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 related to 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. We focus mainly on non-classical versions of PDL, PAL and logics of soft information update, and dynamic substructural logics of questions.

The project is based at the Institute of Computer Science of the Czech Academy of Sciences and funded by the Czech Science Foundation, grant no. 18-19162Y.

The project team

Igor Sedlár (principal investigator), Vít Punčochář, and Andrew Tedder.

Publications

• V. Punčochář, I. Sedlár: From positive PDL to its non-classical extensions. Logic Journal of the IGPL, 27(4), 522-542, 2019. [Preprint]
  • [Formula-formula sequent-style axiomatization and decidability of the positive fragment of PDL with semantics using Kripke models; axiomatization and decidability of positive PDL extended with connectives of the Nonassociative Lambek Calculus; axiomatization and decidability of positive PDL extended with De Morgan negation.]
  
  
• V. Punčochář, I. Sedlár, A. Tedder: First Degree Entailment with group attitudes and information updates. P. Blackburn, E. Lorini, M. Guo (Eds.): Proc. LORI-VII, pp. 273-285. Lecture Notes in Computer Science 11813, Springer, 2019. [Preprint]
  
  • [We extend the epistemic logic with De Morgan negation by Fagin et al. (Artif. Intell. 79, 203-240, 1995) by adding operators for universal and common knowledge in a group of agents, and with a formalization of information update using a generalized version of the left division connective of the non-associative Lambek calculus. We provide sound and complete axiomatizations of the basic logic with the group operators and the basic logic with group operators and updates. Both logics are shown to be decidable.]

Presentations

• Upcoming: 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.


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