Most existing work on strategic reasoning simply adopts either an informed or an uninformed semantics. We propose a model where knowledge of strategies can be specified on a fine-grained level. In particular, it is possible to distinguish first-order, higher-order, and common knowledge of strategies. We illustrate the effect of higher-order knowledge of strategies by studying the game Hanabi. Further, we show that common knowledge of strategies is necessary to solve the consensus problem. Finally, we study the decidability of the model checking problem.

Intelligent systems, such as Multi-Agent Systems (MAS), can be seen as a set of intelligent entities capable of proactively decide how to act to fulfill their own goals. These entities, called generally agents, are notoriously autonomous, i.e., they do not expect input from an user to act, and social, i.e., they usually communicate amongst each other to achieve common goals. Software systems are not easy to trust in general. This is especially true in the case of complex and distributed systems, such as MAS. Because of this, we need verification techniques to verify that such systems behave as expected. More specifically, in the case of MAS, it is relevant to know whether the agents are capable of achieving their own goals, by themselves or by collaborating with other agents by forming a coalition. This is usually referred to as the process of finding a strategy for the agent(s). A well-known formalism for reasoning about strategic behaviours in MAS is Alternating-time Temporal Logic (AT L) [1]. Before verifying AT L specifications, two questions need to be answered: (i) does each agent know everything about the system?

The model checking problem for multi-agent systems against specifications in the alternating-time temporal logic ATL, hence ATL∗, under perfect recall and imperfect information is known to be undecidable. To tackle this problem, in this paper we investigate a notion of bounded recall under incomplete information. We present a novel three-valued semantics for ATL∗ in this setting and analyse the corresponding model checking problem. We show that the three-valued semantics here introduced is an approximation of the classic two-valued semantics, then give a sound, albeit partial, algorithm for model checking two-valued perfect recall via its approximation as three-valued bounded recall. Finally, we extend MCMAS, an open-source model checker for ATL and other agent specifications, to incorporate bounded recall; we illustrate its use and present experimental results.

We explore the paradigm of artifact-centric systems from a knowledge-based perspective. We provide a semantics based on interpreted-systems to interpret a first-order temporal- epistemic language with identity in a multi-agent setting. We consider the model checking problem for this language and provide abstraction results. We isolate a natural subclass of artifact-systems for which the model checking problem is decidable. We give an upper bound on the complexity of the model checking problem.

Probabilistic model checking has been developed for verifying systems that have stochastic and nondeterministic behavior. Given a probabilistic system, a probabilistic model checker takes a property and checks whether or not the property holds in that system. For this reason, probabilistic model checking provide rigorous guarantees. So far, however, probabilistic model checking has focused on propositional models where a state is represented by a symbol. On the other hand, it is commonly required to make relational abstractions in planning and reinforcement learning. Various frameworks handle relational domains, for instance, STRIPS planning and relational Markov Decision Processes. Using propositional model checking in relational settings requires one to ground the model, which leads to the well known state explosion problem and intractability. We present pCTL-REBEL, a lifted model checking approach for verifying pCTL properties of relational MDPs. It extends REBEL, a relational model-based reinforcement learning technique, toward relational pCTL model checking. PCTL-REBEL is lifted, which means that rather than grounding, the model exploits symmetries to reason about a group of objects as a whole at the relational level. Theoretically, we show that pCTL model checking is decidable for relational MDPs that have a possibly infinite domain, provided that the states have a bounded size. Practically, we contribute algorithms and an implementation of lifted relational model checking, and we show that the lifted approach improves the scalability of the model checking approach.

Autonomous systems are often required to operate in partially observable environments. They must reliably execute a specified objective even with incomplete information about the state of the environment. We propose a methodology to synthesize policies that satisfy a linear temporal logic formula in a partially observable Markov decision process (POMDP). By formulating a planning problem, we show how to use point-based value iteration methods to efficiently approximate the maximum probability of satisfying a desired logical formula and compute the associated belief state policy. We demonstrate that our method scales to large POMDP domains and provides strong bounds on the performance of the resulting policy.

Dynamic epistemic logic (DEL) is a logical framework for representing and reasoning about knowledge change for multiple agents. An important computational task in this framework is the model checking problem, which has been shown to be PSPACE-hard even for S5 models and two agents. We answer open questions in the literature about the complexity of this problem in more restricted settings. We provide a detailed complexity analysis of the model checking problem for DEL, where we consider various combinations of restrictions, such as the number of agents, whether the models are single-pointed or multi-pointed, and whether postconditions are allowed in the updates. In particular, we show that the problem is already PSPACE-hard in (1) the case of one agent, multi-pointed S5 models, and no postconditions, and (2) the case of two agents, only single-pointed S5 models, and no postconditions. In addition, we study the setting where only semi-private announcements are allowed as updates. We show that for this case the problem is already PSPACE-hard when restricted to two agents and three propositional variables.

Reasoning about temporal knowledge is a fundamental task in the area of artificial intelligence and knowledge representation. A key problem in this area is model checking, and indispensable for the state-of-the-art in solving this problem in large-scale settings is the technique of bounded model checking. We investigate the theoretical possibilities of this technique using parameterized complexity theory. In particular, we provide a complete parameterized complexity classification for the model checking problem for symbolically represented Kripke structures for various fragments of the temporal logics LTL, CTL and CTL*. We argue that a known result from the literature for a restricted fragment of LTL can be seen as an fpt-reduction to SAT, and show that such reductions are not possible for any of the other fragments of the temporal logics that we consider. As a by-product of our investigation, we develop a novel parameterized complexity class that can be seen as a parameterized variant of the Polynomial Hierarchy.

Model checking is one of the most powerful and widespread tools for system verification with applications in many areas of computer science and artificial intelligence. The large majority of model checkers deal with properties expressed in point-based temporal logics, such as LTL and CTL. However, there exist relevant properties of systems which are inherently interval-based. Model checking algorithms for interval temporal logics (ITLs) have recently been proposed to check interval properties of computations. As the model checking problem for full Halpern and Shoham's ITL (HS for short) turns out to be decidable, but computationally heavy, research has focused on its well-behaved fragments. In this paper, we provide an almost final picture of the computational complexity of model checking for HS fragments with modalities for (a subset of) Allen's relations meets , met by , starts , and ends .

We introduce EHS*, a novel temporal-epistemic logic defined on temporal intervals characterised by regular expressions. We investigate the complexity of verifying multi-agent systems against EHS* specifications for a number of fragments of EHS* with results ranging from PSPACE-completeness to non-elementary time. The findings show that, at least for the fragments under analysis, the increase in expressiveness obtained by using regular expressions rather than end-points as standard, can be achieved without increasing the complexity of the problem. We show that the expressiveness of regular expressions can also be adopted at the level of specifications without severe computational cost. To do so we introduce a further temporal-epistemic logic, called EHSre, in which regular expressions are used within propositions, and give a polynomial time reduction of the model checking problem from EHSre to EHS*.