About the project

Dynamic logics such as versions of Propositional Dynamic Logic (PDL), Public Announcement Logic (PAL), and various logics of soft information update are well known logical models of phenomena involving change of the information available to agents such as humans, databases or computer programs. Change of information relates to dynamics of questions resolved on the basis of the information, a phenomenon formalized by dynamic logics of questions. All these models are based on classical logic, which entails a number of limitations (monotonicity, closure under classical consequence, inconsistency intolerance).

This project explores dynamic logics based on a family of non-classical logics, known as substructural logics, and their applications in modelling information dynamics. Firstly, the project focuses on internal non-classical models of information dynamics, that is, non-classical logics characterized by models with accessibility relations that express change of information. These can be binary relations in the style of PDL, or ternary relations in the style of the relational semantics for substructural logics. Secondly, the project focuses on external non-classical models of information dynamics, that is, extensions of non-classical logics with modalities pertaining to transformations of models in the style of dynamic epistemic logic.

The project was based at the Institute of Computer Science of the Czech Academy of Sciences and funded by the Czech Science Foundation, grant no. 18-19162Y. It run from January 2018 till June 2021.

The project team

Igor Sedlár (principal investigator)

Vít Punčochář

Andrew Tedder

Results

Generalizations of PDL. We obtained general completeness and decidability results on versions of PDL based on substructural, many-valued and inquisitive logics; see [J1], [J2], [C3] and [C7] below.

Information dynamics in non-classical logics. We provided a number of information-dynamic interpretations and extensions of various non-classical logics, including the Lambek calculus [C2, J3], weak relevant logics [J4], and paraconsistent epistemic logic [C1].

Generalizations of PAL. We established a completeness result on non-classical inquisitive PAL [C4], with preparatory results on non-classical inquisitive epistemic logic [J5]. We studied epistemic updates in the context of Kripke semantics of intuitionistic and relevant logics in [C5], adding common knowledge to the framework and studying the relationship to the inquisitive framwork of [C4] in [C6].

(This list will be updated.)

Publications

Papers in journals:

• [J1] V. Punčochář, I. Sedlár: From positive PDL to its non-classical extensions. Logic Journal of the IGPL, 27(4), 522-542, 2019.
  [Preprint]
• [J2] V. Punčochář, I. Sedlár: Inquisitive propositional dynamic logic. Journal of Logic, Language and Information, 30, 91-116, 2021.
• [J3] I. Sedlár, A. Tedder: Lambek calculus with conjugates. Studia Logica 109, 447-470, 2021.
• [J4] A. Tedder: Information Flow in Logics in the Vicinity of BB. Australasian Journal of Logic, 18(1), 1-24, 2021.
• [J5] V. Punčochář, I. Sedlár: Epistemic extensions of substructural inquisitive logics. Journal of Logic and Computation, 31(7), 1820-1844, 2021.
  [Preprint]
• [J6] A. Tedder: Neighbourhood Semantics for Quantified Relevant Logics. Journal of Philosophical Logic, 51, 457-484, 2022.
• [J7] A. Tedder, M. Bílková: Relevant Propositional Dynamic Logic. To appear in Synthese.

Papers in conference proceedings:

• [C1] V. Punčochář, I. Sedlár, A. Tedder: First Degree Entailment with group attitudes and information updates. In: Blackburn P., Lorini E., Guo M. (eds): Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science, vol 11813. Springer, Berlin, Heidelberg, 2019.
  [Preprint]
• [C2] I. Sedlár: Iterative division in the Distributive Full Non-associative Lambek Calculus. In: Soares Barbosa L., Baltag A. (eds): Dynamic Logic. New Trends and Applications. DALI 2019. Lecture Notes in Computer Science, vol 12005. Springer, Cham, 2020.
  [Preprint]
• [C3] I. Sedlár: Finitely-valued propositional dynamic logics. In: Olivetti N., Verbrugge R., Negri S., Sandu G. (eds): Advances in Modal Logic, Volume 13, pp. 561-579. College Publications, London, 2020.
  [Preprint]
• [C4] V. Punčochář: Inquisitive Dynamic Epistemic Logic in a Non-classical Setting. In: Martins M.A., Sedlár I. (eds): Dynamic Logic. New Trends and Applications. DaLi 2020. Lecture Notes in Computer Science, vol 12569. Springer, Cham, 2020.
• [C5] I. Sedlár, A. Tedder: Situated Epistemic Updates. In: S. Ghosh, T. Icard (eds): Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science, vol 13039, pp. 192-200. Springer, Cham, 2021.
  [Preprint]
• [C6] V. Punčochář, I. Sedlár: Relevant Epistemic Logic with Public Announcements and Common Knowledge. In: P. Baroni, C. Benzmüller, Y. N. Wáng (Eds.): Logic and Argumentation. CLAR 2021. Lecture Notes in Computer Science, vol 13040. Springer, Cham, 2021.
  [Preprint]
• [C7] I. Sedlár: Decidability and Complexity of Some Finitely-valued Dynamic Logics. In: M. Bienvenu, G. Lakemeyer, E. Erdem (Eds.): Proc. 18th International Conference on Principles of Knowledge Representation and Reasoning (KR 2021), pp. 570-580, IJCAI Organization, 2021.

Other publications:

• M. A. Martins, I. Sedlár: Dynamic Logic. New Trends and Applications. Third International Workshop, DaLí 2020, Prague, Czech Republic, October 9–10, 2020, Revised Selected Papers. Volume 12569 of Lecture Notes in Computer Science. Springer, 2020.

Presentations (incomplete list)

• V. Punčochář: Inquisitive Dynamic Epistemic Logic in a Non-Classical Setting. DaLí 2020, Online, 9-10 October 2020.
• I. Sedlár: Relevant logic of action. 24th Czechoslovak Symposium on Analytic Philosophy. Olomouc, 8-11 September 2020.
• I. Sedlár: Finitely-valued propositional dynamic logic. Advances in Modal Logic 2020. Online, 24-28 August 2020.
• I. Sedlár: A general completeness argument for propositional dynamic logic. (Short presentation) Advances in Modal Logic 2020. Online, 24-28 August 2020.
• I. Sedlár: FDE-based dynamic logics. A Workshop on FDE-based modal logics. Bochum, Germany. 28 November 2019.
• I. Sedlár: First Degree Entailment with group attitudes and information updates. LORI-VII. Chongquing, China, 18-21 October 2019.
• I. Sedlár: Iterative division in the product-free Distributive Full Non-associative Lambek Calculus. 2nd DaLí Workshop. Porto, Portugal, 9 October 2019.
• V. Punčochář: Substructural Inquisitive Epistemic Logics. Trends in Logic 2019. Moscow, Russia, 2-4 October 2019.
• I. Sedlár: Fixpoints in generalized Lambek calculus. Logic Colloquium 2019. Prague, The Czech Republic, 11-16 August 2019.
• A. Tedder: Residuals and conjugates in positive substructural logic, CLMPST 2019. Prague, The Czech Republic, 10-15 August 2019.
• I. Sedlár: Almost arbitrary information updates. SEGA Project Final Meeting. Bayreuth, Germany, 18-20 July 2019.
• A. Tedder: Conjugates in relational semantics for positive substructural logics, ASL 2019 Annual North American Meeting. New York, USA, 20-23 May 2019.
• V. Punčochář: Inquisitive propositional dynamic logic, Non-Classical Logic. Theory and Applications. Toruń, Poland, 24-27 September, 2018.