Conservativity for Logics of Justified Belief
- Cite this paper as:
- Milnikel R.S. (2008) Conservativity for Logics of Justified Belief. In: Artemov S., Nerode A. (eds) Logical Foundations of Computer Science. LFCS 2009. Lecture Notes in Computer Science, vol 5407. Springer, Berlin, Heidelberg
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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