Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   give a base of admissible rules for every proper axiomatic extension of the infinite valued Łukasiewicz logic.  first prove that single-conclusion admissible rules of any proper axiomatic extension are finitely based. The proof strongly relies on the characterization of least  V -quasivarieties given in   [11]  .
['Joan Gispert']
I am writing a research paper on a idea Bases of admissible rules of proper axiomatic extensions of Łukasiewicz logic
[{"from": "human", "value": "I am writing a research paper on a idea Bases of admissible rules of proper axiomatic extensions of \u0141ukasiewicz logic"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   give a base of admissible rules for every proper axiomatic extension of the infinite valued \u0141ukasiewicz logic.  first prove that single-conclusion admissible rules of any proper axiomatic extension are finitely based. The proof strongly relies on the characterization of least  V -quasivarieties given in   [11]  ."}]