Artificial intelligence and machine learning applications (AI/ML) offer unique opportunities for documentation, assessment and protection of world cultural heritage, at risk from natural disasters such as earthquakes, climate change, uncontrolled urbanization, etc. Earlier work of the authors focused on developing an ontology-based, deep learning framework to support the analysis of earthquake damage data for heritage structures. An important part of the assessment process and preservation of cultural heritage structures is the extraction of lessons learned from observed damage and performance data from previous catastrophic earthquakes. The assessment process requires three elements: 1) a model of the existing state of a structure, 2) damage data with images, 3D scans, and other types of data about the damaging event, and 3) a cultural value associated with the structure. An ontology is developed to capture all three elements and the relationships that exist among them, and a discussion of the data sources and data types that can be used to populate the ontology, is then presented. Machine learning systems can be developed using this ontology to provide context to damage data, relating the damage to the cultural value of the structure. This paper also presents the results of an effort to use AI/ML applications to automate the extraction of damage classification and damage mechanisms based on the deep knowledge bases of observed damage data about historic churches damaged during the catastrophic earthquakes in Italy (2016 and earlier), Mexico (2017), and the historic mosques damaged during the devastating earthquakes in Turkey/Syria (2023), and Morocco (2023).