Abstract
The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL.
| Original language | English |
|---|---|
| Article number | 24 |
| Pages (from-to) | 1-75 |
| Number of pages | 75 |
| Journal | ACM Transactions on Computational Logic |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Aug 2019 |
Funding
The research of the second to third author has been funded by the NWO Vidi grant vidi 016.138.314, by the NWO Aspasia grant 015.008.054, and by a Delft Technology Fellowship awarded in 2013. Authors’ addresses: W. Conradie, School of Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Braam-fontein 2000, Johannesburg, South Africa; email: [email protected]; S. Frittella, INSA Centre Val de Loire, Univ. Orléans, LIFO EA 4022, Bourges, France; email: [email protected]; A. Palmigiano and A. Tzimoulis (corresponding author), Vrije Universiteit Amsterdam, Department of Management & Organisation Studies, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands; emails: {a.palmigiano, a.tzimoulis}@vu.nl; N. Wijnberg, Amsterdam Business School, University of Amsterdam, Plantage Muidergracht 12, 1018 TV Amsterdam, Amsterdam, the Netherlands, College of Business and Economics, University of Johannesburg, Johannesburg, South Africa; email: [email protected]. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM. 1529-3785/2019/08-ART24 $15.00 https://doi.org/10.1145/3341725
| Funders | Funder number |
|---|---|
| NWO Aspasia | |
| Vidi grant | |
| Not added | 015.008.054 |
| NWO VIDI | vidi 016.138.314 |