## Inference in conditional probability logic.(English)Zbl 1249.68262

Summary: An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets common sense expressions of the form “if $$\ldots$$, then $$\ldots$$” as conditional probabilities and not as the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to the unit interval $$[0,1]$$. Not all logically valid inference rules are probabilistically informative and vice versa. The relationship between logically valid and probabilistically informative inference rules is discussed and illustrated by examples such as modus ponens or affirming-the-consequent. We propose a method to evaluate the strength of CPL inference rules. Finally, an example of a proof is given that is purely based on CPL inference rules.

### MSC:

 68T37 Reasoning under uncertainty in the context of artificial intelligence 03B48 Probability and inductive logic 03B65 Logic of natural languages

### Keywords:

probability logic; conditional; modus ponens
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### References:

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