The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models, now in widespread use.There is a natural extension of the definition of a bisimulation to action models.Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect. We first concentrate on the general case, and next focus on the important case of action models with propositional preconditions. Our notion of action emulation yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action.
The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown.We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. We analyse one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that becomes false because it is announced.The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking and the complexity is experimentally investigated for several representations and parameter settings.
We give a relation between a logic of knowledge and change, with a semantics on Kripke models, and a logic of knowledge and time, with a semantics on interpreted systems. In particular, given an epistemic state (pointed Kripke model with equivalence relations) and a formula in a dynamic epistemic logic (a logic describing the consequences of epistemic actions), we construct an interpreted system relative to that epistemic state and that formula that satisfies the translation of the formula into a temporal epistemic logic. The construction involves that the protocol that is implicit in the dynamic epistemic formula, i.e., the set of sequences of actions being executed to evaluate the formula, is made explicit. We first focus on the logic of knowledge and change that is known as public announcement logic, then generalize our results to a dynamic epistemic logic.
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