@inproceedings{Bezhanishvili:19,
	author = {Bezhanishvili, Nick and Grilletti, Gianluca and Holliday, Wesley},
	booktitle = {International Workshop on Logic, Language, Information, and Computation},
	organization = {Springer},
	keywords={inquisitive logic},
	pages = {35--52},
	title = {Algebraic and topological semantics for inquisitive logic via choice-free duality},
	abstract={We introduce new algebraic and topological semantics for
inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations
ranging over only the double negation fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra
B, we define its inquisitive extension H(B) and prove that H(B) is
the unique inquisitive algebra having B as its algebra of double negation fixpoints.
We also show that inquisitive algebras determine Medvedev’s logic of
finite problems. In addition to the algebraic characterization of H(B),
we give a topological characterization of H(B) in terms of the recently
introduced choice-free duality for Boolean algebras using so-called upper
Vietoris spaces (UV-spaces). In particular, while a Boolean algebra
B is realized as the Boolean algebra of compact regular open elements
of a UV-space dual to B, we show that H(B) is realized as the algebra
of compact open elements of this space. This connection yields a new
topological semantics for inquisitive logic.},
	year = {2019}}

{"_id":"dqduACTeiQmRtQrhd","bibbaseid":"bezhanishvili-grilletti-holliday-algebraicandtopologicalsemanticsforinquisitivelogicviachoicefreeduality-2019","author_short":["Bezhanishvili, N.","Grilletti, G.","Holliday, W."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"propositions":[],"lastnames":["Bezhanishvili"],"firstnames":["Nick"],"suffixes":[]},{"propositions":[],"lastnames":["Grilletti"],"firstnames":["Gianluca"],"suffixes":[]},{"propositions":[],"lastnames":["Holliday"],"firstnames":["Wesley"],"suffixes":[]}],"booktitle":"International Workshop on Logic, Language, Information, and Computation","organization":"Springer","keywords":"inquisitive logic","pages":"35–52","title":"Algebraic and topological semantics for inquisitive logic via choice-free duality","abstract":"We introduce new algebraic and topological semantics for inquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations ranging over only the double negation fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra B, we define its inquisitive extension H(B) and prove that H(B) is the unique inquisitive algebra having B as its algebra of double negation fixpoints. We also show that inquisitive algebras determine Medvedev’s logic of finite problems. In addition to the algebraic characterization of H(B), we give a topological characterization of H(B) in terms of the recently introduced choice-free duality for Boolean algebras using so-called upper Vietoris spaces (UV-spaces). In particular, while a Boolean algebra B is realized as the Boolean algebra of compact regular open elements of a UV-space dual to B, we show that H(B) is realized as the algebra of compact open elements of this space. This connection yields a new topological semantics for inquisitive logic.","year":"2019","bibtex":"@inproceedings{Bezhanishvili:19,\n\tauthor = {Bezhanishvili, Nick and Grilletti, Gianluca and Holliday, Wesley},\n\tbooktitle = {International Workshop on Logic, Language, Information, and Computation},\n\torganization = {Springer},\n\tkeywords={inquisitive logic},\n\tpages = {35--52},\n\ttitle = {Algebraic and topological semantics for inquisitive logic via choice-free duality},\n\tabstract={We introduce new algebraic and topological semantics for\ninquisitive logic. The algebraic semantics is based on special Heyting algebras, which we call inquisitive algebras, with propositional valuations\nranging over only the double negation fixpoints of the algebra. We show how inquisitive algebras arise from Boolean algebras: for a given Boolean algebra\nB, we define its inquisitive extension H(B) and prove that H(B) is\nthe unique inquisitive algebra having B as its algebra of double negation fixpoints.\nWe also show that inquisitive algebras determine Medvedev’s logic of\nfinite problems. In addition to the algebraic characterization of H(B),\nwe give a topological characterization of H(B) in terms of the recently\nintroduced choice-free duality for Boolean algebras using so-called upper\nVietoris spaces (UV-spaces). In particular, while a Boolean algebra\nB is realized as the Boolean algebra of compact regular open elements\nof a UV-space dual to B, we show that H(B) is realized as the algebra\nof compact open elements of this space. This connection yields a new\ntopological semantics for inquisitive logic.},\n\tyear = {2019}}\n\n","author_short":["Bezhanishvili, N.","Grilletti, G.","Holliday, W."],"key":"Bezhanishvili:19","id":"Bezhanishvili:19","bibbaseid":"bezhanishvili-grilletti-holliday-algebraicandtopologicalsemanticsforinquisitivelogicviachoicefreeduality-2019","role":"author","urls":{},"keyword":["inquisitive logic"],"metadata":{"authorlinks":{}}},"bibtype":"inproceedings","biburl":"https://projects.illc.uva.nl/inquisitivesemantics/assets/files/papers.bib","dataSources":["LaLDs2mrYhQpgH6Lk"],"keywords":["inquisitive logic"],"search_terms":["algebraic","topological","semantics","inquisitive","logic","via","choice","free","duality","bezhanishvili","grilletti","holliday"],"title":"Algebraic and topological semantics for inquisitive logic via choice-free duality","year":2019}