Autonomous Vehicles (AV) are inevitable entities in future mobility systems thatdemand safety and adaptability as two critical factors in replacing/assisting human drivers. Safety arises in defining, standardizing, quantifying, and monitoring requirements for all autonomous components. Adaptability, on the other hand, involves efficient handling of uncertainty and inconsistencies in models and data. First, I address safety by presenting a search-based test-case generation framework that can be used in training and testing deep-learning components of AV. Next, to address adaptability, I propose a framework based on multi-valued linear temporal logic syntax and semantics that allows autonomous agents to perform model-checking on systems with uncertainties. The search-based test-case generation framework provides safety assurance guarantees through formalizing and monitoring Responsibility Sensitive Safety (RSS) rules. I use the RSS rules in signal temporal logic as qualification specifications for monitoring and screening the quality of generated test-drive scenarios. Furthermore, to extend the existing temporal-based formal languages’ expressivity, I propose a new spatio-temporal perception logic that enables formalizing qualification specifications for perception systems. All-in-one, my test-generation framework can be used for reasoning about the quality of perception, prediction, and decision-making components in AV. Finally, my efforts resulted in publicly available software. One is an offline monitoring algorithm based on the proposed logic to reason about the quality of perception systems. The other is an optimal planner (model checker) that accepts mission specifications and model descriptions in the form of multi-valued logic and multi-valued sets, respectively. My monitoring framework is distributed with the publicly available S-TaLiRo and Sim-ATAV tools.