Abstract
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*.
Highlights
For the specification of ongoing behaviours of reactive systems, the use of temporal logics has become one of the significant developments in formal reasoning [1,2,3]
In [6], Chatterjee et al proposed strategy logic, which treats strategies as explicit first-order objects in turn-based games with only two agents; Mogavero et al extended this logic with explicit strategy quantifications and agent bindings in multi-agent concurrent systems [7]; in order to reason about uniqueness of Nash Equilibria, Aminof et al introduced a graded strategic logic [8]; in [9], Bozzelli et al considered strategic reasoning with linear past in alternating-time temporal logic; and in [10], Belardinelli et al studied strategic reasoning with knowledge
We propose logic LDL-Strategy Logic (SL), an expressive new strategic logic based on linear dynamic logic, which can naturally express ω-regular properties
Summary
For the specification of ongoing behaviours of reactive systems, the use of temporal logics has become one of the significant developments in formal reasoning [1,2,3]. 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. We study fragments of LDL-SL and their model-checking complexities, and we define three types of strategic logics: ATL-like, one-goal, and star-free. The former two, which are fragments for LDL-SL, have the same expressivity as those based on LTL or CTL∗ , and the model-checking problems are the same.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
