A Modal Logic for Joint Abilities under Strategy Commitments

Liu, Zhaoshuai; Xiong, Liping; Liu, Yongmei; Lespérance, Yves; Xu, Ronghai; Shi, Hongyi

doi:10.24963/ijcai.2020/250

Cited by 2 publications

(5 citation statements)

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“…To handle elimination of strategies, Liu et al introduce the concept of strategy spaces. A strategy space specifies the set of possible strategies for each agent [17].…”

Section: Preliminariesmentioning

confidence: 99%

“…Here we need ⟨⟨A⟩⟩ψ because when the strategy space is infinite, it might become empty after iterative EDS, as illustrated by Example 3 from [17]. Intuitively, ((A)) ∞ ψ means group A has joint ability to ensure ψ, i.e., after iterative EDS, ψ holds no matter how the agents play.…”

Section: Preliminariesmentioning

confidence: 99%

“…We first review the main idea of model checking memoryless JAADL from [17]. Recall JAADL path formulas are LDL formulas over JAADL state formulas.…”

Section: Memoryless Ejaadlmentioning

confidence: 99%

“…So they only eliminate punishment strategies, hence their concept of joint ability is much weaker than that of [11]. Recently, based on Ghaderi et al's idea, Liu et al proposed JAADL [17], a modal logic for joint abilities under strategy commitments, which extends ATL * . Firstly, they introduce an operator (A) ∞ ψ ϕ, meaning ϕ holds after iterated elimination of dominated strategies w.r.t.…”

Section: Introductionmentioning

confidence: 99%

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Epistemic JAADL: A Modal Logic for Joint Abilities with Imperfect Information

Liu,

Liang,

Liu

2023

Frontiers in Artificial Intelligence and Applications

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Coordination and joint ability are important problems in representation and reasoning about multi-agent systems. Ghaderi et al. presented a formalization of joint ability of coalitions in the expressive first-order language of the situation calculus. Essentially, a coalition has joint ability to achieve a goal if after iterated elimination of dominated strategies, any remaining joint strategy achieves the goal. Based on their work, Liu et al. proposed JAADL, a modal logic for joint abilities under strategy commitments. In this paper, we propose EJAADL, an epistemic extension of JAADL, for imperfect information games where agents may have incomplete knowledge or even false beliefs about the world. Like Ghaderi et al.’s work, elimination of dominated strategies is now based on beliefs about the world, rather than facts about the world as in JAADL. Strategies are required to be uniform, i.e., they select the same action in all accessible histories. We illustrate EJAADL with examples, analyze its properties, and show that model checking memoryless EJAADL is in EXPTIME. Moreover, we consider the fragment of EJAADL without the iterated elimination operator, and show that model-checking the memoryless version of this fragment can be done in PSPACE.

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“…To handle elimination of strategies, Liu et al introduce the concept of strategy spaces. A strategy space specifies the set of possible strategies for each agent [17].…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…We first review the main idea of model checking memoryless JAADL from [17]. Recall JAADL path formulas are LDL formulas over JAADL state formulas.…”

Section: Memoryless Ejaadlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Epistemic JAADL: A Modal Logic for Joint Abilities with Imperfect Information

Liu,

Liang,

Liu

2023

Frontiers in Artificial Intelligence and Applications

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“…In order to express any ω-regular properties in strategic logic, in [22], Liu et al propose a logic JAADL to specify joint abilities of coalitions, which combines alternating-time temporal logic with LDL. However, in JAADL, the authors consider a very complex semantics and study the model checking complexity with imperfect recall for JAADL.…”

Section: Introductionmentioning

confidence: 99%

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

Xiong

Guo

2021

Mathematics

Self Cite

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Specification and verification of coalitional strategic abilities have been an active research area in multi-agent systems, artificial intelligence, and game theory. Recently, many strategic logics, e.g., Strategy Logic (SL) and alternating-time temporal logic (ATL*), have been proposed based on classical temporal logics, e.g., linear-time temporal logic (LTL) and computational tree logic (CTL*), respectively. However, these logics cannot express general ω-regular properties, the need for which are considered compelling from practical applications, especially in industry. To remedy this problem, in this paper, based on linear dynamic logic (LDL), proposed by Moshe Y. Vardi, we propose LDL-based Strategy Logic (LDL-SL). Interpreted on concurrent game structures, LDL-SL extends SL, which contains existential/universal quantification operators about regular expressions. Here we adopt a branching-time version. This logic can express general ω-regular properties and describe more programmed constraints about individual/group strategies. Then we study three types of fragments (i.e., one-goal, ATL-like, star-free) of LDL-SL. Furthermore, we show that prevalent strategic logics based on LTL/CTL*, such as SL/ATL*, are exactly equivalent with those corresponding star-free strategic logics, where only star-free regular expressions are considered. Moreover, results show that reasoning complexity about the model-checking problems for these new logics, including one-goal and ATL-like fragments, is not harder than those of corresponding SL or ATL*.

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A Modal Logic for Joint Abilities under Strategy Commitments

Cited by 2 publications

References 1 publication

Epistemic JAADL: A Modal Logic for Joint Abilities with Imperfect Information

Epistemic JAADL: A Modal Logic for Joint Abilities with Imperfect Information

Representation and Reasoning about Strategic Abilities with ω-Regular Properties

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