Abstract
How can a database express and conclude that it has information on some sentence Φ but not on Ψ? We develop a formal semantics for an operator □, to be read as “It is entailed by the database that ... ”. We define a consequence relation based on a preference semantics and analyze under which circumstances this relation fulfils the condition that ¬□Φ is entailed by a set X of formulas whenever □ ∉ Cn(X). It turns out that this condition holds if the elements of X are modal Horn clauses or propositional sentences. We further relate our logic to some well known nonmonotonic logics. We show that it is located between autoepistemic logic and McDermott's nonmonotonic S5; moreover, all S5 theorems are valid. But unlike McDermott's nonmonotonic S5 it does not collapse to the monotonic case.
The author would like to thank Gerd Brewka and Joachim Hertzberg for invaluable comments on a draft version of this paper.
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© 1996 Springer-Verlag Berlin Heidelberg
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Weber, S. (1996). On the semantics of the unknown. In: Gabbay, D.M., Ohlbach, H.J. (eds) Practical Reasoning. FAPR 1996. Lecture Notes in Computer Science, vol 1085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61313-7_105
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DOI: https://doi.org/10.1007/3-540-61313-7_105
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