We investigate the belief revision problem in epistemic planning, i.e., what will be the beliefs of all agents in a multi-agent system after an agent gains the belief in some state property. Based on the standard representation in epistemic planning of agents' beliefs via a single multi-agent Kripke model, we generalize the classical AGM belief revision postulates to the multi-agent setting, with the aim to provide a formal framework for evaluating dynamic epistemic reasoning frameworks in which the beliefs of all agents as the result of actions are computed. As an example of a simple operator that satisfies all of the generalized AGM postulates, we present generalized full-meet multi-agent belief revision. We moreover define a generalization of the standard postulates for iterated revision, present a more sophisticated, event model based revision operator, and discuss the potential issues in defining an epistemic operator on Kripke models that can satisfy all of the generalized postulates for iterated multi-agent belief revision.

The Game Description Language (GDL) is a widely used formalism for specifying the rules of general games. Writing correct GDL descriptions can be challenging, especially for non-experts. Automated theorem proving has been proposed to assist game design by verifying if a GDL description satisfies desirable logical properties. However, when a description is proved to be faulty, the repair task itself can only be done manually. Motivated by the work on repairing unsolvable planning domain descriptions, we define a more general problem of finding minimal repairs for GDL descriptions that violate formal requirements, and we provide complexity results for various computational problems related to minimal repair. Moreover, we present an Answer Set Programming-based encoding for solving the minimal repair problem and demonstrate its application for automatically repairing ill-defined game descriptions.

The Game Description Language with Imperfect Information (GDL-II) is a lightweight formalism for representing the rules of arbitrary games, including those where players have private information. Its purpose is to build general game-playing systems, that is, automated players that can understand the rules of games and learn how to play them without human intervention. Epistemic Strategy Logic (SLK), on the other hand, is a rich logical framework for reasoning about multi-agent systems and the strategic behavior of agents with partial observability. To enable a general game-playing system to take advantage of this rich formalism for the automatic verification of properties of games, we present a formal translation from GDL-II to SLK models. We prove the correctness of this translation and show how crucial properties of general games, including playability and the existence of Nash equilibria, can be expressed as formulas in SLK. Finally, we demonstrate the application of an existing model-checking system for SLK to verify the properties of GDL-II games.

The recent popularity of Wordle has revived interest in guessing games. We develop a general method for finding optimal strategies for guessing games while avoiding an exhaustive search. Our main contribution are several theorems that build towards a general theory to prove optimality of a strategy for a guessing game. This work is developed to apply to any guessing game, but we use Wordle as an example to present concrete results.

Communication actions in games are usually given meaning by either the effect they have on the game state or a possible reduction in the size of the information set of an agent. However, this precludes analysis of games involving state-independent communication, in which players are given the ability to communicate with each other but are not required to be truthful. As such, these communication actions cannot be used to reduce the size of the information set or update beliefs in states without considering the intent of the communicating agent. In this paper, we introduce a language to describe the rules of such games as an extension of the Game Description Language (GDL). We also identify a set of scenarios involving state-independent communication actions in which an effective agent should be able to derive information, and propose and evaluate strategies for reasoning about such actions in these scenarios.

The standard representation formalism for multi-agent epistemic planning has one central disadvantage: When you use event models in dynamic epistemic logic (DEL) to describe the action of one agent, the model must specify not only the actual change and the change of that agent's knowledge. Also required is the epistemic change of any agents that may be observing the first agent performing the action, plus the epistemic change for any further agents that failed to observe that anything had taken place. To overcome the gap between this complex DEL notion of events and a more commonsense notion of actions, we propose a simple high-level action description language for multi-agent epistemic planning domains with just one type of effect laws: a causes x if y. Effect x can either be a physical effect, or an observation from an independent set that is specific to individual agents. We formally prove that any DEL event model can be described in this way. We show how this language provides a framework for expressing a variety of executability and action models; such as describing actions that are both ontic and epistemic, partially observable, or nondeterministic. We further combine our representation of event models with a description language for finitary initial epistemic theories, and we show how this allows us to reason about the effects of a sequence of actions in a multi-agent epistemic domain by updating a single multi-pointed epistemic model.

General Game Playing agents are required to play games they have never seen before simply by looking at a formal description of the rules of the game at runtime. Previous successful agents have been based on search with generic heuristics, with almost no work done into using machine learning. Recent advances in deep reinforcement learning have shown it to be successful in some two-player zero-sum board games such as Chess and Go. This work applies deep reinforcement learning to General Game Playing, extending the AlphaZero algorithm and finds that it can provide competitive results.

General Game Playing is a field which allows the researcher to investigate techniques that might eventually be used in an agent capable of Artificial General Intelligence. Game playing presents a controlled environment in which to evaluate AI techniques, and so we have seen an increase in interest in this field of research. Games of imperfect information offer the researcher an additional challenge in terms of complexity over games with perfect information. In this article, we look at imperfect-information games: their expression, their complexity, and the additional demands of their players. We consider the problems of working with imperfect information and introduce a technique called HyperPlay, for efficiently sampling very large information sets, and present a formalism together with pseudo code so that others may implement it. We examine the design choices for the technique, show its soundness and completeness then provide some experimental results and demonstrate the use of the technique in a variety of imperfect-information games, revealing its strengths, weaknesses, and its efficiency against randomly generating samples. Improving the technique, we present HyperPlay-II, capable of correctly valuing information-gathering moves. Again, we provide some experimental results and demonstrate the use of the new technique revealing its strengths, weaknesses and its limitations.

Several different frameworks have been proposed to model and reason about knowledge in dynamic multi-agent settings, among them the logic-programming-based game description language GDL-III, and dynamic epistemic logic (DEL), based on possible-worlds semantics. GDL-III and DEL have complementary strengths and weaknesses in terms of ease of modeling and simplicity of semantics. In this paper, we formally study the expressiveness of GDL-III vs. DEL. We clarify the commonalities and differences between those languages, demonstrate how to bridge the differences where possible, and identify large fragments of GDL-III and DEL that are equivalent in the sense that they can be used to encode games or planning tasks that admit the same legal action sequences. We prove the latter by providing compilations between those fragments of GDL-III and DEL.

We show that the HyperPlay technique, which maintains a bag of updatable models for sampling an imperfect-information game, is more efficient than taking random samples of play sequences. Also, we demonstrate that random sampling may become impossible under the practical constraints of a game. We show the HyperPlay sample can become biased and not uniformly distributed across an information set and present a remedy for this bias, showing the impact on game results for biased and unbiased samples. We extrapolate the use of the technique beyond General Game Playing and in particular for enhanced security games with in-game percepts to facilitate a flexible defense response.

GDL-III, a description language for general game playing with imperfect information and introspection, supports the specification of epistemic games. These are characterised by rules that depend on the knowledge of players. GDL-III provides a simpler language for representing actions and knowledge than existing formalisms: domain descriptions require neither explicit axioms about the epistemic effects of actions, nor explicit specifications of accessibility relations. We develop a formal semantics for GDL-III and demonstrate that this language, despite its syntactic simplicity, is expressive enough to model the famous Muddy Children domain. We also show that it significantly enhances the expressiveness of its predecessor GDL-II by formally proving that termination of games becomes undecidable, and we present experimental results with a reasoner for GDL-III applied to general epistemic puzzles.

The use of the Monte Carlo playouts as an evaluation function has proved to be a viable, general technique for searching intractable game spaces. This facilitate the use of statistical techniques like Monte Carlo Tree Search (MCTS), but is also known to require significant processing overhead. We seek to improve the quality of information extracted from the Monte Carlo playout in three ways. Firstly, by nesting the evaluation function inside another evaluation function; secondly, by measuring and utilising the depth of the playout; and thirdly, by incorporating pruning strategies that eliminate unnecessary searches and avoid traps. Our experimental data, obtained on a variety of two-player games from past General Game Playing (GGP) competitions and others, demonstrate the usefulness of these techniques in a Nested Player when pitted against a standard, optimised UCT player.

We propose an extension of the standard game description language for general game playing to include epistemic games, which are characterised by rules that depend on the knowledge of players. A single additional keyword suffices to define GDL-III, a general description language for games with imperfect information and introspection. We present an Answer Set Program for automatically reasoning about GDL-III games. Our extended language along with a suitable basic reasoning system can also be used to formalise and solve general epistemic puzzles.

General Game Playing is the design of AI systems able to understand the rules of new games and to use such descriptions to play those games effectively. Games with incomplete information have recently been added as anew challenge for general game-playing systems. The only published solutions to this challenge are based on sampling complete information models. In doing so they ground all of the unknown information, thereby making information gathering moves of no value; a well-known criticism of such sampling based systems. We present and analyse a method for escalating reasoning from complete information models to incomplete information models and show how this enables a general game player to correctly value information in incomplete information games. Experimental results demonstrate the success of this technique over standard model sampling.

This paper introduces a modal logic for reasoning about game strategies. The logic is based on a variant of the well-known game description language for describing game rules and further extends it with two modalities for reasoning about actions and strategies. We develop an axiomatic system and prove its soundness and completeness with respect to a specific semantics based on the state transition model of games. Interestingly, the completeness proof makes use of forgetting techniques that have been widely used in the KR&R literature. We demonstrate how general game-playing systems can apply the logic to develop game strategies.

The Game Description Language GDL is the standard input language for general game-playing systems. While players can gain a lot of traction by an efficient inference algorithm for GDL, state-of-the-art reasoners suffer from a variant of a classical KR problem, the inferential frame problem. We present a method by which general game players can transform any given game description into a representation that solves this problem. Our experimental results demonstrate that with the help of automatically generated domain knowledge, a significant speedup can thus be obtained for the majority of the game descriptions from the AAAI competition.

General game players can drastically reduce the cost of search if they are able to solve smaller subproblems individually and synthesise the resulting solutions. To provide a systematic solution to this (de-)composition problem, we start off with generalising the standard decomposition problem in planning by allowing the composition of individual solutions to be further constrained by domain-dependent requirements of the global planning problem. We solve this generalised problem based on a systematic analysis of composition operators for transition systems, and we demonstrate how this solution can be further generalised to general game playing.

A general game player is a system that can play previously unknown games just by being given their rules. For this purpose, the Game Description Language (GDL) has been developed as a high-level knowledge representation formalism to communicate game rules to players. In this paper, we address a fundamental limitation of state-of-the-art methods and systems for General Game Playing, namely, their being confined to deterministic games with complete information about the game state. We develop a simple yet expressive extension of standard GDL that allows for formalising the rules of arbitrary finite, n-player games with randomness and incomplete state knowledge. In the second part of the paper, we address the intricate reasoning challenge for general game-playing systems that comes with the new description language. We develop a full embedding of extended GDL into the Situation Calculus augmented by Scherl and Levesque's knowledge fluent. We formally prove that this provides a sound and complete reasoning method for players' knowledge about game states as well as about the knowledge of the other players.

Motivated by the problem of building a basic reasoner for general game playing with imperfect information, we address the problem of filtering with logic programs, whereby an agent updates its incomplete knowledge of a program by observations. We develop a filtering method by adapting an existing backward-chaining and abduction method for so-called open logic programs. Experimental results show that this provides a basic effective and efficient "legal" player for general imperfect-information games.

General Game Playing is the design of AI systems able to understand the rules of new games and to use such descriptions to play those games effectively. Games with imperfectinformation have recently been added as a new challenge forexisting general game-playing systems. The HyperPlay technique presents a solution to this challenge by maintaining a collection of models of the true game as a foundation for reasoning, and move selection. The technique provides existing game players with a bolt-on solution to convert from perfect-information games to imperfect-information games. In this paper we describe the HyperPlay technique, show how it was adapted for use with a Monte Carlo decision making process and give experimental results for its performance.

A general game player automatically learns to play arbitrary new games solely by being told their rules. For this purpose games are specified in the game description language GDL, a variant of Datalog with function symbols and a few known keywords. In its latest version GDL allows to describe nondeterministic games with any number of players who may have imperfect, asymmetric information. We analyse the epistemic structure and expressiveness of this language in terms of epistemic modal logic and present two main results:The operational semantics of GDL entails that the situation at any stage of a game can be characterised by a multi-agent epistemic (i.e., S5-) model;(2) GDL is sufficiently expressive to model any situation that can be described by a (finite) multi-agent epistemic model.

Recently the general Game Description Language (GDL) has been extended so as to cover arbitrary games with incomplete/imperfect information. Learning — without human intervention — to play such games poses a reasoning challenge for general game-playing systems that is much more intricate than in case of complete information games. Action formalisms like the Situation Calculus have been developed for precisely this purpose. In this paper we present a full embedding of the Game Description Language into the Situation Calculus (with Scherl and Levesque's knowledge fluent). We formally prove that this provides a sound and complete reasoning method for players' knowledge about game states as well as about the knowledge of the other players.

The Game Description Language is a high-level, rule-based formalisms for communicating the rules of arbitrary games to general game-playing sys-tems, whose challenging task is to learn to play pre-viously unknown games without human interven-tion. Originally designed for deterministic games with complete information about the game state, the language was recently extended to include ran-domness and imperfect information. However, de-termining the extent to which this enhancement al-lows to describe truly arbitrary games was left as an open problem. We provide a positive answer to this question by relating the extended Game Descrip-tion Language to the universal, mathematical con-cept of extensive-form games, proving that indeed just any such game can be described faithfully.

Abstract Logic programming is a powerful paradigm for programming autonomous agents in dynamic domains as witnessed by languages such as Golog and Flux. In this work we present ALPprolog, an expressive, yet efficient, logic programming language for the online control of agents that have to reason about incomplete information and sensing actions.

A General Game Player is a system that can play previously unknown games given nothing but their rules. The Game Description Language (GDL) has been developed as a high-level knowledge representation formalism for axiomatising the rules of any game, and a basic requirement of a General Game Player is the ability to reason logically about a given game description. In this paper, we address the fundamental limitation of existing GDL to be confined to deterministic games with complete information about the game state. To this end, we develop an extension of GDL that is both simple and elegant yet expressive enough to allow to formalise the rules of arbitrary (discrete and finite) n-player games with randomness and incomplete state knowledge. We also show that this extension suffices to provide players with all information they need to reason about their own knowledge as well as that of the other players up front and during game play.

A general game player is a system that understands the rules of unknown games and learns to play these games well without human intervention. A major challenge for research in General Game Playing is to endow a player with the ability to extract and prove game-specific knowledge from the mere game rules. We define a formal language to express temporally extended — yet local — properties of games. We also develop a provably correct proof theory for this language using the paradigm of Answer Set Programming, and we report on experiments with a practical implementation of this proof system in combination with a successful general game player.

The capability of revising its beliefs upon new information in a rational and efficient way is crucial for an intelligent agent. The classical work in belief revision focuses on idealized models and is not concerned with computational aspects. In particular, many researchers are interested in the logical properties (e.g. the AGM postulates) that a rational revision operator should possess. For the implementation of belief revision, however, one has to consider that any realistic agent is a finite being and that calculations take time. In this article, we introduce a new operation for revising beliefs which we call reinforcement belief revision. The computational model for this operation allows us to assess it in terms of time and space consumption. Moreover, the operation is proved equivalent to a (semantical) model based on the concept of possible worlds, which facilitates showing that reinforcement belief revision satisfies all desirable rationality postulates.

The theme of this special issue is the formalization of commonsense reasoning, i.e. the kind of reasoning that people perform in their everyday lives. Its very name suggests that there is nothing much to it—everyone does it, so how hard can it be? It turns out however that commonsense reasoning is a rather intricate business, much harder to formalize than other more classical types of reasoning, such as mathematical reasoning. The main difficulty with commonsense reasoning is that, in contrast to expert reasoning (e.g. economic, legal, medical, etc.), much of the knowledge that is required for commonsense inferences is implicit. Take for example the following scenario: ‘John picked up the newspaper and walked to the kitchen. He made some coffee and started reading about last night's soccer match’. Based on this information alone, the average person would infer that John is now in the kitchen (and therefore he is not in the garden), drinking coffee and reading his newspaper, which is also in the kitchen, and which contains an article about a soccer match that took place the night before.

FLUX is a programming method for the design of agents that reason logically about their actions and sensor information in the presence of incomplete knowledge. The core of FLUX is a system of Constraint Handling Rules, which enables agents to maintain an internal model of their environment by which they control their own behavior. The general action representation formalism of the fluent calculus provides the formal semantics for the constraint solver. FLUX exhibits excellent computational behavior due to both a carefully restricted expressiveness and the inference paradigm of progression.

Agents situated in proactive environments are acting autonomously while the environment is evolving alongside, whether or not the agents carry out any particular actions. A formal framework for simulating and reasoning about this generalized kind of dynamic system is proposed. The capabilities of the agents are modelled by a set of conditional rules in a temporal-logical format. The environment itself is modelled by an independent transition relation of the state space. The temporal language is given a declarative semantics on the basis of an abstract, general model structure for formal specifications of proactive environments. Key words: Agent programming, logic of proactive environments, executable temporal logic.