Integrating Linear Arithmetic Constraints Into Conditional Maximum Entropy Reasoning

The principle of maximum entropy (MaxEnt principle) constitutes a valuable methodology for probabilistic commonsense reasoning by adding missing information to probabilistic conditional belief bases in an information theoretically optimal way. In this paper, we integrate linear arithmetic constraints over the integers and reals into propositional probabilistic conditionals in order to be able to formalize uncertain beliefs about arithmetic expressions. The satisfiability of (sets of) constraints is decided modulo theory such that probabilistic reasoning stays finite although the constraints range over infinite domains. Therewith, we provide a novel extension of the MaxEnt principle to beliefs about infinite domains.