Abstract
Many realistic scenarios call for answers to questions involving vague expressions like almost all, about half, or at least about a third. We present a modular extension of classical first-order queries over relational databases, with binary, proportional, semi-fuzzy quantifiers modeling such expressions via random sampling. The extended query language has an intuitive semantics and allows one to pose natural queries with probabilistic answers. This is also demonstrated by experiments with an implementation involving the (geographical) MONDIAL data set.
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Notes
- 1.
Although this is not a main concern in this work, we point out that a sampling based semantics may also be useful to compute quick, approximative answers in face of massive volumes of data. For example it might be useful to quickly obtain a highly, but not perfectly reliable answer to a query like Have at least about a quarter of all citizens lived abroad at some time? without having to visit each relevant entry in a huge database containing such data for all citizens.
- 2.
Unary quantification, as in All are B and Some are B, can be considered as a special instance of binary quantification, where the range predicate A is suppressed since it is identified with the one satisfied by all elements of the range of discourse.
- 3.
Actually the overall game is more involved than indicated here, since whole multisets of formulas have to be considered in general, when decomposing formulas into subformulas in accordance with the rules. For details we refer to [7].
- 4.
As it is the distribution function of standard normally distributed random variables.
- 5.
We use a simple definition, compatible with more complex notions of schema, which may assign, e.g., names and domains to attributes, and integrity constraints.
- 6.
We remark that very large values of m do not usually occur in natural language.
- 7.
MONDIAL database. (Last accessed January 30th, 2017). Retrieved from: https://www.dbis.informatik.uni-goettingen.de/Mondial/.
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Acknowledgements
This work was supported by the Austrian Science Fund (FWF) projects I1897-N25 and W1255-N23.
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Fermüller, C.G., Hofer, M., Ortiz, M. (2017). Querying with Vague Quantifiers Using Probabilistic Semantics. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Legind Larsen, H. (eds) Flexible Query Answering Systems. FQAS 2017. Lecture Notes in Computer Science(), vol 10333. Springer, Cham. https://doi.org/10.1007/978-3-319-59692-1_2
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