Avoiding impossibility theorems in radical inquisitive semantics. (English) Zbl 1429.03069
Ju, Shier (ed.) et al., Modality, semantics and interpretations. The second Asian workshop on philosophical logic, Guangzhou, China, 2014. Berlin: Springer. Log. Asia: Stud. Log. Libr., 107-120 (2015).
Summary: In nonradical inquisitive semantics, an intuitionistic Kripke model captures how group knowledge increases throughout a conversation and allows the inquisitive meaning of a sentence to be derived from its classical meaning. In radical inquisitive semantics, as proposed by Groenendijk and Roelofsen, positive and negative ways of reacting to a proposal are captured by the positive and negative inquisitive meanings of a sentence, respectively, which are inductively defined without employing any Kripke-type semantics. This paper demonstrates that, in principle, it is impossible to provide any natural Kripke-type semantics under radical inquisitive semantics. Moreover, an alternative way to establish the semantics is proposed that avoids this negative result.
For the entire collection see [Zbl 1321.03010].
For the entire collection see [Zbl 1321.03010].
MSC:
| 03B42 | Logics of knowledge and belief (including belief change) |
| 03B20 | Subsystems of classical logic (including intuitionistic logic) |
Keywords:
intuitionistic logic; Kripke model; impossibility theorem; strong negation; declarative sentenceReferences:
| [1] | M. Aher. Free choice in deontic inquisitive semantics (DIS). In M. Aloni, et al. editor, Amsterdam Colloquium 2011, volume 7218 of LNCS, pages 22-31. Springer-Verlag, 2012. · Zbl 1366.03012 |
| [2] | I. Ciardelli. Inquisitive semantics and intermediate logics. Master’s thesis, Institute for Logic, Language and Computation, University of Amsterdam, 2009. |
| [3] | I. Ciardelli. A first-order inquisitive semantics. In M. Aloni, H. Bastiaanse, T. de Jager, and K. Schulz, editors, Logic, Language, and Meaning: Selected Papers from the Seventeenth Amsterdam Colloquium. volume 6042 of LNCS, pages 234-243. Springer-Verlag, 2010. · Zbl 1298.03084 |
| [4] | I. Ciardelli and F. Roelofsen. Generalized Inquisitive Logic: Completeness via Intuitionistic Kripke Models. In TARK ’09 Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge, pages 71-80, ACM New York, 2009. |
| [5] | I. Ciardelli and F. Roelofsen. Inquisitive logic. Journal of Philosophical Logic, 40(1):55-94, 2011. · Zbl 1214.03019 · doi:10.1007/s10992-010-9142-6 |
| [6] | B. Ellis, F. Jackson, and R. Pargetter. An objection to possible worlds semantics for counterfactual logics. Journal of Philosophical Logic, 6:355-357, 1977. · Zbl 0376.02002 · doi:10.1007/BF00262069 |
| [7] | K. Fine. Truth-maker semantics for intuitionistic logic. Journal of Philosophical Logic, 43:549-577, 2014. · Zbl 1335.03011 · doi:10.1007/s10992-013-9281-7 |
| [8] | J. Groenendijk and F. Roelofsen. Toward a suppositional inquisitive semantics. To appear in M. Aher, D. Hole, E. Jerabek, and C. Kupke, editors, Logic, Language, and Computation: revised selected papers from the 10th International Tbilisi Symposium on Language, Logic, and Computation. Springer, 2014. Available from www.illc.uva.nl/inquisitive-semantics. · Zbl 1326.03036 |
| [9] | J. Groenendijk and F. Roelofsen. Inquisitive semantics and pragmatics. In J. M. Larrazabal and L. Zubeldia, editors, Meaning, Content, and Argument: Proceedings of the ILCLI International Workshop on Semantics, Pragmatics, and Rhetoric, pages 41-72, University of the Basque Country Publication Service, 2009. www.illc.uva.nl/inquisitive-semantics. · Zbl 1383.03038 |
| [10] | J. Groenendijk and F. Roelofsen. Radical inquisitive semantics. Presented at the Sixth International Symposium on Logic, Cognition, and Communication at the University of Latvia. Latest version available via www.illc.uva.nl/inquisitive-semantics, 2010. |
| [11] | D. Nelson. Constructible falsity. Journal of Symbolic Logic, 14:16-26, 1949. · Zbl 0033.24304 |
| [12] | S. Odintsov. Constructive Negations and Paraconsistency. Springer-Verlag, Dordrecht, 2008. · Zbl 1161.03014 · doi:10.1007/978-1-4020-6867-6 |
| [13] | H. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
