Abstract Though Propositional Dynamic Logic (PDL) as well as its relation to planning has been widely studied, there is as of yet no consensus as to how to handle parallelism in the framework. In this paper, we propose a parallel version of the Dynamic Logic of Propositional Assignments (${\textsf{DL-PA} } $), a simple fragment of PDL in which atomic programs are assignments of the truth value of a formula to a propositional variable. We introduce two new operators for ${\textsf{DL-PA} }$, namely parallel composition and inclusive non-deterministic composition. For the former, we suppose that two programs can be executed in parallel if they do not assign different values to the same variable. We give a polynomial translation of the resulting Dynamic Logic of Parallel Propositional Assignments (${\textsf{DL-PPA} }$) into ${\textsf{DL-PA} }$, thereby showing that complexity remains in PSpace. We then turn to planning and show how to capture executability of parallel STRIPS-like actions and solvability of planning tasks by parallel plans in ${\textsf{DL-PPA} }$, following three different semantics for parallelism: one closely following our criterion for parallelism in ${\textsf{DL-PPA} }$, and two from the literature based on interleaving.

We introduce a novel language for reasoning about agents' cognitive attitudes of both epistemic and motivational type. We interpret it by means of a computationally grounded semantics using belief bases. Our language includes five types of modal operators for implicit belief, complete attraction, complete repulsion, realistic attraction and realistic repulsion. We give an axiomatization and show that our operators are not mutually expressible and that they can be combined to represent a large variety of psychological concepts including ambivalence, indifference, being motivated, being demotivated and preference. We present a dynamic extension of the language that supports reasoning about the effects of belief change operations. Finally, we provide a succinct formulation of model checking for our languages and a PSPACE model checking algorithm relying on a reduction into TQBF. We present some experimental results for the implemented algorithm on computation time in a concrete example.

The card game Hanabi has recently gained popularity as a benchmark for handling epistemic reasoning in AI systems. However it has until now mostly been approached through the lens of machine learning rather than formal logical analysis. This is mostly due to the fact that modeling Hanabi in the standard epistemic logic DEL is untractable. In this paper we take a different approach to formalizing Hanabi, using the simple epistemic logic EL-O as a starting point. We generalize common knowledge in EL-O to arbitrary groups of agents and show how to overcome some of the limitations EL-O places on agent reasoning by introducing a special reasoning action. Analyzing our formalization of Hanabi finally leads us to introduce an alternative semantics for our generalization of EL-O in which models are finite and satisfiability checking is NP-complete, and which is enough to fully describe the evolution of knowledge in a game of Hanabi.

Epistemic planning is useful in situations where multiple agents have different knowledge and beliefs about the world, such as in robot-human interaction. One aspect that has been largely neglected in the literature is planning with observations in the presence of false beliefs. This is a particularly challenging problem because it requires belief revision. We introduce a simple specification language for reasoning about actions with knowledge and belief. We demonstrate our approach on well-known false-belief tasks such as the Sally-Anne Task and compare it to other action languages. Our logic leads to an epistemic planning formalism that is expressive enough to model second-order false-belief tasks, yet has the same computational complexity as classical planning.

We introduce a simple model of agency that is based on the concepts of control and attempt. Both relate agents and propositional variables. Moreover, they can be nested: an agent i may control whether another agent j controls a propositional variable p; i may control whether j attempts to change p; i may attempt to change whether j controls p; i may attempt to change whether j attempts to change p; and so on. In this framework we define several modal operators of time and agency: the LTL operators on the one hand, and the Chellas and the deliberative stit operator on the other. While in the standard stit framework the model checking problem is unfeasible because its models are infinite, in our framework models are represented in a finite and compact way: they are grounded on the primitive concepts of control and attempt. This makes model checking practically feasible. We prove its PSPACE-completeness and we show how the concept of social influence can be captured.

Existing dynamic epistemic logics combine standard epistemic logic with a restricted version of dynamic logic. Instead, we here combine a restricted epistemic logic with a rich version of dynamic logic. The epistemic logic is based on `knowing-whether' operators and basically disallows disjunctions and conjunctions in their scope; it moreover captures `knowing-what'. The dynamic logic has not only all the standard program operators of Propositional Dynamic Logic, but also parallel composition as well as an operator of inclusive nondeterministic composition; its atomic programs are assignments of propositional variables. We show that the resulting dynamic epistemic logic is powerful enough to capture several kinds of sequential and parallel planning, and so both in the unbounded and in the finite horizon version.

International audience

We study a simple version of multi-agent epistemic planning where the number of parallel steps has to be minimized. We prove that this extension of classical planning is in PSPACE. We propose an encoding in PDDL and present some experiments providing evidence that this encoding allows us to solve practical problems. The types of problems we can encode include problems in which one agent can teach another agent how to perform a task and communication problems where some information must not be revealed to some agents.