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This paper 1) discusses the astonishing complexity of intelligence analysis by using the popular metaphor of "connecting the dots," 2) outlines a systematic computational approach, grounded in the Science of Evidence, that allows coping with this complexity, and 3) introduces an innovative intelligent software agent, called TIACRITIS, for teaching intelligence analysts how to perform evidence-based reasoning. TIACRITIS is a web-based system with case studies and knowledge bases incorporating a significant amount of knowledge about evidence, its properties, uses, and discovery. It is a personalizable agent that helps analysts acquire the knowledge, skills, and abilities involved in discovering and processing of evidence and in drawing defensible and persuasive conclusions from it, by employing an effective learning-by-doing approach. It allows analysts to practice and learn how to link evidence to hypotheses through abductive, deductive, and inductive reasoning that establish the basic credentials of evidence: its relevance, believability, and inferential force or weight. Analysts can also experiment with what-if scenarios and study the influence of various assumptions on the final result of analysis., Published in the American Intelligence Journal, v28 n2, Dec 2010. Sponsored in part by NSF.