Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard \(\mathsf {BL}\)-algebras,  focus on a uniform approach to the following problem: given a left-continuous t-norm \(*\), find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra Open image in new window This system will be an expansion of Monoidal t-norm-based logic. First,  introduce an infinitary axiomatic system \(\mathsf {L}_*^\infty \), expanding the language with \(\Delta \) and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then  show that \(\mathsf {L}_*^\infty \) is indeed strongly complete with respect to the standard algebra Open image in new window. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions.
['A. Vidal', 'Félix Bou', 'Francesc Esteva', 'Lluís Godo']
I am writing a research paper on a idea On strong standard completeness in some MTL $$_\Delta $$ Δ expansions
[{"from": "human", "value": "I am writing a research paper on a idea On strong standard completeness in some MTL $$_\\Delta $$ \u0394 expansions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard \\(\\mathsf {BL}\\)-algebras,  focus on a uniform approach to the following problem: given a left-continuous t-norm \\(*\\), find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra Open image in new window This system will be an expansion of Monoidal t-norm-based logic. First,  introduce an infinitary axiomatic system \\(\\mathsf {L}_*^\\infty \\), expanding the language with \\(\\Delta \\) and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti\u2013Titani density rule. Then  show that \\(\\mathsf {L}_*^\\infty \\) is indeed strongly complete with respect to the standard algebra Open image in new window. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions."}]