12 found
Sort by:
  1. Gerard Allwein, William L. Harrison & David Andrews (forthcoming). Simulation Logic. Logic and Logical Philosophy.
    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 (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation  
  2. Gerard Allwein, Yingrui Yang & William L. Harrison (2011). Qualitative Decision Theory Via Channel Theory. 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 (...)
    Direct download (12 more)  
     
    My bibliography  
     
    Export citation  
  3. Gerard Allwein, Hilmi Demir & Lee Pike (2004). Logics for Classes of Boolean Monoids. 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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  4. Benedek Nagy & Gerard Allwein (2004). Diagrams and Non-Monotonicity in Puzzles. In A. Blackwell, K. Marriott & A. Shimojima (eds.), Diagrammatic Representation and Inference. Springer. 82--96.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  5. Nik Swoboda & Gerard Allwein (2002). A Case Study of the Design and Implementation of Heterogeneous Reasoning Systems. In L. Magnani, N. J. Nersessian & C. Pizzi (eds.), Logical and Computational Aspects of Model-Based Reasoning. Kluwer Academic Publishers. 3--20.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  6. Gerard Allwein & Wendy MacCaull (2001). A Kripke Semantics for the Logic of Gelfand Quantales. 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 (...)
    Direct download (7 more)  
     
    My bibliography  
     
    Export citation  
  7. Petr Hájek, Arithmetical Hierarchy Iii, Gerard Allwein & Wendy MacCaull (2001). Special Issue: Methods for Investigating Self-Referential Truth Edited by Volker Halbach Volker Halbach/Editorial Introduction 3. Studia Logica 68:421-422.
    Direct download  
     
    My bibliography  
     
    Export citation  
  8. Gerard Allwein & Jon Barwise (eds.) (1996). Logical Reasoning with Diagrams. 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 (...)
    Direct download  
     
    My bibliography  
     
    Export citation  
  9. Steven D. Johnson, Jon Barwise & Gerard Allwein (1996). Toward the Rigorous Use of Diagrams in Reasoning About Hardware. In Gerard Allwein & Jon Barwise (eds.), Logical Reasoning with Diagrams. Oxford University Press.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  10. Gerard Allwein (1994). Book Reviews. [REVIEW] Mind 103 (410):188-191.
    No categories
    Direct download (3 more)  
     
    My bibliography  
     
    Export citation  
  11. Gerard Allwein & J. Michael Dunn (1993). A Kripke Semantics for Linear Logic. Journal of Symbolic Logic 58:514-545.
     
    My bibliography  
     
    Export citation  
  12. Gerard Allwein & J. Michael Dunn (1993). Kripke Models for Linear Logic. 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, (...)
    Direct download (6 more)  
     
    My bibliography  
     
    Export citation