Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The variety \({\mathcal{SH}}\) of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Universidad Nacional del Sur, Bahia Blanca, 2008) [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo (Studia Logica 98(1–2):9–25, 2011) [6]. In this article  introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this presentation of the logic is that  can prove a cut-elimination theorem for GsH that allows us to prove the decidability of the logic. As a direct consequence,  also obtain the decidability of the equational theory of semi-Heyting algebras.
['Diego N. Castaño', 'Juan Manuel Cornejo']
I am writing a research paper on a idea Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic
[{"from": "human", "value": "I am writing a research paper on a idea Gentzen-Style Sequent Calculus for Semi-intuitionistic Logic"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The variety \\({\\mathcal{SH}}\\) of semi-Heyting algebras was introduced by H. P. Sankappanavar (in: Proceedings of the 9th \u201cDr. Antonio A. R. Monteiro\u201d Congress, Universidad Nacional del Sur, Bahia Blanca, 2008) [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo (Studia Logica 98(1\u20132):9\u201325, 2011) [6]. In this article  introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this presentation of the logic is that  can prove a cut-elimination theorem for GsH that allows us to prove the decidability of the logic. As a direct consequence,  also obtain the decidability of the equational theory of semi-Heyting algebras."}]