Abstract
We propose a general framework for modelling and formal reasoning about multi-agent systems and, in particular, multi-stage games where both quantitative and qualitative objectives and constraints are involved. Our models enrich concurrent game models with payoffs and guards on actions associated with each state of the model and propose a quantitative extension of the logic {textsf {ATL}}^{*} that enables the combination of quantitative and qualitative reasoning. We illustrate the framework with some detailed examples. Finally, we consider the model-checking problems arising in our framework and establish some general undecidability and decidability results for them.
Highlights
Quantitative and qualitative reasoning about agents and multi-agent systems is pervasive in many areas of AI and game theory, including multi-agent planning and intelligent robotics
In multi-agent planning and robotics it is important to achieve the agents’ qualitative goals while satisfying various quantitative constraints on time and resource consumption. This motivates the need for developing a modelling framework for combining qualitative and quantitative reasoning, which is the main objective of the present paper
To enable combined qualitative and quantitative logical reasoning we introduce a quantitative extension of the logic ∗, introduced in [6], provide formal semantics for it in concurrent game models enriched with payoffs and guards, and show how it can be used for specifying properties of the running examples combining qualitative and quantitative objectives
Summary
Quantitative and qualitative reasoning about agents and multi-agent systems is pervasive in many areas of AI and game theory, including multi-agent planning and intelligent robotics. The studies of cooperative and non-cooperative multi-player games deal with both aspects of strategic abilities of agents, but usually separately. Quantitative reasoning studies the abilities of agents to achieve quantitative objectives, such as optimizing payoffs (e.g., maximizing rewards or minimizing cost) or, more generally, preferences on outcomes. This tradition comes from game theory and economics and usually studies one-shot. This paper is a revised and substantially expanded version of the extended abstract [20]
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