 The most important distinction is that between probability logic and inductive logic. Classically, an argument is said to be (deductively) valid if and only if it is impossible that the premises of \(A\) are all true, while its conclusion is false. In other words, deductive validity amounts to truth preservation: in a valid argument, the truth of the premises guarantees the truth of the conclusion. In some arguments, however, the truth of the premises does not fully guarantee the truth of the conclusion, but it still renders it highly likely. A typical example is the argument with premises ‘The first swan I saw was white’, …, ‘The 1000th swan I saw was white’, and conclusion ‘All swans are white’. Such arguments are studied in inductive logic, which makes extensive use of probabilistic notions, and is therefore considered by some authors to be related to probability logic. There is some discussion about the exact relation between inductive logic and probability logic, which is summarized in the introduction of Kyburg (1994). The dominant position (defended by Adams and Levine (1975), among others), which is also adopted here, is that probability logic entirely belongs to deductive logic, and hence should not be concerned with inductive reasoning. Still, most work on inductive logic falls within the ‘probability preservation’ approach, and is thus closely connected to the systems discussed in  Section 2.  For more on inductive logic, the reader can consult Jaynes (2003), Fitelson (2006), Romeijn (2011), and the entries on  the problem of induction  and  inductive logic  of this encyclopedia.