Propositional and Predicate Logics of Incomplete Information

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

Abstract / Description of output

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 Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR-18)
Place of PublicationTempe, Arizona, USA
PublisherAAAI Press
Number of pages10
ISBN (Print)978-1-57735-803-9
Publication statusPublished - 2 Nov 2018
Event16th International Conference on Principles of Knowledge Representation and Reasoning - Tempe, United States
Duration: 30 Oct 20182 Nov 2018

Publication series

NamePrinciples of Knowledge Representation and Reasoning
PublisherAAAI Press
ISSN (Print)2334-1025
ISSN (Electronic)2334-1033


Conference16th International Conference on Principles of Knowledge Representation and Reasoning
Abbreviated titleKR 2018
Country/TerritoryUnited States
Internet address


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