Concurrent Game Structures Research Articles

On Alternating-Time Temporal Logic, Hyperproperties, and Strategy Sharing

Alternating-time temporal logic (ATL*) is a well-established framework for formal reasoning about multi-agent systems. However, while ATL* can reason about the strategic ability of agents (e.g., some coalition A can ensure that a goal is reached eventually), we cannot compare multiple strategic interactions, nor can we require multiple agents to follow the same strategy. For example, we cannot state that coalition A can reach a goal sooner (or more often) than some other coalition A'. In this paper, we propose HyperATL*_S, an extension of ATL* in which we can (1) compare the outcome of multiple strategic interactions w.r.t. a hyperproperty, i.e., a property that refers to multiple paths at the same time, and (2) enforce that some agents share the same strategy. We show that HyperATL*_S is a rich specification language that captures important AI-related properties that were out of reach of existing logics. We prove that model checking of HyperATL*_S on concurrent game structures is decidable. We implement our model-checking algorithm in a tool we call HyMASMC and evaluate it on a range of benchmarks.

An abstraction-refinement framework for verifying strategic properties in multi-agent systems with imperfect information

We investigate the verification of Multi-Agent Systems against strategic properties expressed in Alternating-time Temporal Logic under the assumptions of imperfect information and perfect recall. To this end, we develop a three-valued semantics for concurrent game structures upon which we define an abstraction method. We prove that concurrent game structures with imperfect information admit perfect information abstractions that preserve three-valued satisfaction. Furthermore, to deal with cases in which the value of a specification is undefined, we develop a novel automata-theoretic technique for the linear-time logic (LTL), then apply it to finding “failure” states. The latter can then be fed into a refinement procedure, thus providing a sound, albeit incomplete, verification method. We illustrate the overall procedure in a variant of the Train Gate Controller scenario and a simple voting protocol under imperfect information and perfect recall. We also present an implementation of our procedure and provide preliminary experimental results.

Modal characterisation of simulation relations in probabilistic concurrent games

Probabilistic game structures combine both nondeterminism and stochasticity, where players repeatedly take actions simultaneously to move to the next state of the concurrent game. Probabilistic alternating simulation and bisimulation are important tools to compare the behaviour of different probabilistic game structures. In this paper, we present a sound and complete modal characterisation of these two relations by proposing a new modal logic based on probability distributions. This logic enables a player to enforce a property in the next state or distribution. We further extend the logic with fixpoint operators, which also characterises the simulation relations. This logic can express a lot of interesting properties in practical applications. • Modal characterization for Probabilistic Alternating Simulation (and Bisimulation). • A new modal logic for probability distributions in concurrent game structures. • Extends the modal logic with fixpoint operators.

Unbounded Model Checking for ATL

In this paper, we deal with verification of multi-agent systems represented as concurrent game structures. To express properties to be verified, we use Alternating-Time Temporal Logic (ATL) formulas. We provide an implementation of symbolic model checking for ATL and preliminary, but encouraging experimental results.

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*.

Probabilistic Alternating-Time Temporal Logic of Incomplete Information and Synchronous Perfect Recall

A probabilistic variant of ATL* logic is proposed to work with multi-player games of incomplete information and synchronous perfect recall. The semantics of the logic is settled over probabilistic interpreted system and partially observed probabilistic concurrent game structure. While unexpectedly, the model checking problem is in general undecidable even for single-group fragment, we find a fragment whose complexity is in 2-EXPTIME. The usefulness of this fragment is shown over a land search scenario.

Fuzzy Alternating Refinement Relations Under the Gödel Semantics

Refinement relations, such as trace containment, simulation preorder, and their alternating versions, have been successfully applied in formal verification of concurrent systems. Recently, trace containment and simulation preorder have been adopted and developed in fuzzy systems, but the generalization of their alternating versions to fuzzy systems has not been investigated. To satisfy the need for modeling and analyzing fuzzy systems, this article proposes two types of refinement relations called fuzzy alternating trace containment and fuzzy alternating simulation preorder, based on fuzzy concurrent game structures (FCGSs) under the Gödel semantics. These two fuzzy notions inherit properties from the corresponding classical setting. For example, fuzzy alternating simulation preorder for finite-state FCGSs can be computed in polynomial time; fuzzy alternating simulation preorder is a fuzzy subset of fuzzy alternating trace containment, and both relations can be logically characterized in terms of fuzzy version of alternating-time temporal logic. These properties make the theory developed here suitable for the modeling and verification of fuzzy systems.

An Abstraction-Based Method for Verifying Strategic Properties in Multi-Agent Systems with Imperfect Information

We investigate the verification of Multi-agent Systems against strategic properties expressed in Alternating-time Temporal Logic under the assumptions of imperfect information and perfect recall. To this end, we develop a three-valued semantics for concurrent game structures upon which we define an abstraction method. We prove that concurrent game structures with imperfect information admit perfect information abstractions that preserve three-valued satisfaction. Further, we present a refinement procedure to deal with cases where the value of a specification is undefined. We illustrate the overall procedure in a variant of the Train Gate Controller scenario under imperfect information and perfect recall.

Making Agents’ Abilities Explicit

Alternating-time temporal logics (ATL/ATL*) represent a family of modal logics for reasoning about agents' strategic abilities in multiagent systems (MAS). The interpretations of ATL/ATL* over the semantic model Concurrent Game Structures (CGS) usually vary depending on the agents' abilities, for instance, perfect vs. imperfect information, perfect vs. imperfect recall, resulting in a variety of variants which have been studied extensively in literature. However, they are defined at the semantic level, which may limit modeling flexibilities and may give counter-intuitive interpretations. To mitigate these issues, in this work, we propose to extend CGS with agents' abilities and study the new semantics of ATL/ATL* under this model. We give PSACE/2EXPTIME model-checking algorithms for ATL/ATL* and implement them as a prototype tool. Experiment results show the practical feasibility of the approach.

Relaxing Exclusive Control in Boolean Games

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are formulas of Linear Temporal Logic. Both notions of BG are characterised by the fact that agents have exclusive control over their set of atoms, meaning that no two agents can control the same atom. In the present contribution we drop the exclusivity assumption and explore structures where an atom can be controlled by multiple agents. We introduce Concurrent Game Structures with Shared Propositional Control (CGS-SPC) and show that they ac- count for several classes of repeated games, including iterated boolean games, influence games, and aggregation games. Our main result shows that, as far as verification is concerned, CGS-SPC can be reduced to concurrent game structures with exclusive control. This result provides a polynomial reduction for the model checking problem of specifications in Alternating-time Temporal Logic on CGS-SPC.

Norm-based mechanism design

The increasing presence of autonomous (software) systems in open environments in general, and the complex interactions taking place among them in particular, require flexible control and coordination mechanisms to guarantee desirable overall system level properties without limiting the autonomy of the involved systems. In artificial intelligence, and in particular in the multi-agent systems research field, social laws, norms, and sanctions have been widely proposed as flexible means for coordinating the behaviour of autonomous agents in multi-agent settings. Recently, many languages have been proposed to specify and implement norm-based environments where the behaviour of autonomous agents is monitored, evaluated based on norms, and possibly sanctioned if norms are violated.In this paper, we first introduce a formal setting of multi-agent environments based on concurrent game structures which abstracts from concrete specification languages. We extend this formal setting with norms and sanctions, and show how concepts from mechanism design can be used to formally analyse and verify whether a specific behaviour can be enforced (or implemented) if agents follow their subjective preferences. We relate concepts from mechanism design to our setting, where agents' preferences are modelled by linear time temporal logic (LTL) formulae. This proposal bridges the gap between norms and mechanism design allowing us to formally study and analyse the effect of norms and sanctions on the behaviour of rational agents. The proposed machinery can be used to check whether specific norms and sanctions have the designer's expected effect on the rational agents' behaviour or if a set of norms and sanctions that realise the effect exists at all. We investigate the computational complexity of our framework, focusing on its implementation in Nash equilibria and we show that it is located at the second and third level of the polynomial hierarchy. Despite this high complexity, on the positive side, these results are in line with existing complexity results of related problems. Finally, we propose a concrete executable specification language that can be used to implement multi-agent environments. We show that the proposed specification language generates specific concurrent game structures and that the abstract multi-agent environment setting can be applied to study and analyse the behaviour of multi-agent programs with and without norms.

Model checking open systems with alternating projection temporal logic

To specify properties of open systems with interval based temporal logics, Alternating Projection Temporal Logic (APTL) is proposed by introducing Concurrent Game Structures (CGS) to Propositional Projection Temporal Logic (PPTL). Further, examples are given to show how properties of open systems can be specified by APTL formulas. Moreover, to establish the automata based model theory for the new proposed logic, Generalized alternating Büchi automata over Concurrent Game structures (GBCGs) are defined, and a transformation from APTL formulas to GBCGs is presented. In addition, a decision procedure for checking the satisfiability of APTL formulas, and a model checking approach for APTL with Concurrent Game Structures (CGSs) being models are presented.

Quantitative Verification of Knowledge Precondition for Open System

A quantitative verification method is proposed to quantitatively verify knowledge precondition of actions and plans. Probability epistemic game structure (PEGS) is proposed to model knowledge preconditions in open systems, an extension of concurrent game structure with probabilistic transition. We introduce a probability operator P−λ into Alternating temporal epistemic logic (ATEL) and define a Probability alternating-time temporal epistemic logic (PATEL) for quantitatively model checking the properties of PEGS. We designed an algorithm to compute the probability aiming at model checking verification problems of PATEL based on DTMC and CTMC. We convert a portion of the PATEL verification problems into PATL problems by defining the knowledge formulas Ka φ, EAs φ and CAs φ as atomic propositions. We study a train controller using PRISM-games to demonstrate the applicability of above quantitative verification method.

Verification of JADE Agents Using ATL Model Checking

It is widely accepted that the key to successfully developing a system is to produce a thorough system specification and design. This task requires an appropriate formal method and a suitable tool to determine whether or not an implementation conforms to the specifications. In this paper we present an advanced technique to analyse, design and debug JADE software agents, using Alternating-time Temporal Logic (ATL) which is interpreted over concurrent game structures, considered as natural models for compositions of open systems. In development of the proposed solution, we will use our original ATL model checker. In contrast to previous approaches, our tool permits an interactive or programmatic design of the ATL models as state-transition graphs, and is based on client/server architecture: ATL Designer, the client tool, allows an interactive construction of the concurrent game structures as a directed multi-graphs and the ATL Checker, the core of our tool, represents the server part and is published as Web service.

State and path coalition effectivity models of concurrent multi-player games

We consider models of multi-player games where abilities of players and coalitions are defined in terms of sets of outcomes which they can effectively enforce. We extend the well studied state effectivity models of one-step games in two different ways. On the one hand, we develop multiple state effectivity functions associated with different long-term temporal operators. On the other hand, we define and study coalitional path effectivity models where the outcomes of strategic plays are infinite paths. For both extensions we obtain representation results with respect to concrete models arising from concurrent game structures. We also apply state and path coalitional effectivity models to provide alternative, arguably more natural and elegant semantics to the alternating-time temporal logic ATL*, and discuss their technical and conceptual advantages.

Concurrent Game Structures with Roles

In the following paper we present a new semantics for the well-known strategic logic ATL. It is based on adding roles to concurrent game structures, that is at every state, each agent belongs to exactly one role, and the role specifies what actions are available to him at that state. We show advantages of the new semantics, provide motivating examples based on sensor networks, and analyze model checking complexity.

Strategic Ability Updating in Concurrent Games by Coalitional Commitment.

Strategic ability updating relates to establishing some required properties, which can be expressed by strategic abilities, in a multicomponent reactive system. We model such a reactive system as a concurrent game structure (CGS), which is the semantic model of Alternating-time Temporal Logic (ATL). Then, we propose coalitional commitment as a tool for achieving the required strategic ability updating. Intuitively, a coalitional commitment can extend the state space of a CGS by a context function and then delete some transitions by a coalitional normative system (CNS). We propose coordinated ATL (co-ATL) for reasoning about strategic abilities in the structures obtained from a CGS by implementing a CNS. The model-checking problem for co-ATL is proved to be PTIME-complete, just like that of ATL, and is thus tractable. Then, we characterize the limitation of coalitional commitment power by identifying the set of co-ATL formulas whose satisfaction cannot be established and the set of co-ATL formulas whose satisfaction cannot be avoided. Afterward, we show that the effectiveness problem, feasibility problem, and synthesis problem for coalitional commitment are PTIME-complete, NP-complete, and FNP-complete, respectively. Finally, we treat the coalitional commitment synthesis problem as an extended planning problem and present an algorithm based on the planning as model checking paradigm. Our work can be seen as an improvement for both social law research and planning via model checking research.

On the Expressiveness and Complexity of ATL

ATL is a temporal logic geared towards the specification and verification of properties in multi-agents systems. It allows to reason on the existence of strategies for coalitions of agents in order to enforce a given property. In this paper, we first precisely characterize the complexity of ATL model-checking over Alternating Transition Systems and Concurrent Game Structures when the number of agents is not fixed. We prove that it is \Delta^P_2 - and \Delta^P_?_3-complete, depending on the underlying multi-agent model (ATS and CGS resp.). We also consider the same problems for some extensions of ATL. We then consider expressiveness issues. We show how ATS and CGS are related and provide translations between these models w.r.t. alternating bisimulation. We also prove that the standard definition of ATL (built on modalities "Next", "Always" and "Until") cannot express the duals of its modalities: it is necessary to explicitely add the modality "Release".

Model Checking Abilities of Agents: A Closer Look

Alternating-time temporal logic (atl) is a logic for reasoning about open computational systems and multi-agent systems. It is well known that atl model checking is linear in the size of the model. We point out, however, that the size of an atl model is usually exponential in the number of agents. When the size of models is defined in terms of states and agents rather than transitions, it turns out that the problem is (1) Δ3P-complete for concurrent game structures, and (2) Δ2P-complete for alternating transition systems. Moreover, for “Positive atl” that allows for negation only on the level of propositions, model checking is (1) Σ2P-complete for concurrent game structures, and (2) NP-complete for alternating transition systems. We show a nondeterministic polynomial reduction from checking arbitrary alternating transition systems to checking turn-based transition systems, We also discuss the determinism assumption in alternating transition systems, and show that it can be easily removed. In the second part of the paper, we study the model checking complexity for formulae of atlwith imperfect information (atlir). We show that the problem is Δ2P-complete in the number of transitions and the length of the formula (thereby closing a gap in previous work of Schobbens in Electron. Notes Theor. Comput. Sci. 85(2), 2004). Then, we take a closer look and use the same fine structure complexity measure as we did for atl with perfect information. We get the surprising result that checking formulae of atlir is also Δ3P-complete in the general case, and Σ2P-complete for “Positive atlir”. Thus, model checking agents’ abilities for both perfect and imperfect information systems belongs to the same complexity class when a finer-grained analysis is used.

Comparing Semantics of Logics eor Multi-Agent Systems

We draw parallels between several closely related logics that combine – in different proportions – elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly in 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.