In this paper we introduce a class of inquisitive Heyting algebras as algebraic structures that are isomorphic to algebras of finite antichains of bounded implicative meet semilattices. It is argued that these structures are suitable for algebraic semantics of inquisitive superintuitionistic logics, i.e. logics of questions based on intuitionistic logic and its extensions. We explain how questions are represented in these structures (prime elements represent declarative propositions, non-prime elements represent questions, join is a question-forming operation) and provide several alternative characterizations of these algebras. For instance, it is shown that a Heyting algebra is inquisitive if and only if its prime filters and filters generated by sets of prime elements coincide and prime elements are closed under relative pseudocomplement. We prove that the weakest inquisitive superintuitionistic logic is sound with respect to a Heyting algebra iff the algebra is what we call a homomorphic p-image of some inquisitive Heyting algebra. It is also shown that a logic is inquisitive iff its Lindenbaum–Tarski algebra is an inquisitive Heyting algebra.

在本文中，我们介绍了一类好奇的Heyting代数与有界蕴涵的有限反链的代数同构的代数结构满足半格。有人认为，这些结构适合于查询式超直觉逻辑的代数语义，即基于直觉逻辑及其扩展的问题的逻辑。我们将解释问题在这些结构中的表示方式（素数元素代表陈述性命题，非素数元素代表问题，join是一个形成问题的运算），并提供了这些代数的几种替代特征。例如，表明Heyting代数是询问性的，当且仅当其素数过滤器和由素数元素集生成的过滤器重合并且素数元素在相对伪补码下闭合时。我们证明，对于Heyting代数，最弱的查询性超直觉逻辑是合理的，前提是该代数是我们称为某些查询性Heyting代数的同态p图像。如果林登堡姆-塔斯基代数是一个好奇的海廷代数，那么它也表明逻辑是好奇的。