Undefinability in Inquisitive Logic with Tensor

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Ciardelli , I & Barbero , F 2019 , Undefinability in Inquisitive Logic with Tensor . in P Blackburn , E Lorini & M Guo (eds) , Logic, Rationality and Interaction : 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings . Lecture Notes in Computer Science edn , vol. 11813 , Lecture Notes in Computer Science , vol. 11813 , Springer , pp. 29-42 , 7th International Workshop, LORI 2019 , Chongqing , China , 18/10/2019 . https://doi.org/10.1007/978-3-662-60292-8_3

Title: Undefinability in Inquisitive Logic with Tensor
Author: Ciardelli, Ivano; Barbero, Fausto
Other contributor: University of Helsinki, Theoretical Philosophy
Blackburn, Patrick
Lorini, Emiliano
Guo, Meiyun

Publisher: Springer
Date: 2019
Language: eng
Number of pages: 14
Belongs to series: Logic, Rationality and Interaction 7th International Workshop, LORI 2019, Chongqing, China, October 18–21, 2019, Proceedings
Belongs to series: Lecture Notes in Computer Science
ISBN: 9783662602911
9783662602928
DOI: https://doi.org/10.1007/978-3-662-60292-8_3
URI: http://hdl.handle.net/10138/310282
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.
Subject: 111 Mathematics
611 Philosophy
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