Rhodes, Greece. September 2-8, 2023.

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ISSN: 2334-1033

ISBN: 978-1-956792-02-7

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Copyright © 2023 International Joint Conferences on Artificial Intelligence Organization

- Nonmonotonic logics, default logics, conditional logics
- Commonsense reasoning
- Probabilistic reasoning and learning
- Reasoning about knowledge, beliefs, and other mental attitudes

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.