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Deep neural networks (DNNs) detect patterns in data and have shown versatility and strong performance in many computer vision applications. However, DNNs alone are susceptible to obvious mistakes that violate simple, common sense concepts and are limited in their ability to use explicit knowledge to guide their search and decision making. While overall DNN performance metrics may be good, these obvious errors, coupled with a lack of explainability, have prevented widespread adoption for crucial tasks such as medical image analysis. The purpose of this paper is to introduce SimpleMind, an open-source software framework for Cognitive AI focused on medical image understanding. It allows creation of a knowledge base that describes expected characteristics and relationships between image objects in an intuitive human-readable form. The SimpleMind framework brings thinking to DNNs by: (1) providing methods for reasoning with the knowledge base about image content, such as spatial inferencing and conditional reasoning to check DNN outputs; (2) applying process knowledge, in the form of general-purpose software agents, that are chained together to accomplish image preprocessing, DNN prediction, and result post-processing, and (3) performing automatic co-optimization of all knowledge base parameters to adapt agents to specific problems. SimpleMind enables reasoning on multiple detected objects to ensure consistency, providing cross checking between DNN outputs. This machine reasoning improves the reliability and trustworthiness of DNNs through an interpretable model and explainable decisions. Example applications are provided that demonstrate how SimpleMind supports and improves deep neural networks by embedding them within a Cognitive AI framework.