787 research outputs found
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
From ATL to Stit
I present a technical embedding of alternating-time temporal logic into stit
theory.Comment: Preprin
Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic
Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems.
Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization
of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of
agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node,
the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant
of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification
enables agents to “relent” and change their goals and strategies depending on their history.
In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain
node of a path by taking into account both the future and the past. We study the expressive power of mATL ,
its succinctness, as well as related decision problems. We also investigate the relationship between memoryful
quantification and past modalities and show their equivalence. We show that both the memoryful and the past
extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking
problems are 2EXPTIME-COMPLETE, as they are for AT
Formalizing alternating-time temporal logic in the coq proof assistant
This work presents a complete formalization of Alternating-time Temporal Logic (ATL) and its semantic model, Concurrent Game Structures (CGS), in the Calculus of (Co)Inductive Constructions, using the logical framework Coq. Unlike standard ATL semantics, temporal operators are formalized in terms of inductive and coinductive types, employing a fixpoint characterization of these operators. The formalization is used to model a concurrent system with an unbounded number of players and states, and to verify some properties expressed as ATL formulas. Unlike automatic techniques, our formal model has no restrictions in the size of the CGS, and arbitrary state predicates can be used as atomic propositions of ATL. Keywords: Reactive Systems and Open Systems, Alternating-time Temporal Logic, Concurrent Game Structures, Calculus of (Co)Inductive Constructions, Coq Proof Assistant
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