# Catalogue of Artificial Intelligence Techniques

## Incidence Calculus

**Aliases:**
Probabilistic Logic

**Keywords:**
possible worlds

### Categories: Inference and Reasoning , Knowledge Representation

Author(s): **Alan Bundy**

A multi-valued logic in which the value of a formula is a set of situations in which the formula is true. These situations can be possible worlds, models or members of any set of objects. The values of composite formulae are defined to be set theoretic combinations of the values of their sub-formulae, e.g., the value of a conjunction is the intersection of the values of the conjuncts. The formulae can be assigned a number, e.g., a probability, by applying an arithmetic function to their assigned sets, e.g., the sum of the probabilities of each member of the set. In this way incidence calculus can be used to represent the uncertainty of a formulae, e.g., as a probability. The main advantage of this indirect route of assigning probabilities is that the correlation between two formulae is implicitly represented by the degree of intersection between formulae. Thus it is not necessary to assume conditional independence. When a new conclusion is deduced from some hypotheses the value of the conclusion is not completely determined by the values of the hypotheses, but it is possible to calculate tight upper and lower bounds on value of the conclusion.

### References:

- Bundy, A.,
*Incidence Calculus: A Mechanism for Probabilistic Reasoning*Journal of Automated Reasoning**1**(1985), 263--284.

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