A logic of explicit knowledge
| Abstract | A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. One kind of reason is a formal proof. Sergei Artemov has introduced a logic of explicit proofs, LP. I present a semantics for this, based on the idea that it is a logic of knowledge with explicit reasons. A number of fundamental facts about LP can be established using this semantics. But it is equally important to realize that it provides a natural logic of more general applicability than its original provenance, arithmetic provability. | |||||||||
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Similar books and articlesHarry Collins (2011). Analysing Tacit Knowledge. Tradition and Discovery 38 (1):38-42.
Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
Corine Besson (2009). Logical Knowledge and Gettier Cases. Philosophical Quarterly 59 (234):1-19.
Eduardo Mercado & Scott O. Murray (1999). Explicit Knowledge in Dolphins? Behavioral and Brain Sciences 22 (5):774-775.
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