Completeness by Modal Deﬁnitions. Application to the Epistemic Logic With Hypotheses
Keywords:Knowledge representation and reasosning, epistemic logic, Kripke Completeness, Topological Semantics
We investigate the variant of epistemic logic S5 for reasoning about knowledge under hypotheses. The logic is equipped with a modal operator of necessity that can be parameterized with a hypothesis representing background assumptions. The modal operator can be described as relative necessity and the resulting logic turns out to be a variant of Chellas’ Conditional Logic. We present an axiomatization of the logic and its extension with the common knowledge operator and distributed knowledge operator. We show that the logics are decidable, complete w.r.t. Kripke as well as topological structures. The topological completeness results are obtained by utilizing the Alexandroﬀ connection between preorders and Alexandroﬀ spaces.
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Copyright (c) 2020 Iberamia & The Authors
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ISSN: 1988-3064 (on line).
(C) IBERAMIA & The Authors