We present a comprehensive task-based approach as the foundation for developing explainable and trustworthy AI systems. A task \(\mathcal {T}\) is formally defined as a 6-tuple including Goal, Input, Constraints, Output, verification Criterion, and domain Ontology. The framework emphasizes hierarchical decomposition, where complex goals are broken into verifiable subtasks, enabling traceable, human-interpretable explanations through satisfaction proofs \((\pi _i)\) for each criterion \(\mathcal {K}_i\) . It integrates symbolic reasoning and probabilistic learning via functional systems, hierarchies, and semantic probabilistic inference for the knowledge induction. The approach supports hybrid multi-agent systems, combining LLMs for goal-oriented reasoning with logic-based agents for constraint enforcement. The key design principles ensure task-centric architecture, explicit criteria, ontological alignment, and criterion-centric explanations. Validation across diverse domains demonstrates its capacity to deliver mathematically verifiable, robust, and auditable AI solutions. Bibliography: 28 titles. Illustrations: 3 figures.
