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Our goal is to answer this question. Using an epistemic approach, we first characterize possible levels of partial knowledge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connectives of the propositional logic, and prove that Kleene’s logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For extensions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete information represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpretation of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.
|Title of host publication||Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR-18)|
|Place of Publication||Tempe, Arizona, USA|
|Number of pages||10|
|Publication status||Published - 2 Nov 2018|
|Event||16th International Conference on Principles of Knowledge Representation and Reasoning - Tempe, United States|
Duration: 30 Oct 2018 → 2 Nov 2018
|Name||Principles of Knowledge Representation and Reasoning|
|Conference||16th International Conference on Principles of Knowledge Representation and Reasoning|
|Abbreviated title||KR 2018|
|Period||30/10/18 → 2/11/18|
1/10/16 → 31/05/22
Console, M., Guagliardo, P. & Libkin, L., 31 Aug 2019, Proceedings of the Twenty-Eighth International Joint Conferences on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, p. 6141-6145 5 p.
Research output: Chapter in Book/Report/Conference proceeding › Conference contributionOpen AccessFile