Given two vectors and and a dyadic logical matrix , a scalar probabilistic logic is provided by the projection over vector s:

In this way, subjective logic becomes a probabilistic logic for uncertain probabilities.

A difficulty with probabilistic logics is that they tend to multiply the computational complexities of their probabilistic and logical components.

There are numerous proposals for probabilistic logics.

The term "probabilistic logic" was first used in a paper by Nils Nilsson published in 1986, where the truth values of sentences are probabilities.

In a series of works in the early 1950s he surveyed modal, intuitionistic, probabilistic, and other philosophical logics.

Interpreting these values as logical truth values yields a multi-valued logic, which forms the basis for fuzzy logic and probabilistic logic.

Subjective logic generalises probabilistic logic by including parameters for uncertainty in the input arguments.

Fuzzy logic is a form of many-valued logic or probabilistic logic; it deals with reasoning that is approximate rather than fixed and exact.

The upper and lower probabilities are also related with probabilistic logic: see Gerla (1994).