David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Citations of this work BETA
Alexandru Baltag, Bryan Renne & Sonja Smets (2014). The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence. Annals of Pure and Applied Logic 165 (1):49-81.
Giuseppe Primiero (2009). An Epistemic Logic for Becoming Informed. Synthese 167 (2):363 - 389.
Ren-June Wang (2014). Non-Circular Proofs and Proof Realization in Modal Logic. Annals of Pure and Applied Logic 165 (7-8):1318-1338.
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