Do We Need Many-valued Logics for Incomplete Information?

Research output: Chapter in Book/Report/Conference proceedingConference contribution


One of the most common scenarios of handling incomplete information occurs in relational databases. They describe incomplete knowledge with three truth values, using Kleene’s logic for propositional formulae and a rather peculiar extension to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and predicate logics?

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.
Original languageEnglish
Title of host publicationProceedings of the Twenty-Eighth International Joint Conferences on Artificial Intelligence
PublisherInternational Joint Conferences on Artificial Intelligence Organization
Number of pages5
ISBN (Electronic)978-0-9992411-4-1
Publication statusPublished - 31 Aug 2019
EventInternational Joint Conference in Artificial Intelligence - Macao, China
Duration: 10 Aug 201916 Aug 2019
Conference number: 28th


ConferenceInternational Joint Conference in Artificial Intelligence
Abbreviated titleIJCAI 2019
Internet address

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