In the two most relevant categories of legal systems, the codified law systems and the case law systems, legal argumentation and legal reasoning are at the heart of legal theory and practice. Here we show that the concept of legal syllogism can be used as a starting point in both legal systems for new computational models of legal reasoning. We argue that legal syllogisms are not merely analytic logical inference rules but involve ampliative analogical inference. We aim to operationalize our account in terms of Context Graphs, i.e. internally consistent logical theories linked through rigorously defined analogical relations called views and argumentative relations such as attack and support.