NDLI: $${\in_K}$$ : a Non-Fregean Logic of Explicit Knowledge

Content Provider	Springer Nature Link
Author	Lewitzka, Steffen
Copyright Year	2011
Abstract	We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. $${\in_K}$$ (Epsilon-K) is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K $_{i}$ φ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between $${\in_K}$$ and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in $${\in_K}$$ . Every specific $${\in_K}$$ -logic is defined as a certain extension of some underlying classical abstract logic.
Starting Page	233
Ending Page	264
Page Count	32
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	97
Issue Number	2
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-02-18
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	epistemic logic non-Fregean Logic logical omniscience explicit knowledge classical abstract logic self-reference epistemic paradox liar paradox Logic Computational Linguistics Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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