Dynamic Logic of Propositional Assignments: A Well-Behaved Variant of PDL

We study a version of Propositional Dynamic Logic (PDL) that we call Dynamic Logic of Propositional Assignments (DL-PA). The atomic programs of DL-PA are assignments of propositional variables to true or to false. We show that DL-PA behaves better than PDL, having e.g. compactness and eliminability of the Kleene star. We establish tight complexity results: both satisfiability and model checking are EXPTIME-complete.

[1]  Wiebe van der Hoek,et al.  Dynamic epistemic logic with assignment , 2005, AAMAS '05.

[2]  Giuseppe De Giacomo,et al.  Combining Deduction and Model Checking into Tableaux and Algorithms for Converse-PDL , 2000, Inf. Comput..

[3]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[4]  Hans van Ditmarsch,et al.  The Russian Cards Problem , 2003, Stud Logica.

[5]  Johann A. Makowsky,et al.  Propositional Dynamic Logic with Local Assignments , 1985, Theor. Comput. Sci..

[6]  Karl Winklmann,et al.  On the expressive power of Dynamic Logic (Preliminary Report) , 1979, STOC.

[7]  Lawrence S. Moss,et al.  The Undecidability of Iterated Modal Relativization , 2005, Stud Logica.

[8]  Barteld P. Kooi,et al.  Expressivity and completeness for public update logics via reduction axioms , 2007, J. Appl. Non Class. Logics.

[9]  Jelle Gerbrandy,et al.  Logics of propositional control , 2006, AAMAS '06.

[10]  Emiliano Lorini,et al.  A Dynamic Logic of Normative Systems , 2011, IJCAI.

[11]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[12]  Michael Wooldridge,et al.  Reasoning About the Transfer of Control , 2014, J. Artif. Intell. Res..

[13]  Michael Wooldridge,et al.  On the logic of cooperation and propositional control , 2005, Artif. Intell..

[14]  A. Wilm,et al.  Determinism and Non-determinism in PDL , 1991, Theor. Comput. Sci..

[15]  Michael Wooldridge,et al.  On the dynamics of delegation, cooperation, and control: a logical account , 2005, AAMAS '05.

[16]  Zakaria Maamar,et al.  Proceedings of the Workshop on Service-Oriented Computing and Agent Based Engineering (SOCABE 2006) held in conjunction with the 5th International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS 2006), Hakodate, Japan, 08-12 May 2006 , 2006 .

[17]  Andreas Herzig,et al.  From Situation Calculus to Dynamic Epistemic Logic , 2011, J. Log. Comput..

[18]  Larry J. Stockmeyer,et al.  Provably Difficult Combinatorial Games , 1979, SIAM J. Comput..