Projects per year
Abstract
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.
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 language | English |
---|---|
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 |
Publisher | AAAI Press |
Pages | 592-601 |
Number of pages | 10 |
ISBN (Print) | 978-1-57735-803-9 |
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 http://reasoning.eas.asu.edu/kr2018/ |
Publication series
Name | Principles of Knowledge Representation and Reasoning |
---|---|
Publisher | AAAI Press |
ISSN (Print) | 2334-1025 |
ISSN (Electronic) | 2334-1033 |
Conference
Conference | 16th International Conference on Principles of Knowledge Representation and Reasoning |
---|---|
Abbreviated title | KR 2018 |
Country/Territory | United States |
City | Tempe |
Period | 30/10/18 → 2/11/18 |
Internet address |
Fingerprint
Dive into the research topics of 'Propositional and Predicate Logics of Incomplete Information'. Together they form a unique fingerprint.Projects
- 2 Finished
-
-
VADA: Value Added Data Systems: Principles and Architecture
Libkin, L., Buneman, P., Fan, W. & Pieris, A.
1/04/15 → 30/09/20
Project: Research
Research output
- 1 Conference contribution
-
Do We Need Many-valued Logics for Incomplete Information?
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 contribution
Open AccessFile
Profiles
-
Leonid Libkin
- School of Informatics - Chair of Foundations of Data Management
- Laboratory for Foundations of Computer Science
- Foundations of Computation
Person: Academic: Research Active
Prizes
-
The 2018 Ray Reiter Best Paper Prize
Console, Marco (Recipient), Guagliardo, Paolo (Recipient) & Libkin, Leonid (Recipient), 25 Sep 2018
Prize: Prize (including medals and awards)