Computational aspects of satisfiability in probability logic

We consider the complexity of satisfiability in ε‐logic, a probability logic. We show that for the relational fragment this problem is ‐complete for rational , answering a question by Terwijn. In contrast, we show that satisfiability in 0‐logic is decidable. The methods we employ to prove this fact also allow us to show that 0‐logic is compact, while it was previously shown that ε‐logic is not compact for .