TitleSimulation Logic
Publication TypeJournal Article
Year of PublicationIn Press
AuthorsHarrison, W. L., D. Andrews, and G. Allwein
JournalLogic 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 rst-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 modalities by axioms for requiring the underlying modeling simulations
to be bisimulations or to be p-morphisms. The modal systems presented are multi-sorted and
both sound and complete with respect to their algebraic and Kripke semantics.

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