolic Logic 50 (4):865-873.
  • The Number of One-Generated Cylindric Set Algebras of Dimension Greater Than Two.Jean A. Larson - 1985 - Journal of Symbolic Logic 50 (1):59-71.
    S. Ulam asked about the number of nonisomorphic projective algebras with k generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of nonisomorphic one-generated structures of finite dimension n, where n is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, cylindric set algebras, and cylindric algebras. The results of this paper extend earlier (...)
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  • Weak Cylindric Set Algebras and Weak Subdirect Indecomposability.H. Andréka, I. Németi & R. J. Thompson - 1990 - Journal of Symbolic Logic 55 (2):577-588.
    In this note we prove that the abstract property "weakly subdirectly indecomposable" does not characterize the class IWs α of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWs α . The original property does characterize the directed unions of members of $\mathrm{IWs}_alpha \operatorname{iff} \alpha$ is countable. Free algebras will be shown to satisfy the original property.
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  • Cylindric Algebras with Terms.Norman Feldman - 1990 - Journal of Symbolic Logic 55 (2):854-866.
  • Nonfinite Axiomatizability Results for Cylindric and Relation Algebras.Roger D. Maddux - 1989 - Journal of Symbolic Logic 54 (3):951-974.
    The set of equations which use only one variable and hold in all representable relation algebras cannot be derived from any finite set of equations true in all representable relation algebras. Similar results hold for cylindric algebras and for logic with finitely many variables. The main tools are a construction of nonrepresentable one-generated relation algebras, a method for obtaining cylindric algebras from relation algebras, and the use of relation algebras in defining algebraic semantics for first-order logic.
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  • Cylindric Modal Logic.Yde Venema - 1995 - Journal of Symbolic Logic 60 (2):591-623.
    Treating the existential quantification ∃ν i as a diamond $\diamond_i$ and the identity ν i = ν j as a constant δ ij , we study restricted versions of first order logic as if they were modal formalisms. This approach is closely related to algebraic logic, as the Kripke frames of our system have the type of the atom structures of cylindric algebras; the full cylindric set algebras are the complex algebras of the intended multidimensional frames called cubes. The main (...)
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  • Relational Proof System for Relevant Logics.Ewa Orlowska - 1992 - Journal of Symbolic Logic 57 (4):1425-1440.
    A method is presented for constructing natural deduction-style systems for propositional relevant logics. The method consists in first translating formulas of relevant logics into ternary relations, and then defining deduction rules for a corresponding logic of ternary relations. Proof systems of that form are given for various relevant logics. A class of algebras of ternary relations is introduced that provides a relation-algebraic semantics for relevant logics.
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  • Perfect Extensions and Derived Algebras.Hajnal Andréka, Steven Givant & István Németi - 1995 - Journal of Symbolic Logic 60 (3):775-796.
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  • Using Mathematica to Understand the Computer Proof of the Robbins Conjecture.Branden Fitelson - manuscript
    mathematicians for over 60 years. Amazingly, the Argonne team's automated theorem-proving program EQP took only 8 days to find a proof of it. Unfortunately, the proof found by EQP is quite complex and difficult to follow. Some of the steps of the EQP proof require highly complex and unintuitive substitution strategies. As a result, it is nearly impossible to reconstruct or verify the computer proof of the Robbins conjecture entirely by hand. This is where the unique symbolic capabilities of Mathematica (...)
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  • On Universal Algebraic Constructions of Logics.H. Andréka, T. Gergely & I. Németi - 1977 - Studia Logica 36 (1-2):9 - 47.
  • Visions of Henkin.María Manzano & Enrique Alonso - 2015 - Synthese 192 (7):2123-2138.
    Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his articles with (...)
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  • Stone Space of Cylindric Algebras and Topological Model Spaces.Charles C. Pinter - 2016 - Journal of Symbolic Logic 81 (3):1069-1086.
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  • Zusammenhang zwischen der TheorieF der Faktorenimplikation und der Theorie der Zylinderalgebren, Reduktion der Vollständigkeit der Axiome vonF.August Plattner - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):561-572.
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