🤖 AI Summary
Existing Hybrid MKNF knowledge bases lack support for classical negation in their rule component, making it difficult to express explicit negative knowledge and thereby limiting their applicability in safety-critical scenarios. This work addresses this limitation by formally integrating classical negation into the Hybrid MKNF rule component through a principled fusion of description logics and logic programming. The paper presents an extended Hybrid MKNF language that accommodates classical negation, rigorously defines its syntax and semantics, and introduces a novel inference framework grounded in well-founded semantics. A key contribution is the development of a general and efficient procedure for computing well-founded models of the extended language, substantially enhancing the system’s capacity to represent and reason with explicit negative information.
📝 Abstract
Hybrid MKNF knowledge bases under the well-founded semantics integrate Description Logics with Logic Programming. However, they do not support classical negation in the rule component, limiting their ability to represent explicit negative knowledge. This limitation is particularly significant in safety-critical applications, where reasoning often requires explicit negative information rather than interpreting the absence of information as evidence of absence. To address this issue, we introduce an extension of Hybrid MKNF that supports classical negation in the rule component. We formally define the syntax and semantics of the extended language and present a general procedure for computing its well-founded model.