# Catalogue of Artificial Intelligence Techniques

## Possibilistic Logic

**Keywords:**
possible worlds

### Categories: Inference and Reasoning , Knowledge Representation

Author(s): **Fl\'avio Corr\^ea da Silva**

Possibilistic logics assign degrees of necessity and possibility
to sentences, which express the extent to which these sentences are
believed to be necessarily or possibly true, respectively. The
semantics of possibilistic logics is defined based on a
Fuzzy Set of
possible worlds, i.e., a set of possible worlds together with a fuzzy membership
function that describes the extent to which each possible world
belongs to a referential set. Given a sentence $a$
, the *necessity
measure* $N(a)$
expresses the greatest lower bound for the degree of
membership of the worlds that support $a$
, and the related *possibility measure* $\Pi (a)$
expresses the least upper bound for this
degree of membership.
Possibilistic logics should not be confused with Fuzzy
Logics. Although the concept of fuzzy
measures is central to the description of both of them, in
possibilistic logics the truth-values of sentences range on $true,false$
only and necessity and possibility measures describe states
of belief, whereas in fuzzy logics the truth-values of sentences range
on the interval $[0,1]$
and fuzzy measures describe `degrees of
trueness'.

### References:

- Sombé, L.,
*Reasoning Under Incomplete Information in Artificial Intelligence: a Comparison of Formalisms Using a Single Example*International Journal of Intelligent Systems**5**(1990) no.4, 323--472.

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