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We prove the canonical models introduced in [D] do not exist for some graded normal logics with symmetric models, namelyKB°, KBD°, KBT°, so that we define a new kind of canonical models, the general ones, and show they exist and work well in every case. |
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We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results. |
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This work intends to be a generalization and a simplification of the techniques employed in [2], by the proposal of a general strategy to prove satisfiability theorems for NLGM-s (= normal logics with graded modalities), analogously to the well known technique of the canonical models by Lemmon and Scott for classical modal logics. |
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Graded epistemic logic is a logic for reasoning about uncertainties. Graded epistemic logic is interpreted on graded models. These models are generalizations of Kripke models. We obtain completeness of some graded epistemic logics. We further develop dynamic extensions of graded epistemic logics, along the framework of dynamic epistemic logic. We give an extension with public announcements, i.e., public events, and an extension with graded event models, a generalization also including nonpublic events. We present complete axiomatizations for both logics. |
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This work intends to be a generalization and a simplification of the techniques employed in [2], by the proposal of a general strategy to prove satisfiability theorems for NLGM-s, analogously to the well known technique of the canonical models by Lemmon and Scott for classical modal logics. |
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