First-order probabilistic conditional logic and maximum entropy.

*(English)*Zbl 1257.68133The paper starts by pointing out the weaknesses of various formalisms that combine fragments of first-order logic and probability. Then the author introduces FO-PCL (first-order probabilistic conditional logic). The theories under consideration are referred to as knowledge bases, defined as finite pairs of the form \((\psi\wedge C\rightarrow\phi,\xi)\) with \(\xi\in[0,1]\) (the conditional probability), and \(\psi\) (the premise), \(C\) (the constraint) and \(\phi\) (the conclusion) formulas over a multi-sorted first-order language having no function symbol of arity 1 or more and having at most finitely many constants (\(\psi\) and \(\phi\) are omitted when they would be tautologies), and such that 5mm

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- all variables which occur free in \(C\) occur free in \(\psi\) or \(\phi\);
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- \(\psi\) and \(\varphi\) are Boolean combinations of atomic formulas, equality excluded;
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- \(C\) is a Boolean combination of equalities.

Reviewer: Éric Martin (Sydney)

##### MSC:

68T27 | Logic in artificial intelligence |

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

03B48 | Probability and inductive logic |

68T30 | Knowledge representation |