Socrates is an online demo of my library for formal argumentation. Argumentation is a form of reasoning using logic and a higher level "semantic" layer which describes what arguments are accepted/rejected within the given semantic. Arguments are created from logical rules and the relations within a set of the rules.
This all sounds a bit more complicated then it is. Essentially, you start with a knowledge base containing information about your domain. This information is encoded in some kind of logic. In our case, the logic is simplified to literals (these can represent a statement such as "it is wet") and two kinds of rules: strict and defeasible. A stric rule is something that is always true. For example, mammals are animals (m --> a). Defeasible rules are things that are usually true. For example, birds can fly (b ==> f). This is usually true, except for, for example, penguins.
Argumentation differs from other logical reasoning systems in being able to cope with conflicting rules. This is sometimes called non-monotonic logic. Unlike, for example, ontologies where you have to maintain consistency, argumentation allows you to have rules with conflicting conclusion. The resolution of what is an "accepted" conclusion is based on higher level semantics and potentially individual preferences.