#3723. Propositional and predicate logics of incomplete information

October 2026publication date
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Journal’s subject area:
Language and Linguistics;
Linguistics and Language;
Artificial Intelligence;
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Abstract:
One of the most common scenarios of handling incomplete information occurs in relational databases. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. 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. 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.
Keywords:
Incomplete information; Many-valued logics; Database management systems.

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