Modeling Uncertainty and Imprecision in Nonmonotonic Reasoning using Fuzzy Numbers
This work addresses the challenge of handling vague and uncertain information in nonmonotonic reasoning for AI and knowledge representation, though it appears incremental as it builds on existing interval-valued logic.
The paper tackled the problem of representing uncertainty and imprecision in nonmonotonic reasoning by extending interval-valued logic with triangular and trapezoidal fuzzy numbers to capture varying degrees of belief, resulting in an answer set framework with defined logical connectives for efficient knowledge representation.
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and trapezoidal fuzzy numbers are used as the set of truth values along with traditional intervals. Preorder-based truth and knowledge ordering are defined over the set of fuzzy numbers defined over $[0,1]$. Based on this enhanced set of epistemic states, an answer set framework is developed, with properly defined logical connectives. This type of framework is efficient in knowledge representation and reasoning with vague and uncertain information under nonmonotonic environment where rules may posses exceptions.