Robust Alternating-Time Temporal Logic

In multi-agent system design, a crucial aspect is to ensure robustness, meaning that for a coalition of agents A, small violations of adversarial assumptions only lead to small violations of A's goals. In this paper we introduce a logical framework for robust strategic reasoning about multi-agent systems. Specifically, inspired by recent works on robust temporal logics, we introduce and study rATL and rATL*, logics that extend the well-known Alternating-time Temporal Logic ATL and ATL* by means of an opportune multi-valued semantics for the strategy quantifiers and temporal operators. We study the model-checking and satisfiability problems for rATL and rATL* and show that dealing with robustness comes at no additional computational cost. Indeed, we show that these problems are PTime-complete and ExpTime-complete for rATL, respectively, while both are 2ExpTime-complete for rATL*

Game-Theoretic Semantics for Alternating-Time Temporal Logic

We introduce versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective appears in the framework of ATL on two semantic levels: on the object level in the standard semantics of the strategic operators, and on the meta-level where game-theoretic logical semantics is applied to ATL. We unify these two perspectives into semantic evaluation games specially designed for ATL. The game-theoretic perspective enables us to identify new variants of the semantics of ATL based on limiting the time resources available to the verifier and falsifier in the semantic evaluation game. We introduce and analyse an unbounded and (ordinal) bounded GTS and prove these to be equivalent to the standard (Tarski-style) compositional semantics. We show that in these both versions of GTS, truth of ATL formulae can always be determined in finite time, i.e., without constructing infinite paths. We also introduce a non-equivalent finitely bounded semantics and argue that it is natural from both logical and game-theoretic perspectives.Comment: Preprint of a paper published in ACM Transactions on Computational Logic, 19(3): 17:1-17:38, 201

Alternating-time temporal logic with resource bounds

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 describe 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 a model-checking algorithm for it

Group synthesis for alternating-time temporal logic

We present an extension of Alternating-time Temporal Logic ATL, called ATLP (Parametric ATL), where parameters are allowed in place of concrete groups of agents. We devise a procedure to nd all instantiations for the parameters in a given formula of ATLP so that is true in a given model. We propose a formalisation of the problem and symbolic algorithms for its solution. We discuss an experimental implementation of the approach on top of the open-source model checker mcmas and demonstrate the bene ts of the technique through experimental results

Alternating-time temporal logic with resource bounds

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 article, we describe 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 axiomatization of the resulting logic, Resource-Bounded ATL (RB-ATL) and a model-checking algorithm for it

Alternating-time temporal logic with finite-memory strategies

Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based on finite-memory strategies. One where the memory size allowed is bounded and one where the memory size is unbounded (but must be finite). This is motivated by the high complexity of model-checking with perfect recall semantics and the severe limitations of memoryless strategies. We show that both types of semantics introduced are different from perfect recall and memoryless semantics and next focus on the decidability and complexity of model-checking in both complete and incomplete information games for ATL/ATL*. In particular, we show that the complexity of model-checking with bounded-memory semantics is Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete information games just as in the memoryless case. We also present a proof that ATL and ATL* model-checking is undecidable for n >= 3 players with finite-memory semantics in incomplete information games.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Model-checking Quantitative Alternating-time Temporal Logic on One-counter Game Models

We consider quantitative extensions of the alternating-time temporal logics ATL/ATLs called quantitative alternating-time temporal logics (QATL/QATLs) in which the value of a counter can be compared to constants using equality, inequality and modulo constraints. We interpret these logics in one-counter game models which are infinite duration games played on finite control graphs where each transition can increase or decrease the value of an unbounded counter. That is, the state-space of these games are, generally, infinite. We consider the model-checking problem of the logics QATL and QATLs on one-counter game models with VASS semantics for which we develop algorithms and provide matching lower bounds. Our algorithms are based on reductions of the model-checking problems to model-checking games. This approach makes it quite simple for us to deal with extensions of the logical languages as well as the infinite state spaces. The framework generalizes on one hand qualitative problems such as ATL/ATLs model-checking of finite-state systems, model-checking of the branching-time temporal logics CTL and CTLs on one-counter processes and the realizability problem of LTL specifications. On the other hand the model-checking problem for QATL/QATLs generalizes quantitative problems such as the fixed-initial credit problem for energy games (in the case of QATL) and energy parity games (in the case of QATLs). Our results are positive as we show that the generalizations are not too costly with respect to complexity. As a byproduct we obtain new results on the complexity of model-checking CTLs in one-counter processes and show that deciding the winner in one-counter games with LTL objectives is 2ExpSpace-complete.Comment: 22 pages, 12 figure

Reducing Validity in Epistemic ATL to Validity in Epistemic CTL

We propose a validity preserving translation from a subset of epistemic Alternating-time Temporal Logic (ATL) to epistemic Computation Tree Logic (CTL). The considered subset of epistemic ATL is known to have the finite model property and decidable model-checking. This entails the decidability of validity but the implied algorithm is unfeasible. Reducing the validity problem to that in a corresponding system of CTL makes the techniques for automated deduction for that logic available for the handling of the apparently more complex system of ATL.Comment: In Proceedings SR 2013, arXiv:1303.007

From ATL to Stit

I present a technical embedding of alternating-time temporal logic into stit theory.Comment: Preprin