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  1.  4
    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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    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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    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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    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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