Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect Information, Perfect Recall and Communicating Coalitions

We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of cooperation between members of the coalition in which agents issue their actions based on the distributed knowledge, for that coalition, of the system history. We show that model-checking is decidable for this logic. The technique utilizes two variants of games with imperfect information and partially observable objectives, as well as a subset construction for identifying states whose histories are indistinguishable to the considered coalition

Reasoning about actions meets strategic logics (LORI 2013)

International audienceWe introduce ATLEA, a novel extension of Alternating-time Temporal Logic with explicit actions in the object language. ATLEA allows to reason about abilities of agents under commitments to play certain actions. Pre- and postconditions as well as availability and unavailability of actions can be expressed. We show that the multiagent extension of Reiter’s solution to the frame problem can be encoded into ATLEA. We also consider an epistemic extension of ATLEA. We demonstrate that the resulting logic is sufficiently expressive to reason about uniform choices of actions. Complexity results for the satisfiability problem of ATLEA and its epistemic extension are given in the paper

Internal Calculi for Separation Logics

We present a general approach to axiomatise separation logics with heaplet semantics with no external features such as nominals/labels. To start with, we design the first (internal) Hilbert-style axiomatisation for the quantifier-free separation logic SL(?, -*). We instantiate the method by introducing a new separation logic with essential features: it is equipped with the separating conjunction, the predicate ls, and a natural guarded form of first-order quantification. We apply our approach for its axiomatisation. As a by-product of our method, we also establish the exact expressive power of this new logic and we show PSpace-completeness of its satisfiability problem

Dependences in Strategy Logic

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: First, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula, revisiting the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014]. We explain why elementary dependences, as defined by Mogavero et al., do not exactly capture the intended concept of behavioral strategies. We address this discrepancy by introducing timeline dependences, and exhibit a large fragment of SL for which model checking can be performed in 2-EXPTIME under this new semantics

Model Checking an Epistemic mu-calculus with Synchronous and Perfect Recall Semantics

We identify a subproblem of the model-checking problem for the epistemic \mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that avoids embodying any form of common knowledge. Our subproblem subsumes known decidable fragments of epistemic CTL/LTL, may express winning strategies in two-player games with one player having imperfect information and non-observable objectives, and, with a suitable encoding, decidable instances of the model-checking problem for ATLiR.Comment: 10 pages, Poster presentation at TARK 2013 (arXiv:1310.6382) http://www.tark.or

Completeness of Flat Coalgebraic Fixpoint Logics

Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular fixpoint logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL, and the logic of common knowledge. Extending this notion to the generic semantic framework of coalgebraic logic enables covering a wide range of logics beyond the standard mu-calculus including, e.g., flat fragments of the graded mu-calculus and the alternating-time mu-calculus (such as alternating-time temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We give a generic proof of completeness of the Kozen-Park axiomatization for such flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer Science, Springer, 2010, pp. 524-53

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".Comment: 25 page