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In this paper we address the problem of provisioning Quality of Service (QoS) to Voice over IP applications in a Wireless LAN scenario based on the IEEE 802.11 standard. We propose the use of a Cognitive Network approach to design a Call Admission Control (CAC) scheme, according to which each user stores relevant information on its past network experience and then uses such information to build a Bayesian Network (BN), a probabilistic graphical model to describe the statistical relationships among network parameters. The BN is exploited to predict the voice call quality, as a function of the Link Layer conditions in the particular scenario considered. Such prediction on the present and future values of the QoS provided is directly exploited to design the cognitive CAC scheme, which is shown to significantly outperform state of the art CAC techniques in a realistic scenario.