Conservativity for Logics of Justified Belief
In , Fitting showed that the standard hierarchy of logics of justified knowledge is conservative (e.g. a logic with positive introspection operator ! is conservative over the logic without !). We do the same with most logics of justified belief, but taking a semantic approach rather than Fitting’s syntactic one. A brief example shows that conservativity does not hold for logics of justified consistent belief.
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- 1.Fitting, M.: Explicit logics of knowledge and conservativity. In: Tenth International Symposium on Artificial Intelligence and Mathematics, ISAIM 2008, Fort Lauderdale, Florida, January 2–4, 2008, Online Proceedings (2008)Google Scholar
- 3.Artemov, S.N.: Explicit provability: the intended semantics for intuitionistic and modal logic. Technical Report CFIS 98–10, Cornell University (September 1998)Google Scholar
- 6.Brezhnev, V.N.: On the logic of proofs. In: Striegnitz, K. (ed.) Proceedings of the sixth ESSLLI Student Session, Helsinki, pp. 35–46 (August 2001)Google Scholar