We introduce a logical language for reasoning about quantized aggregate-combine graph neural networks with global readout (ACR-GNNs). We provide a logical characterization and use it to prove that verification tasks for quantized GNNs with readout are (co)NEXPTIME-complete. This result implies that the verification of quantized GNNs is computationally intractable, prompting substantial research efforts toward ensuring the safety of GNN-based systems. We also experimentally demonstrate that quantized ACR-GNN models are lightweight while maintaining good accuracy and generalization capabilities with respect to non-quantized models.

We introduce Qiana, a logic framework for reasoning on formulas that are true only in specific contexts. In Qiana, it is possible to quantify over both formulas and contexts to express, e.g., that “everyone knows everything Alice says”. Qiana also permits paraconsistent logics within contexts, so that contexts can contain contradictions. Furthermore, Qiana is based on first-order logic, and is finitely axiomatizable, so that Qiana theories are compatible with pre-existing first-order logic theorem provers. We show how Qiana can be used to represent temporality, event calculus, and modal logic. We also discuss different design alternatives of Qiana.

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.

In this paper, we investigate verification of quantized Graph Neural Networks (GNNs), where some fixed-width arithmetic is used to represent numbers. We introduce the linear-constrained validity (LVP) problem for verifying GNNs properties, and provide an efficient translation from LVP instances into a logical language. We show that LVP is in PSPACE, for any reasonable activation functions. We provide a proof system. We also prove PSPACE-hardness, indicating that while reasoning about quantized GNNs is feasible, it remains generally computationally challenging.

Logics for reasoning about knowledge and actions have seen many applications in various domains of multi-agent systems, including epistemic planning. Change of knowledge based on observations about the surroundings forms a key aspect in such planning scenarios. Public Observation Logic (POL) is a variant of public announcement logic for reasoning about knowledge that gets updated based on public observations. Each state in an epistemic (Kripke) model is equipped with a set of expected observations. These states evolve as the expectations get matched with the actual observations. In this work, we prove that the satisfiability problem of POL is 2EXPTIME-complete.

We present a new algorithm for solving the connected multi-agent path finding problem (connected MAPF) which consists in finding paths for a set of agents that avoid collisions but also ensure connectivity between agents during the mission. Our algorithm is based on heuristic search and combines ODrM*, a well known algorithm without connectivity constraints, and an efficient but incomplete solver for the connected MAPF from the literature. We present a formal analysis of the termination and completeness of our algorithm, and present an experimental evaluation, showing a significant improvement over the state of the art.

We introduce Qiana, a logic framework for reasoning on formulas that are true only in specific contexts. In Qiana, it is possible to quantify over both formulas and contexts to express, e.g., that ``everyone knows everything Alice says''. Qiana also permits paraconsistent logics within contexts, so that contexts can contain contradictions. Furthermore, Qiana is based on first-order logic, and is finitely axiomatizable, so that Qiana theories are compatible with pre-existing first-order logic theorem provers.

Public observation logic (POL) reasons about agent expectations and agent observations in various real world situations. The expectations of agents take shape based on certain protocols about the world around and they remove those possible scenarios where their exceptions and observations do not match. This in turn influences the epistemic reasoning of these agents. In this work, we study the computational complexity of the satisfaction problems of various fragments of POL. In the process, we also highlight the inevitable link that these fragments have with the well-studied Public announcement logic.

We introduce the formula-synthesis problem for Propositional Dynamic Logic with Shuffle (PDL || ). This problem, which generalises the model-checking problem againsts PDL || is the following: given a finite transition system and a regular term-grammar that generates (possibly infinitely many) PDL || formulas, find a formula generated by the grammar that is true in the structure (or return that there is none). We prove that the problem is undecidable in general, but add certain restrictions on the input structure or on the input grammar to yield decidability. In particular, we prove that (1) if the grammar only generates formulas in PDL (without shuffle), then the problem is EXPTIME-complete, and a further restriction to linear grammars is PSPACE-complete, and a further restriction to non-recursive grammars is NP-complete, and (2) if one restricts the input structure to have only simple paths then the problem is in 2-EXPTIME. This work is motivated by and opens up connections to other forms of synthesis from hierarchical descriptions, including HTN problems in Planning and Attack-tree Synthesis problems in Security.

In multi-player games, players take their decisions on the basis of their knowledge about what other players have done, or currently do, or even, in some cases, will do. An ability to reason in games with temporal dependencies between players' decisions is a challenging topic, in particular because it involves imperfect information. In this work, we propose a theoretical framework based on dependency matrices that includes many instances of strategic dependencies in multi-player imperfect information games. For our framework to be well-defined, we get inspiration from quantified linear-time logic where each player has to label the timeline with truth values of the propositional variable she owns. We study the problem of the existence of a winning strategy for a coalition of players, show it is undecidable in general, and exhibit an interesting subclass of dependency matrices that makes the problem decidable: the class of perfect-information dependency matrices.

Public observation logic (POL) is a variant of dynamic epistemic logic to reason about agent expectations and agent observations. Agents have certain expectations, regarding the situation at hand, that are actuated by the relevant protocols, and they eliminate possible worlds in which their expectations do not match with their observations. In this work, we investigate the computational complexity of the model checking problem for POL and prove its PSPACE-completeness. We also study various syntactic fragments of POL. We exemplify the applicability of POL model checking in verifying different characteristics and features of an interactive system with respect to the distinct expectations and (matching) observations of the system. Finally, we provide a discussion on the implementation of the model checking algorithms.

Consider a set of agents with initial beliefs and a formal operator for incorporating new information. Now suppose that, for each agent, we have a formula that we would like them to believe. Does there exist a single announcement that will lead all agents to believe the corresponding formula? This paper studies the problem of the existence of such an announcement in the context of model-preference definable revision operators. First, we provide two characterisation theorems for the existence of announcements: one in the general case, the other for total partial orderings. Second, we exploit the characterisation theorems to provide upper bound complexity results. Finally, we also provide matching optimal lower bounds for the Dalal and Ginsberg operators.

We present a generalization of belief base revision to the multi-agent case. In our approach agents have belief bases containing both propositional beliefs and higher-order beliefs about their own beliefs and other agents’ beliefs. Moreover, their belief bases are split in two parts: the mutable part, whose elements may change under belief revision, and the core part, whose elements do not change. We study a belief revision operator inspired by the notion of screened revision. We provide complexity results of model checking for our approach as well as an optimal model checking algorithm. Moreover, we study complexity of epistemic planning formulated in the context of our framework.

We present a generic tool to visualize missions of the Connected Multi-Agent Path Finding (CMAPF) problem. This problem is a variant of MAPF which requires a group of agents to navigate from an initial configuration to a goal configuration while maintaining connection. The user can create an instance of CMAPF and can play the generated plan. Any algorithm for CMAPF can be plugged into the tool.

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Action models of Dynamic Epistemic Logic (DEL) represent precisely how actions are perceived by agents. DEL has recently been used to define infinite multi-player games, and it was shown that they can be solved in some cases. However, the dynamics being defined by the classic DEL update product for individual actions, only turn-based games have been considered so far. In this work we define a concurrent DEL product, propose a mechanism to resolve conflicts between actions, and define concurrent DEL games. As in the turn-based case, the obtained concurrent infinite game arenas can be finitely represented when all actions are public, or all are propositional. Thus we identify cases where the strategic epistemic logic ATL*K can be model checked on such games.

Hintikka's World is a graphical and pedagogical tool that shows how artificial agents can reason about higher-order knowledge. In this demonstration paper, we present the implementation of symbolic models in Hintikka's World. They enable the tool to scale, by helping it to face the state explosion, which makes it possible to provide examples featuring real card games, such as Hanabi.

Motivated by the increasing appeal of robots in information-gathering missions, we study multi-agent path planning problems in which the agents must remain interconnected. We model an area by a topological graph specifying the movement and the connectivity constraints of the agents. We study the theoretical complexity of the reachability and the coverage problems of a fleet of connected agents on various classes of topological graphs. We establish the complexity of these problems on known classes, and introduce a new class called sight-moveable graphs which admit efficient algorithms.

We define reachability games based on Dynamic Epistemic Logic (DEL), where the players? actions are finely described as DEL action models. We first consider the setting where a controller with perfect information interacts with an environment and aims at reaching some desired state of knowledge regarding the observers of the system. We study the problem of existence of a strategy for the controller, which generalises the classic epistemic planning problem, and we solve it for several types of actions such as public announcements and public actions. We then consider a yet richer setting where observers themselves are players, whose strategies must be based on their observations. We establish several decidability and undecidability results for the problem of existence of a distributed strategy, depending on the type of actions the players can use, and relate them to results from the literature on multiplayer games with imperfect information.

Abstract We study the symbolic model checking problem against public announcement protocol logic (PAPL), featuring protocols with public announcements, arbitrary public announcements and group announcements. Technically, symbolic models are Kripke models whose accessibility relations are presented as programs described in a dynamic logic style with propositional assignments. We highlight the relevance of such symbolic models and show that the symbolic model checking problem against PAPL is A$_{\textrm{pol}}$Exptime-complete as soon as announcement protocols allow for either arbitrary announcements or iteration of public announcements. However, when both options are discarded, the complexity drops to Pspace-complete.

We propose a variant of public announcement logic for asynchronous systems. To capture asynchrony, we introduce two different modal operators for sending and receiving messages. The natural approach to defining the semantics leads to a circular definition, but we describe two restricted cases in which we solve this problem. The first case requires the Kripke model representing the initial epistemic situation to be a finite tree, and the second one only allows announcements from the existential fragment. After establishing some validities, we study the model checking problem and the satisfiability problem in cases where the semantics is well-defined, and we provide several complexity results.

Qualitative Decentralized Partially Observable Markov Decision Problems (QDec-POMDPs) constitute a very general class of decision problems. They involve multiple agents, decentralized execution, sequential decision, partial observability, and uncertainty. Typically, joint policies, which prescribe to each agent an action to take depending on its full history of (local) actions and observations, are huge, which makes it difficult to store them onboard, at execution time, and also hampers the computation of joint plans. We propose and investigate a new representation for joint policies in QDec-POMDPs, which we call Multi-Agent Knowledge-Based Programs (MAKBPs), and which uses epistemic logic for compactly representing conditions on histories. Contrary to standard representations, executing an MAKBP requires reasoning at execution time, but we show that MAKBPs can be exponentially more succinct than any reactive representation.

We present a tool for graph coverage with a fleet of UAVs. The UAVs must achieve the coverage of an area under the constraint of staying connected with the base, where the mission supervisor starts the plan. With an OpenStreetMap interface, the user is able to choose a specific location on which the mission needs to be generated and observes the resulting plan being executed.

Epistemic planning extends classical planning with knowledge and is based on dynamic epistemic logic (DEL). The epistemic planning problem is undecidable in general. We exhibit a small undecidable subclass of epistemic planning over 2-agent S5 models with a fixed repertoire of one action, 6 propositions and a fixed goal. We furthermore consider a variant of the epistemic planning problem where the initial knowledge state is an automatic structure, hence possibly infinite. In that case, we show the epistemic planning problem with 1 public action and 2 propositions to be undecidable, while it is known to be decidable with public actions over finite models. Our results are obtained by reducing the reachability problem over small universal cellular automata. While our reductions yield a goal formula that displays the common knowledge operator, we show, for each of our considered epistemic problems, a reduction into an epistemic planning problem for a common-knowledge-operator-free goal formula by using 2 additional actions.

In this demonstration paper, we present a pedagogical tool called Hintikka's world for showing how artificial agents can reason about higher-order knowledge (an agent knows that another agent knows that...). The system provides famous AI examples such as Muddy children and Russian cards. The system also allows to implement user's own examples via the description of a Kripke model or via its generation by the generic tableau method prover MetTeL2.

We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

Public announcements cause each agent in a group to modify their beliefs to incorporate some new piece of information, while simultaneously being aware that all other agents are doing the same. Given a set of agents and a set of epistemic goals, it is natural to ask if there is a single announcement that will make each agent believe the corresponding goal. This problem is known to be undecidable in a general modal setting, where the presence of nested beliefs can lead to complex dynamics. In this paper, we consider not necessarily truthful public announcements in the setting of AGM belief revision. We prove that announcement finding in this setting is not only decidable, but that it is simpler than the corresponding problem in the most simplified modal logics. We then describe AnnB, an implemented tool that uses announcement finding as the basis for controlling robot behaviour through belief manipulation.

The article introduces a ceteris paribus modal logic, called CP, interpreted on the equivalence classes induced by finite sets of propositional atoms. This logic is studied and then used to embed three logics of strategic interaction, namely atemporal STIT, the coalition logic of propositional control (CL−PC) and the starless fragment of the dynamic logic of propositional assignments (DL−PA). The embeddings highlight a common ceteris paribus structure underpinning the key operators of all these apparently very different logics and show, we argue, remarkable similarities behind some of the most influential formalisms for reasoning about strategic interaction

STIT is a potential logical framework to capture responsibility, counterfactual emotions and norms, which are main ingredients for specifying behaviors of virtual agents. We identify here a new fragment and its satisfiability problem is NP-complete and in Σ3when the number of agents is unbounded. We also identify a slightly more expressive fragment which is undecidable.