This paper is devoted to the problem of evaluating the quality of experience (QoE) for a given web service based on the values of service parameters (for instance, QoS indicators). Different self-learning algorithms can be used to reach this purpose. In this paper, we propose to use self-learning logic networks, called also circuits, for evaluating the QoE of web services, since modern software tools can efficiently deal with very large logic networks. As usual, for machine learning techniques, statistics are used to design the initial circuit that accepts service parameter values as inputs and produces the QoE value as an output. The circuit is self-adaptive, i.e., when a new end-user provides a feedback of the service satisfaction the circuit is resynthesized in order to behave properly (if needed). Such resynthesis (circuit learning) can be efficiently performed using a number of tools for logic synthesis and verification