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1. The origin of relation algebras in the development and axiomatization of the calculus of relations.Roger D. Maddux - 1991 - 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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2. 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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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. A sequent calculus for relation algebras.Roger Maddux - 1983 - Annals of Pure and Applied Logic 25 (1):73-101.

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5. 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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6. Finitary Algebraic Logic.Roger D. Maddux - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (4):321-332.

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7. Relevance logic and the calculus of relations.Roger D. Maddux - 2010 - 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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8. Finitary Algebraic Logic.Roger D. Maddux - 1989 - Mathematical Logic Quarterly 35 (4):321-332.

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9. Relevance logics and relation algebras.Katalin Bimbó, J. Michael Dunn & Roger D. Maddux - 2009 - 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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10. Relation algebras of every dimension.Roger D. Maddux - 1992 - 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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11. The equational theory of CA 3 is undecidable.Roger Maddux - 1980 - Journal of Symbolic Logic 45 (2):311 - 316.

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12. Representations for Small Relation Algebras.Hajnal Andréka & Roger D. Maddux - 1994 - Notre Dame Journal of Formal Logic 35 (4):550-562.
There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.

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13. Finitary algebraic logic II.Roger D. Maddux - 1993 - Mathematical Logic Quarterly 39 (1):566-569.
This is a supplement to the paper “Finitary Algebraic Logic” [1]. It includes corrections for several errors and some additional results. MSC: 03G15, 03G25.

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14. Undecidable semiassociative relation algebras.Roger D. Maddux - 1994 - 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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15. 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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18.
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19.
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20. Review: H. Andreka, T. Gergely, I. Nemeti, On Universal Algebraic Constructions of Logics. [REVIEW]Roger Maddux - 1981 - Journal of Symbolic Logic 46 (3):663-664.

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21.
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22. Finite, integral, and finite-dimensional relation algebras: a brief history.Roger D. Maddux - 2004 - Annals of Pure and Applied Logic 127 (1-3):117-130.
Relation algebras were invented by Tarski and his collaborators in the middle of the 20th century. The concept of integrality arose naturally early in the history of the subject, as did various constructions of finite integral relation algebras. Later the concept of finite-dimensionality was introduced for classifying nonrepresentable relation algebras. This concept is closely connected to the number of variables used in proofs in first-order logic. Some results on these topics are presented in chronological order.

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23. H. Andréka, T. Gergely, and I. Németi. On universal algebraic constructions of logics. Studia logica, vol. 36 , pp. 9–47. [REVIEW]Roger Maddux - 1981 - Journal of Symbolic Logic 46 (3):663-664.

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24. Review: Maarten Marx, Laszlo Polos, Michael Masuch, Arrow Logic and Multi-Modal Logic. [REVIEW]Roger Maddux - 1998 - Journal of Symbolic Logic 63 (1):333-336.

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25.
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26. Alfred Tarski, Life and Logic. [REVIEW]Roger D. Maddux - 2005 - Bulletin of Symbolic Logic 11 (4):535-540.

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28. Anita Burdman Feferman and Solomon Feferman. Alfred Tarski, Life and Logic Cambridge University Press, Cambridge, 2004, vi + 425 pp. [REVIEW]Roger D. Maddux - 2005 - Bulletin of Symbolic Logic 11 (4):535-540.

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29. Books received. [REVIEW]Janusz Czelakowski, Roger Maddux, Gerhard Schurz & Kazimierz Trzesicki - 1986 - Studia Logica 45 (2):425-430.

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30. books to ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA.Julia Knight, Michael C. Laskowski, Roger Maddux, Volker Peckhaus & Wolfram Pohlers - 2004 - Bulletin of Symbolic Logic 10 (3).

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31. Schechter Eric. Classical and nonclassical logic: an introduction to the mathematics of propositions. Princeton University Press, Princeton and Oxford, 2005, x+ 507 pp. [REVIEW]Roger D. Maddux - 2006 - Bulletin of Symbolic Logic 12 (2):308-309.
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34. On the number of variables required for proofs.Robin Hirsch, I. Hodkinson & Roger Maddux - 2002 - Journal of Symbolic Logic 67 (1):197-213.

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36. REVIEWS-Decision problems for equational theories of relation algebras.H. Andreka, S. Givant, I. Nemeti & Roger D. Maddux - 2003 - Bulletin of Symbolic Logic 9 (1):37-38.

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38. Robin Hirsch and Ian Hodkinson. Relation algebras by games. Elsevier, Amsterdam, 2002, xviii + 691 pp. [REVIEW]Roger D. Maddux - 2003 - Bulletin of Symbolic Logic 9 (4):515-520.

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39. Review: Leon Henkin, J. Donald Monk, Alfred Tarski, Cylindric Algebras. Part II. [REVIEW]Roger D. Maddux - 1988 - Journal of Symbolic Logic 53 (2):651-653.

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