Reasoning About the Transfer of Control

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form coalition C can cooperate to bring about phi. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form agent i gives control of variable p to agent j; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a direct semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control

Advances in modal logic 3: papers from the third conference on advances in modal logic

Advances in Modal Logic is a unique forum for presenting the latest results and new directions of research in modal logic. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics. Volume 3 presents substantial advances in the relational model theory and the algorithmic treatment of modal logics. It contains invited and contributed papers from the third conference on “Advances in Modal Logic”, held at the University of Leipzig (Germany) in October 2000. It includes papers on dynamic logic, description logic, hybrid logic, epistemic logic, combinations of modal logics, tense logic, action logic, provability logic, and modal predicate logic. Contents: From Description to Hybrid Logics, and Back (C Areces & M de Rijke) Homophonic Theory of Truth for Tense Logic (Torben Braüner) Weak Necessity on Weak Kleene Matrices (F Correia) Bimodal Logics for Reasoning About Continuous Dynamics (J M Davoren & R P Goré) From Bisimulation Quantifiers to Classifying Toposes (S Ghilardi & M Zawadowski) Normal Products of Modal Logics (Y Hasimoto) A Tableau Algorithm for the Clique Guarded Fragment (C Hirsch & S Tobies) The Complexity of Reasoning with Boolean Modal Logics (C Lutz & U Sattler) Outline of a Logic of Action (K Segerberg) Belief, Names, and Modes of Presentation (R Ye & M Fitting) and other paper