On Two Models of Provability

Artëmov, Sergei

doi:10.1007/978-0-387-69245-6_1

Cited by 5 publications

(1 citation statement)

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“…Such an operation '?' does not exist for formal mathematical proofs since ?t should be a single proof of infinitely many propositions ¬t:F , which is impossible 6 . For what it's worth, we include Negative Introspection in the list of additional justification principles, and leave the decision of whether to accept it or not to the user.…”

Section: Negative Introspectionmentioning

confidence: 99%

The Logic of Justification

Artëmov

2008

The Review of Symbolic Logic

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We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the Goldman–Kripke ‘Red Barn’ paradox and analyze Russell’s ‘prime minister example’ in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning.

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Section: Negative Introspectionmentioning

confidence: 99%