Undefinability in Inquisitive Logic with Tensor. Ciardelli, I. & Barbero, F. In Blackburn, P., Lorini, E., & Guo, M., editors, Logic, Rationality, and Interaction, pages 29–42, Berlin, Heidelberg, 2019. Springer Berlin Heidelberg. ![Undefinability in Inquisitive Logic with Tensor [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.
@inproceedings{CiardelliBarbero:19,
address = {Berlin, Heidelberg},
author = {Ciardelli, Ivano and Barbero, Fausto},
booktitle = {Logic, Rationality, and Interaction},
editor = {Blackburn, Patrick and Lorini, Emiliano and Guo, Meiyun},
isbn = {978-3-662-60292-8},
pages = {29--42},
publisher = {Springer Berlin Heidelberg},
title = {Undefinability in Inquisitive Logic with Tensor},
abstract={Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.},
url={https://link.springer.com/chapter/10.1007/978-3-662-60292-8_3},
keywords={inquisitive logic},
year = {2019}}
Downloads: 0
{"_id":"AKHNB3hYruxnuJffo","bibbaseid":"ciardelli-barbero-undefinabilityininquisitivelogicwithtensor-2019","author_short":["Ciardelli, I.","Barbero, F."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","address":"Berlin, Heidelberg","author":[{"propositions":[],"lastnames":["Ciardelli"],"firstnames":["Ivano"],"suffixes":[]},{"propositions":[],"lastnames":["Barbero"],"firstnames":["Fausto"],"suffixes":[]}],"booktitle":"Logic, Rationality, and Interaction","editor":[{"propositions":[],"lastnames":["Blackburn"],"firstnames":["Patrick"],"suffixes":[]},{"propositions":[],"lastnames":["Lorini"],"firstnames":["Emiliano"],"suffixes":[]},{"propositions":[],"lastnames":["Guo"],"firstnames":["Meiyun"],"suffixes":[]}],"isbn":"978-3-662-60292-8","pages":"29–42","publisher":"Springer Berlin Heidelberg","title":"Undefinability in Inquisitive Logic with Tensor","abstract":"Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.","url":"https://link.springer.com/chapter/10.1007/978-3-662-60292-8_3","keywords":"inquisitive logic","year":"2019","bibtex":"@inproceedings{CiardelliBarbero:19,\n\taddress = {Berlin, Heidelberg},\n\tauthor = {Ciardelli, Ivano and Barbero, Fausto},\n\tbooktitle = {Logic, Rationality, and Interaction},\n\teditor = {Blackburn, Patrick and Lorini, Emiliano and Guo, Meiyun},\n\tisbn = {978-3-662-60292-8},\n\tpages = {29--42},\n\tpublisher = {Springer Berlin Heidelberg},\n\ttitle = {Undefinability in Inquisitive Logic with Tensor},\n\tabstract={Logics based on team semantics, such as inquisitive logic and dependence logic, are not closed under uniform substitution. This leads to an interesting separation between expressive power and definability: it may be that an operator O can be added to a language without a gain in expressive power, yet O is not definable in that language. For instance, even though propositional inquisitive logic and propositional dependence logic have the same expressive power, inquisitive disjunction and implication are not definable in propositional dependence logic. A question that has been open for some time in this area is whether the tensor disjunction used in propositional dependence logic is definable in inquisitive logic. We settle this question in the negative. In fact, we show that extending the logical repertoire of inquisitive logic by means of tensor disjunction leads to an independent set of connectives; that is, no connective in the resulting logic is definable in terms of the others.},\n\turl={https://link.springer.com/chapter/10.1007/978-3-662-60292-8_3},\n\tkeywords={inquisitive logic},\n\tyear = {2019}}\n\t\n","author_short":["Ciardelli, I.","Barbero, F."],"editor_short":["Blackburn, P.","Lorini, E.","Guo, M."],"key":"CiardelliBarbero:19","id":"CiardelliBarbero:19","bibbaseid":"ciardelli-barbero-undefinabilityininquisitivelogicwithtensor-2019","role":"author","urls":{"Paper":"https://link.springer.com/chapter/10.1007/978-3-662-60292-8_3"},"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":["undefinability","inquisitive","logic","tensor","ciardelli","barbero"],"title":"Undefinability in Inquisitive Logic with Tensor","year":2019}