Date of Award
Doctor of Philosophy (PhD)
Real-world automated reasoning systems, based on classical logic, face logically inconsistent information, and they must cope with it. It is onerous to develop such systems because classical logic is explosive. Recently, progress has been made towards semantics that deal with logical inconsistency. However, such semantics was never analyzed in the aspect of inconsistency tolerant relational model.
In our research work, we use an inconsistency and incompleteness tolerant relational model called "Paraconsistent Relational Model." The paraconsistent relational model is an extension of the ordinary relational model that can store, not only positive information but also negative information. Therefore, a piece of information in the paraconsistent relational model has four truth values: true, false, both, and unknown.
However, the paraconsistent relational model cannot represent disjunctive information (disjunctive tuples). We then introduce an extended paraconsistent relational model called disjunctive paraconsistent relational model. By using both the models, we handle inconsistency - similar to the notion of quasi-classic logic or four-valued logic -- in deductive databases (logic programs with no functional symbols).
In addition to handling inconsistencies in extended databases, we also apply inconsistent tolerant reasoning technique in semantic web knowledge bases. Specifically, we handle inconsistency assosciated with closed predicates in semantic web. We use again the paraconsistent approach to handle inconsistency.
We further extend the same idea to description logic programs (combination of semantic web and logic programs) and introduce dl-relation to represent inconsistency associated with description logic programs.
Jayakumar, Badrinath, "Handling Inconsistency in Knowledge Bases." Dissertation, Georgia State University, 2017.