Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper  study the consistency problem for the fuzzy Description Logic L - SHI and its sublogics in detail.The contribution of the paper is twofold. On the one hand,  provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI . On the other hand,  identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes,  also provide tight complexity bounds.  describe a family of fuzzy Description Logics over lattices based on crisp SHI.For infinite lattices without zero divisors, ontology consistency is decidable.For infinite lattices with zero divisors, there are decidable and undecidable cases.For finite lattices,  describe a NExpTime tableau algorithm for consistency.The complexity of reasoning in most decidable cases is the same as in the crisp case.
['Stefan Borgwardt', 'Rafael Peñaloza']
I am writing a research paper on a idea Consistency reasoning in lattice-based fuzzy Description Logics
[{"from": "human", "value": "I am writing a research paper on a idea Consistency reasoning in lattice-based fuzzy Description Logics"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning with vague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whether an ontology representing a knowledge domain is consistent. Surprisingly, not much is known about the complexity of this problem for semantics based on complete De Morgan lattices. To cover this gap, in this paper  study the consistency problem for the fuzzy Description Logic L - SHI and its sublogics in detail.The contribution of the paper is twofold. On the one hand,  provide a tableaux-based algorithm for deciding consistency when the underlying lattice is finite. The algorithm generalizes the one developed for classical SHI . On the other hand,  identify decidable and undecidable classes of fuzzy Description Logics over infinite lattices. For all the decidable classes,  also provide tight complexity bounds.  describe a family of fuzzy Description Logics over lattices based on crisp SHI.For infinite lattices without zero divisors, ontology consistency is decidable.For infinite lattices with zero divisors, there are decidable and undecidable cases.For finite lattices,  describe a NExpTime tableau algorithm for consistency.The complexity of reasoning in most decidable cases is the same as in the crisp case."}]