In this work, we present the first general logic of attention. Attention is a powerful cognitive ability that allows agents to focus on potentially complex information, such as logically structured propositions, higher-order beliefs, or what other agents pay attention to. This ability is a strength, as it helps to ignore what is irrelevant, but it can also introduce biases when some types of information or agents are systematically ignored. Existing dynamic epistemic logics for attention cannot model such complex attention scenarios, as they only model attention to atomic formulas. Additionally, such logics quickly become cumbersome, as their size grows exponentially in the number of agents and announced literals. Here, we introduce a logic that overcomes both limitations. First, we generalize edge-conditioned event models, which we show to be as expressive as standard event models yet exponentially more succinct (generalizing both standard event models and generalized arrow updates). Second, we extend attention to arbitrary formulas, allowing agents to also attend to other agents' beliefs or attention. Our work treats attention as a modality, like belief or awareness. We introduce attention principles that impose closure properties on that modality and that can be used in its axiomatization. Throughout, we illustrate our framework with examples of AI agents reasoning about human attention, demonstrating how such agents can discover attentional biases.

We propose a novel algorithm for epistemic planning based on dynamic epistemic logic (DEL). The novelty is that we limit the depth of reasoning of the planning agent to an upper bound b, meaning that the planning agent can only reason about higher-order knowledge to at most (modal) depth b. We then compute a plan requiring the lowest reasoning depth by iteratively incrementing the value of b. The algorithm relies at its core on a new type of "canonical" b-bisimulation contraction that guarantees unique minimal models by construction. This yields smaller states wrt. standard bisimulation contractions, and enables to efficiently check for visited states. We show soundness and completeness of our planning algorithm, under suitable bounds on reasoning depth, and that, for a bound b, it runs in (b+1)-EXPTIME. We implement the algorithm in a novel epistemic planner, DAEDALUS, and compare it to the EFP 2.0 planner on several benchmarks from the literature, showing effective performance improvements.

Abstract Dynamic Belief Update is a model checking problem in Dynamic Epistemic Logic concerning the effect of applying a number of epistemic actions on an initial epistemic model. It can also be considered as a plan verification problem in epistemic planning. The problem is known to be PSPACE-hard. To better understand the source of complexity of the problem, previous research has investigated the complexity of 128 parameterized versions of the problem with parameters such as number of agents and size of epistemic actions. The complexity of many parameter combinations has been determined, but previous research left 14 parameter combinations open. In this paper, we solve all of these open problems. Most of the parameter combinations turns out to be fixed-parameter intractable, except for 3 that are fixed-parameter tractable.

Width-based planning methods have been shown to yield state-of-the-art performance in the Atari 2600 domain using pixel input. One successful approach, RolloutIW, represents states with the B-PROST boolean feature set. An augmented version of RolloutIW, pi-IW, shows that learned features can be competitive with handcrafted ones for width-based search. In this paper, we leverage variational autoencoders (VAEs) to learn features directly from pixels in a principled manner, and without supervision. The inference model of the trained VAEs extracts boolean features from pixels, and RolloutIW plans with these features. The resulting combination outperforms the original RolloutIW and human professional play on Atari 2600 and drastically reduces the size of the feature set.

Epistemic planning based on Dynamic Epistemic Logic (DEL) allows agents to reason and plan from the perspective of other agents. The framework of DEL-based epistemic planning thereby has the potential to represent significant aspects of Theory of Mind in autonomous robots, and to provide a foundation for human-robot collaboration in which coordination is achieved implicitly through perspective shifts. In this paper, we build on previous work in epistemic planning with implicit coordination. We introduce a new notion of indistinguishability between epistemic states based on bisimulation, and provide a novel partition refinement algorithm for computing unique representatives of sets of indistinguishable states. We provide an algorithm for computing implicitly coordinated plans using these new constructs, embed it in a perceive-plan-act agent loop, and implement it on a robot. The planning algorithm is benchmarked against an existing epistemic planning algorithm, and the robotic implementation is demonstrated on human-robot collaboration scenarios requiring implicit coordination.

We present a tool for synthesizing and verifying optimal game playing strategies represented by compact fast-and-frugal trees, i.e., prioritized lists of strategic rules. The purpose of the tool is to create human-friendly optimal strategies for simple board games, e.g. for teaching a human player to play optimally, or to assess the difficulty of a given board game in terms of the length of the generated strategy. The tool supports arbitrary one-or two-player zero-sum games with perfect information specified through the game description language GDL within general game playing. When synthesizing a strategy, the game is initially solved, the solution is turned into a fast-and-frugal tree, and the tree is then minimized. We illustrate the use of the tool to synthesize compact optimal strategies for Tic-tac-toe, Nim, and Sim, which leads us to provide an even shorter optimal strategy for Tic-tac-toe than the well-known Simon & Newell strategy. Additionally, we have developed a visual tool enabling users to build and verify manually crafted fast-and-frugal strategies.

Previous research has claimed dynamic epistemic logic (DEL) to be a suitable formalism for representing essential aspects of a Theory of Mind (ToM) for an autonomous agent. This includes the ability of the formalism to represent the reasoning involved in false-belief tasks of arbitrary order, and hence for autonomous agents based on the formalism to become able to pass such tests. This paper provides evidence for the claims by documenting the implementation of a DEL-based reasoning system on a humanoid robot. Our implementation allows the robot to perform cognitive perspective-taking, in particular to reason about the first- and higher-order beliefs of other agents. We demonstrate how this allows the robot to pass a quite general class of false-belief tasks involving human agents. Additionally, as is briefly illustrated, it allows the robot to proactively provide human agents with relevant information in situations where a system without ToM-abilities would fail. The symbolic grounding problem of turning robotic sensor input into logical action descriptions in DEL is achieved via a perception system based on deep neural networks.

In multi-agent path finding, it is usually assumed that planning is performed centrally and that the destinations of the agents are common knowledge. We will drop both assumptions and analyze under which conditions it can be guaranteed that the agents reach their respective destinations using implicitly coordinated plans without communication.

In multi-agent path finding (MAPF), it is usually assumed that planning is performed centrally and that the destinations of the agents are common knowledge. We will drop both assumptions and analyze under which conditions it can be guaranteed that the agents reach their respective destinations using implicitly coordinated plans without communication. Furthermore, we will analyze what the computational costs associated with such a coordination regime are. As it turns out, guarantees can be given assuming that the agents are of a certain type. However, the implied computational costs are quite severe. In the distributed setting, we either have to solve a sequence of NP-complete problems or have to tolerate exponentially longer executions. In the setting with destination uncertainty, bounded plan existence becomes PSPACE-complete. This clearly demonstrates the value of communicating about plans before execution starts.

In this article we study learnability of fully observable, universally applicable action models of dynamic epistemic logic. We introduce a framework for actions seen as sets of transitions between propositional states and we relate them to their dynamic epistemic logic representations as action models. We introduce and discuss a wide range of properties of actions and action models and relate them via correspondence results. We check two basic learnability criteria for action models: finite identifiability (conclusively inferring the appropriate action model in finite time) and identifiability in the limit (inconclusive convergence to the right action model). We show that deterministic actions are finitely identifiable, while arbitrary (non-deterministic) actions require more learning power—they are identifiable in the limit. We then move on to a particular learning method, i.e. learning via update, which proceeds via restriction of a space of events within a learning-specific action model. We show how this method can be adapted to learn conditional and unconditional deterministic action models. We propose update learning mechanisms for the afore mentioned classes of actions and analyse their computational complexity. Finally, we study a parametrized learning method which makes use of the upper bound on the number of propositions relevant for a given learning scenario. We conclude with describing related work and numerous directions of further work.

In this article we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be ‘intermediate’ logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the article. Our results show that many-valued hybrid logic is indeed a natural enterprise.

Proof systems for hybrid logic typically use @-operators to access information hidden behind modalities; this labelling approach lies at the heart of the best known hybrid resolution, natural deduction and tableau systems. But there is another approach, which we have come to believe is conceptually clearer. We call this Seligman-style inference, as it was first introduced and explored by Jerry Seligman in natural deduction and sequent calculus in the 1990s. The purpose of this article is to introduce a Seligman-style tableau system, to prove its completeness, and to show how it can be made to terminate. The most obvious feature of Seligman-style systems is that they work with arbitrary formulas, not just statements prefixed by @-operators. They do so by introducing machinery for switching to other proof contexts. We capture this idea in the setting of tableaus by introducing a rule called GoTo, which allows us to ‘jump to a named world’ on a tableau branch. We first develop a Seligman-style tableau system for basic hybrid logic and prove its completeness. We then prove termination of a restricted version of the system without resorting to loop checking, and show that the restrictions do not effect completeness. Both completeness and termination results are proved by explicit translations that transform tableaus in a standard labelled system into Seligman-style tableaus and vice-versa.

This article extends and improves work on tableau-based decision methods for hybrid logic by Bolander and Braüner. Their paper gives tableau-based decision procedures for basic hybrid logic (with unary modalities) and the basic logic extended with the global modality. All their proof procedures make use of loop-checks to ensure termination. Here we take a closer look at termination for hybrid tableaus. We cover both types of system used in hybrid logic: prefixed tableaus and internalized tableaus. We first treat prefixed tableaus. We prove a termination result for the basic language (with n-ary operators) that does not involve loop-checks. We then successively add the global modality and n-ary inverse modalities, show why various different types of loop-check are required in these cases, and then re-prove termination. Following this we consider internalized tableaus. At first sight, such systems seem to be more complex. However, we define a internalized system which terminates without loop-checks. It is simpler than previously known internalized systems (all of which require loop-checks to terminate) and simpler than our prefix systems (no non-local side conditions on rules are required).

Hybrid logics are a principled generalization of both modal logics and description logics. It is well known that various hybrid logics without binders are decidable, but decision procedures are usually not based on tableau systems, a kind of formal proof procedure that lends itself to computer implementation. In this article, we give four different tableau-based decision procedures for a very expressive hybrid logic including the universal modality; three of the procedures are based on different tableau systems, and one procedure is based on a Gentzen system. The decision procedures make use of so-called loop-checks, which is a standard technique used in connection with tableau systems for other logics, namely, prefixed tableau systems for transitive modal logics as well as for certain description logics. The loop-checks used in our four decision procedures are similar, but the four proof systems on which the procedures are based constitute a spectrum of different systems: prefixed and internalized systems, tableau and Gentzen systems.