# Reasoning about Quality and Fuzziness of Strategic Behaviours

arXiv: https://arxiv.org/abs/1905.11537 · HTML: https://mlsanity.com/paper/1905.11537/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 May 2019.

## Built on by (most cited first, 4 of 4)

- [Reasoning about Human-Friendly Strategies in Repeated Keyword Auctions](https://mlsanity.com/paper/2201.09616/) (2022)
- [On Alternating-Time Temporal Logic, Hyperproperties, and Strategy Sharing](https://mlsanity.com/paper/2312.12403/) (2023)
- [Hyper Strategy Logic](https://mlsanity.com/paper/2403.13741/) (2024)
- [Discounting in Strategy Logic](https://mlsanity.com/paper/2305.15256/) (2023)

## Abstract (arXiv)

Temporal logics are extensively used for the specification of on-going behaviours of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviours in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalise concepts such as certainty or quality. We introduce and study FSL---a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an FSL formula is a real value in [0,1], reflecting `how much' or `how well' the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of FSL in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL*.