SIMULATION LOGIC

Simulation relations have been discovered in many areas: Computer Science, philosophical and modal logic, and set theory However, the a 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 Etre 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.