Model Checking Abilities of Agents: A Closer Look

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.

Many problems in AI and multi-agent systems research are most naturally formulated in terms of the abilities of a coalition of agents. There exist several excellent logical tools for reasoning about coalitional ability. However, coalitional ability can be affected by the availability of resources, and there is no straightforward way of reasoning about resource requirements in logics such as Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). In this paper, we propose a logic for reasoning about coalitional ability under resource constraints. We extend ATL with costs of actions and hence of strategies. We give a complete and sound axiomatisation of the resulting logic Resource-Bounded ATL (RB-ATL) and an efficient model-checking algorithm for it.

In logics for strategic reasoning the main challenge is represented by their verification in contexts of imperfect information and perfect recall strategies. In this work, we show a technique to approximate the verification of Alternating-time Temporal Logic (ATL*) under imperfect information and perfect recall, which is known to be undecidable. Given a model M and a formula phi, we propose a verification procedure that generates sub-models of M in which each sub-model M' satisfies a sub-formula phi' of phi and the verification of phi' in M' is decidable. Then, we use CTL* model checking to provide a verification result of phi on M. We prove that our procedure is sound and in the same complexity class of ATL* model checking under perfect information and perfect recall. Moreover, we present a tool that uses our procedure and provide experimental results.

A blockchain is a list of data blocks as a publicly distributed ledger, which are linked together using cryptography. By allowing Turing-complete programming languages to implement smart contracts, recent blockchains such as Ethereum can reduce needs in trusted intermediators, arbitrations and enforcement costs. However, subtle errors in smart contracts have induced an enormous financial loss—for examples, the DAO attack, Parity multisignature wallet attacks, and integer underflow/overflow attacks. To identify such errors in smart contracts, various researches are performed, which are based on static analysis and theorem proving. However, they only support inspection for pre-defined error patterns, or they cannot explore the whole searching space exhaustively or be fully automatic. Hence, in this paper, we propose a novel formal verification technique to analyze blockchain smart contracts by using ATL model checking. In our methodology, we represent the interaction between users and smart contracts into a two-player game and verify properties we want to check using MCMAS that is an efficient ATL model checker for multi-agent systems. Moreover, we present three case studies to show that our proposal can successfully identify subtle flaws in real world smart contracts.

In the last few years, argumentation frameworks have been successfully applied to multi agent systems. Recently, argumentation has been used to provide a framework for reasoning about coalition formation. At the same time alternating-time temporal logic has been used to reason about the behavior and abilities of coalitions of agents. However, ATL operators account only for the existence of successful strategies of coalitions. They do not consider whether coalitions can be actually formed.This paper is an attempt to combine both frameworks and to develop a logic through which we can reason at the same time (1) about abilities of coalitions of agents and (2) about the formation of coalitions. We provide a formal extension of ATL, ATLc, in which the actual computation of the coalition is modelled in terms of argumentation semantics. We show that ATLc's proof theory can be understood as a natural extension of the model checking procedure used in ATL.

In logics for strategic reasoning the main challenge is represented by their verification in contexts of imperfect information and perfect recall strategies. In this work, we show the combination of two techniques to approximate the verification of Alternating-time Temporal Logic (ATL∗ ) under imperfect information and perfect recall, which is known to be undecidable. Given a model M and a formula φ, we propose a verification procedure that generates sub-models of M in which each sub-model M′ satisfies a sub-formula φ′ of φ and the verification of φ′ in M′ is decidable. Then, we use CTL∗ model checking to provide a verification result of φ on M. In case the previous step does not give a final result, we exploit a runtime verification mechanism to provide some intermediate result. We prove that our procedure is sound and in the same complexity class of ATL∗ model checking under perfect information and perfect recall. Moreover, we present a tool that uses our procedure and provide experimental results.

We introduce a 3-valued abstraction technique for alternating-time temporal logic (ATL) in contexts of imperfect information. We introduce under- and over-approximations of an agent's strategic abilities in terms of must- and may-strategies and provide a 3-valued semantics for ATL based on agents in interpreted systems (IS). We define a relation of simulation between the agents and prove that it preserves defined truth values of ATL formulas. Finally, we introduce a notion of abstraction on IS and show that it simulates the concrete interpreted system. Under this setting we present a procedure that enables the direct construction of a finite abstraction from an infinite-state system.

Alternating-time temporal logic (ATL) is a well-known logic for reasoning about strategic abilities of agents. An important feature that distinguishes variants of for imperfect scenarios is that the standard fixed point characterizations of temporal modalities do not hold anymore. In this paper, we show that adding explicit fixed point operators to the next-time fragment of already allows to capture abilities that could not be expressed in ATL. We also illustrate that the new language allows to specify important kinds of abilities, namely ones where the agents can always recompute their strategy while executing it. Thus, the agents are not assumed to remember their strategy by definition, like in the existing variants of ATL. Last but not least, we show that verification of such abilities can be cheaper than for all the variants of ATL with imperfect information considered so far.

We analyse the verification problem for synchronous, perfect recall multi-agent systems with imperfect information against a specification language that includes strategic and epistemic operators. While the verification problem is undecidable, we show that if the agents' actions are public, then verification is 2exptime-complete. To illustrate the formal framework we consider two epistemic and strategic puzzles with imperfect information and public actions: the muddy children puzzle and the classic game of battleships.

Recently, the popular logical frameworks on strategy specification and verification in the multi-agent concurrent systems, such as alternating-time temporal logic and Strategy Logic (SL), mainly focus on the strategic abilities of one coalition. In them, the notion of strategy is just viewed as a pure syntax and/or semantics object, we cannot represent or reason about the internal structures of strategies, let alone strategic abilities under these ones. In this paper, based on linear dynamic logic, by extending SL, we propose a new strategic logic, named Dynamic Strategy Logic (DSL), which includes the existential/ universal quantification operators about regular expressions with test expressions. By introducing action atoms, we can specify both the evolution of time and structured strategies by means of regular expressions. Hence, in this logic, we can represent and reason about much more expressive strategic abilities under structured strategies of coalitions, and prove that DSL is more expressive than SL.

We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems. Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic, where one can specify properties of the type “a coalition of (at least) n controllable agents can ensure against (at most) m uncontrollable agents that any possible evolution of the system satisfies a given objective gamma″, where gamma is specified again as a formula of that language and each of n and m is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic {mathcal {L}}_{textsc {hdmas}} and define normal form of its formulae. We then prove that every formula in {mathcal {L}}_{textsc {hdmas}} is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.

We address the problem of learning temporal properties from the branching-time behavior of systems. Existing research in this field has mostly focused on learning linear temporal properties specified using popular logics, such as Linear Temporal Logic (LTL) and Signal Temporal Logic (STL). Branching-time logics such as Computation Tree Logic (CTL) and Alternating-time Temporal Logic (ATL), despite being extensively used in specifying and verifying distributed and multi-agent systems, have not received adequate attention. Thus, in this paper, we investigate the problem of learning CTL and ATL formulas from examples of system behavior. As input to the learning problems, we rely on the typical representations of branching behavior as Kripke structures and concurrent game structures, respectively. Given a sample of structures, we learn concise formulas by encoding the learning problem into a satisfiability problem, most notably by symbolically encoding both the search for prospective formulas and their fixed-point based model checking algorithms. We also study the decision problem of checking the existence of prospective ATL formulas for a given sample. We implement our algorithms in a Python prototype and have evaluated them to extract several common CTL and ATL formulas used in practical applications.

Model checking epistemic–probabilistic logic using probabilistic interpreted systems

Extensive-form games are a powerful framework for modeling sequential multi-agent interactions. In extensive-form games with imperfect information, Nash equilibria are generally used as a solution concept, but computing a Nash equilibrium can be intractable in large games. Instead, a variety of techniques are used to find strategies that approximate Nash equilibria. Traditionally, an approximate Nash equilibrium strategy is evaluated by measuring the strategy's worst-case performance, or exploitability. However, because exploitability fails to capture how likely the worst-case is to be realized, it provides only a limited picture of strategy strength, and there is extensive empirical evidence showing that exploitability can correlate poorly with one-on-one performance against a variety of opponents. In this thesis, we introduce a class of adaptive opponents called pretty-good responses that exploit a strategy but only have limited exploitative power. By playing a strategy against a variety of counter-strategies created with pretty-good responses, we get a more complete picture of strategy strength than that offered by exploitability alone. In addition, we show how standard no-regret algorithms can me modified to learn strategies that are strong against adaptive opponents. We prove that this technique can produce optimal strategies for playing against pretty-good responses. We empirically demonstrate the effectiveness of the technique by finding static strategies that are strong against Monte Carlo opponents who learn by sampling our strategy, including the UCT Monte Carlo tree search algorithm.

During requirement specification process of software development activities, many existing systems or business process requirements have been captured using natural language or specialized tools such as UML. However, the capturing of informal requirements into formalized properties has not been taken into attention by software developers due to time and budget constraints. It is critical for the informally captured requirements to be formally specified in order to perform system verification. Formal verification checks whether a system model meets the formal specifications while validation checks whether the developed system fulfills its intended purpose. Therefore, in this paper, we present our studies of formal verification of multi agent system using model checking approach. We have utilized model checking tool in order to execute the formal verification procedures based on a particular basic theory to verify certain kind of properties of requirement specifications. We show an example of how model checking tool could support the verification of Universiti Teknologi Malaysia (UTM) multi agent online application system and conclude that the propose model checking approach will benefit multi agent system.