Natural deduction for belief at most
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by Johan W. Klüwer, Arild Waaler
http://folk.uio.no/johanw/./nd.pdf
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Abstract:
Abstract. We present a new approach to the logic of at most, introducing the notion of parametric propositions to modal natural deduction proofs. We apply the method with a natural deduction formulation of the doxastic logic N Æ, a new system in the “only knowing ” family. Using parametric proof rules, we give introduction and elimination rules for belief at most that directly match the natural second-order formulation of the concept. N Æ is sound and complete with respect to the class of intended models. We conjecture that it weakly normalizes and that it satisfies the subformula property. 1
Citations
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| 192 | Logical frameworks – Pfenning - 2001 |
| 169 | All I know: a study in autoepistemic logic – Levesque - 1990 |
| 41 | Natural Deduction - A Proof-Theoretical Study – Prawitz - 1965 |
| 31 | Inaccessible worlds. Notre Dame – Humberstone - 1983 |
| 25 | Symbolic Logic: an introduction – Fitch - 1952 |
| 2 | Only knowing with degrees of confidence – Waaler, Klüwer, et al. - 2005 |
| 1 | Fitch-style rules for many modal logics – Siemens - 1977 |
