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  1. Logical Reasoning with Diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - Oxford University Press.
    One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore (...)
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  2.  61
    Kripke Models for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58 (2):514-545.
    We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding a coimplication operator, (...)
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  3.  1
    Language, Proof and Logic.Jon Barwise, John Etchemendy, Gerard Allwein & Dave Barker-Plummer - 2001 - Bulletin of Symbolic Logic 7 (3):377-379.
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  4. A Kripke Semantics for Linear Logic.Gerard Allwein & J. Michael Dunn - 1993 - Journal of Symbolic Logic 58:514-545.
     
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  5.  4
    Toward the Rigorous Use of Diagrams in Reasoning About Hardware.Steven D. Johnson, Jon Barwise & Gerard Allwein - 1996 - In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press.
  6.  26
    A Kripke Semantics for the Logic of Gelfand Quantales.Gerard Allwein & Wendy MacCaull - 2001 - Studia Logica 68 (2):173-228.
    Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for (...)
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  7.  6
    Special Issue: Methods for Investigating Self-Referential Truth Edited by Volker Halbach Volker Halbach/Editorial Introduction 3.Petr Hájek, Arithmetical Hierarchy Iii, Gerard Allwein & Wendy MacCaull - 2001 - Studia Logica 68:421-422.
  8.  2
    Distributed Relation Logic.Gerard Allwein, William L. Harrison & Thomas Reynolds - 2017 - Logic and Logical Philosophy 26 (1):19-61.
    We extend the relational algebra of Chin and Tarski so that it is multisorted or, as we prefer, typed. Each type supports a local Boolean algebra outfitted with a converse operator. From Lyndon, we know that relation algebras cannot be represented as proper relation algebras where a proper relation algebra has binary relations as elements and the algebra is singly-typed. Here, the intensional conjunction, which was to represent relational composition in Chin and Tarski, spans three different local algebras, thus the (...)
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    A Case Study of the Design and Implementation of Heterogeneous Reasoning Systems.Nik Swoboda & Gerard Allwein - 2002 - In L. Magnani, N. J. Nersessian & C. Pizzi (eds.), Logical and Computational Aspects of Model-Based Reasoning. Kluwer Academic Publishers. pp. 3--20.
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  10.  16
    Qualitative Decision Theory Via Channel Theory.Gerard Allwein, Yingrui Yang & William L. Harrison - 2011 - Logic and Logical Philosophy 20 (1-2):81-110.
    We recast parts of decision theory in terms of channel theory concentrating on qualitative issues. Channel theory allows one to move between model theoretic and language theoretic notions as is necessary for an adequate covering. Doing so clarifies decision theory and presents the opportunity to investigate alternative formulations. As an example, we take some of Savage’s notions of decision theory and recast them within channel theory. In place of probabilities, we use a particular logic of preference. We introduce a logic (...)
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  11.  26
    Logics for Classes of Boolean Monoids.Gerard Allwein, Hilmi Demir & Lee Pike - 2004 - Journal of Logic, Language and Information 13 (3):241-266.
    This paper presents the algebraic and Kripke modelsoundness and completeness ofa logic over Boolean monoids. An additional axiom added to thelogic will cause the resulting monoid models to be representable as monoidsof relations. A star operator, interpreted as reflexive, transitiveclosure, is conservatively added to the logic. The star operator isa relative modal operator, i.e., one that is defined in terms ofanother modal operator. A further example, relative possibility,of this type of operator is given. A separate axiom,antilogism, added to the logic (...)
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    Simulation Logic.Gerard Allwein, William L. Harrison & David Andrews - 2014 - Logic and Logical Philosophy 23 (3).
    Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory. However, the simulation condition is strictly a first-order logic statement. We extend modal logic with modalities and axioms, the latter’s modeling conditions are the simulation conditions. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The simulations are considered arrows in a category where the objects are descriptive, general frames. One can augment the simulation (...)
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    Diagrams and Non-Monotonicity in Puzzles.Benedek Nagy & Gerard Allwein - 2004 - In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. pp. 82--96.
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  14.  4
    Book Reviews. [REVIEW]Gerard Allwein - 1994 - Mind 103 (410):188-191.
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  15. Partially-Ordered Modalities.Gerard Allwein & William L. Harrison - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 1-21.
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