Inquisitive Heyting Algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F21%3A00546145" target="_blank" >RIV/67985955:_____/21:00546145 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11225-020-09936-9" target="_blank" >https://doi.org/10.1007/s11225-020-09936-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11225-020-09936-9" target="_blank" >10.1007/s11225-020-09936-9</a>

Result language
angličtina
Original language name
Inquisitive Heyting Algebras
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology

Project
<a href="/en/project/GA20-18675S" target="_blank" >GA20-18675S: Tha nature of logical forms and modern logic</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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