As AI systems increasingly influence critical decisions, they face threats that exploit reasoning mechanisms rather than technical infrastructure. We present a framework for cognitive cybersecurity, a systematic protection of AI reasoning processes from adversarial manipulation. Our contributions are threefold. First, we establish cognitive cybersecurity as a discipline complementing traditional cybersecurity and AI safety, addressing vulnerabilities where legitimate inputs corrupt reasoning while evading conventional controls. Second, we introduce the CIA+TA, extending traditional Confidentiality, Integrity, and Availability triad with Trust (epistemic validation) and Autonomy (human agency preservation), requirements unique to systems generating knowledge claims and mediating decisions. Third, we present a quantitative risk assessment methodology with empirically-derived coefficients, enabling organizations to measure cognitive security risks. We map our framework to OWASP LLM Top 10 and MITRE ATLAS, facilitating operational integration. Validation through previously published studies (151 human participants; 12,180 AI trials) reveals strong architecture dependence: identical defenses produce effects ranging from 96% reduction to 135% amplification of vulnerabilities. This necessitates pre-deployment Cognitive Penetration Testing as a governance requirement for trustworthy AI deployment.