Alternating-time Temporal Epistemic Logic Research Articles

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.

Action and Knowledge in Alternating-Time Temporal Logic

Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly discussed property is that an agent should know about all available actions, i.e., that the same actions should be available in indiscernible states. Van der Hoek and Wooldridge suggest a syntactic expression of this semantic property. This paper shows that this correspondence in fact does not hold. Furthermore, it is shown that the semantic property is not expressible in ATEL at all. In order to be able to express common and interesting properties of action in general and of the interaction between action and knowledge in particular, a generalization of the coalition modalities of ATL is proposed. The resulting logics, ATL-A and ATEL-A, have increased expressiveness without loosing ATL’s and ATEL’s tractability of model checking.

A Sat-Based Approach to Unbounded Model Checking for Alternating-Time Temporal Epistemic Logic

A Sat-Based Approach to Unbounded Model Checking for Alternating-Time Temporal Epistemic Logic

Agents that Know How to Play

We look at ways to enrich Alternating-time Temporal Logic (ATL) - a logic for specification and verification of multi-agent systems - with a notion of knowledge. Starting point of our study is a recent proposal for a system called Alternating-time Temporal Epistemic Logic (ATEL). We show that, assuming that agents act under uncertainty in some states of the system, the notion of allowable strategy should be defined with some caution. Moreover, we demonstrate a subtle difference between an agent knowing that he has a suitable strategy and knowing the strategy itself. We also point out that the agents should be assumed similar epistemic capabilities in the semantics of both strategic and epistemic operators. Trying to implement these ideas, we propose two different modifications of ATEL. The first one, dubbed Alternating-time Temporal Observational Logic (ATOL), is a logic for agents with bounded recall of the past. With the second, ATEL-R*, we present a framework to reason about both perfect and imperfect recall, in which we also incorporate operators for reasoning about the past. We identify some feasible subsystems of this expressive system.

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.

Model checking cooperation, knowledge, and time—a case study

Alternating-time Temporal Logic (ATL) is a logic developed by Alur, Henzinger, and Kupferman for reasoning about coalitional powers in multiagent systems. Since what agents can achieve in a specific state will in general depend on the knowledge they have in that state, in an earlier paper we proposed Alternating-time Temporal Epistemic Logic (ATEL), an epistemic extension to ATL which is interpreted over Alternating-time Temporal Epistemic Transition Systems. The logic ATEL shares with its ancestor ATL the property that its model checking problem is tractable. However, while model checkers have been implemented for ATL, no model checker yet exists for ATEL, or indeed for epistemic logics in general. The aim of this paper is to demonstrate, using the alternating bit protocol as a detailed case study, how existing model checkers for ATL can be deployed to verify epistemic properties.

Cooperation, Knowledge, and Time: Alternating-Time Temporal Epistemic Logic and Its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as “Alternating-time Temporal Logic” (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by “cooperation modalities”, of the form 《Γ》, where Γ is a set of agents. The intended interpretation of an ATL formula 《Γ》ϕ is that the agents Γ can cooperate to ensure that ϕ holds (equivalently, that Γ have a winning strategy for ϕ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as “group Γ can cooperate to bring about ϕ iff it is common knowledge in Γ that ψ”. The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.