Conditional Epistemic Planning

Abstract

Abstract. Recent work has shown that Dynamic Epistemic Logic (DEL) offers a solid foundation for automated planning under partial observability and non-determinism. Under such circumstances, a plan must branch if it is to guarantee achieving the goal under all contingencies (strong planning). Without branching, plans can offer only the possibility of achieving the goal (weak planning). We show how to formulate planning in uncertain domains using DEL and give a language of conditional plans. Translating this language to standard DEL gives verification of both strong and weak plans via model checking. In addition to plan verification, we provide a tableau-inspired algorithm for synthesising plans, and show this algorithm to be terminating, sound and complete.

Learning to act: qualitative learning of deterministic action models

“…In the case of unconditional deterministic actions this makes a significant difference. The time complexity measured in number of distinct observations goes down from O(2 |P| ) to O (1). Here is the argument.…”

“…Two fully observable action models a and b are called propositionally equivalent, written a ≡ p b, if act(a) = act(b). 1 In the definition above, we have used the earlier introduced convention of taking s⊗a to be the set {s⊗e | e ∈ dom(a) and s |= pre(e)}. So 't ∈ s⊗a' in the formula above means 't = s⊗e for some e ∈ dom(a)'.…”

“…An action model can be applied to the epistemic model via the so-called product update operation, resulting in a new up-to-date epistemic model of the situation, after the action has been executed. This setting is particularly useful for modelling the process of epistemic planning (see [1,9]): one can ask which sequence of actions should be executed in order for a given epistemic formula to hold in the resulting epistemic model. A planning agent might not know the effects of her actions, so she will initially not be able to plan to achieve any goals.…”

Cooperative Epistemic Multi-Agent Planning for Implicit Coordination

“…In particular, as soon as branching on nondeterministic action outcomes or obtained observations becomes necessary, we need conditional plans to solve such a task. Unlike Andersen, Bolander, and Jensen [4], who represent conditional plans as action trees with branches depending on knowledge formula conditions, we represent them as policy functions (π i ) i∈A , where each π i maps minimal local states of agent i into actions of agent i. We now define two different types of policies, joint policies and global policies, and later show them to be equivalent.…”

“…Our work is situated in the area of distributed problem solving and planning [15] and directly builds upon the framework introduced by Bolander and Andersen [8] and Löwe, Pacuit, and Witzel [22], who formulated the planning problem in the context of Dynamic Epistemic Logic (DEL) [13]. Andersen, Bolander, and Jensen [4] extended the approach to allow strong and weak conditional planning in the single-agent case. Algorithmically, (multi-agent) epistemic planning can be approached either by compilation to classical planning [2,21,23] or by search in the space of "nested" [8] or "shallow" knowledge states [26,27,28].…”