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  1. 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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  2. Roger D. Maddux (2010). Relevance Logic and the Calculus of Relations. Review of Symbolic Logic 3 (1):41-70.
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  3. Katalin Bimbó, J. Michael Dunn & Roger D. Maddux (2009). Relevance Logics and Relation Algebras. Review of Symbolic Logic 2 (1):102-131.
    Relevance logics are known to be sound and complete for relational semantics with a ternary accessibility relation. This paper investigates the problem of adequacy with respect to special kinds of dynamic semantics (i.e., proper relation algebras and relevant families of relations). We prove several soundness results here. We also prove the completeness of a certain positive fragment of R as well as of the first-degree fragment of relevance logics. These results show that some core ideas are shared between relevance logics (...)
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  4. Roger D. Maddux (2006). Schechter Eric. Classical and Nonclassical Logic: An Introduction to the Mathematics of Propositions. Princeton University Press, Princeton and Oxford, 2005, X+ 507 Pp. [REVIEW] Bulletin of Symbolic Logic 12 (2):308-309.
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  5. A. B. Feferman, S. Feferman & Roger D. Maddux (2005). REVIEWS-Alfred Tarski, Life and Logic. Bulletin of Symbolic Logic 11 (4):535-540.
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  6. Roger D. Maddux (2004). Finite, Integral, and Finite-Dimensional Relation Algebras: A Brief History. Annals of Pure and Applied Logic 127 (1-3):117-130.
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  7. H. Andreka, S. Givant, I. Nemeti & Roger D. Maddux (2003). REVIEWS-Decision Problems for Equational Theories of Relation Algebras. Bulletin of Symbolic Logic 9 (1):37-38.
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  8. 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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  9. Roger D. Maddux (2003). Andréka H., Givant S., and Németi I.. Decision Problems for Equational Theories of Relation Algebras. Memoirs of the American Mathematical Society, Vol. 126, No. 604. American Mathematical Society, Providence, March 1997, Xiv+ 126 Pp. [REVIEW] Bulletin of Symbolic Logic 9 (1):37-39.
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  10. Roger D. Maddux (2003). Hirsch Robin and Hodkinson Ian. Relation Algebras by Games. Elsevier, Amsterdam, 2002, Xviii+ 691 Pp. [REVIEW] Bulletin of Symbolic Logic 9 (4):515-520.
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  11. 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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  12. 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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  13. Hajnal Andréka & Roger D. Maddux (1994). Representations for Small Relation Algebras. Notre Dame Journal of Formal Logic 35 (4):550-562.
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  14. Hajnal Andr Eka & Roger D. Maddux (1994). Representations for Small Relation Algebras. Notre Dame Journal of Formal Logic 35 (4).
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  15. Roger D. Maddux (1994). Undecidable Semiassociative Relation Algebras. Journal of Symbolic Logic 59 (2):398-418.
    If K is a class of semiassociative relation algebras and K contains the relation algebra of all binary relations on a denumerable set, then the word problem for the free algebra over K on one generator is unsolvable. This result implies that the set of sentences which are provable in the formalism Lwx is an undecidable theory. A stronger algebraic result shows that the set of logically valid sentences in Lwx forms a hereditarily undecidable theory in Lwx. These results generalize (...)
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  16. Roger D. Maddux (1993). Finitary Algebraic Logic II. Mathematical Logic Quarterly 39 (1):566-569.
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  17. Roger D. Maddux (1992). Relation Algebras of Every Dimension. Journal of Symbolic Logic 57 (4):1213-1229.
    Conjecture (1) of [Ma83] is confirmed here by the following result: if $3 \leq \alpha < \omega$, then there is a finite relation algebra of dimension α, which is not a relation algebra of dimension α + 1. A logical consequence of this theorem is that for every finite α ≥ 3 there is a formula of the form $S \subseteq T$ (asserting that one binary relation is included in another), which is provable with α + 1 variables, but not (...)
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  18. Roger D. Maddux (1991). The Origin of Relation Algebras in the Development and Axiomatization of the Calculus of Relations. Studia Logica 50 (3-4):421 - 455.
    The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and the (...)
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  19. Roger D. Maddux (1989). Finitary Algebraic Logic. Mathematical Logic Quarterly 35 (4):321-332.
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  20. Roger D. Maddux (1989). Nonfinite Axiomatizability Results for Cylindric and Relation Algebras. 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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  21. Roger D. Maddux (1988). Review: Leon Henkin, J. Donald Monk, Alfred Tarski, Cylindric Algebras. Part II. [REVIEW] Journal of Symbolic Logic 53 (2):651-653.
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