Tyche 0.1.1

Tyche is a library to facilitate the use of aleatoric description logic to construct, query, and update probabilistic belief models.

Tyche is a Python library to support the representation of, and the reasoning about, aleatoric information. Aleatoric information is information that can be modelled by a roll of the dice. It is information that has a probability of truth for each time it is sampled. For example, every text message that people send may include emojis, with a different probability for each individual that sent the message. Tyche provides functionality to reason about this aleatoric information using aleatoric description logic. This allows the probability of truth of logical statements to be efficiently queried, and allows the probability of the tendencies of individuals to be learnt through observation.

Tyche provides its main functionality through its tyche.individuals module, which facilitates the construction of ontological knowledge basea with probabilistic beliefs. This allows the simple representation of individuals, the probabilistic beliefs about them (termed concepts), and the probabilistic relationships between them (termed roles). Aleatoric description logic sentences may then be constructed using the tyche.language model to be used to query a knowledge base for a probability, or to be used as an observation to update a knowledge base. This allows fine-grained modelling of probabilistic belief systems, with a rigorous mathematical foundation.

Related Publications:

• Aleatoric Description Logic for Probabilistic Reasoning: arXiv link
• A modal aleatoric calculus for probabilistic reasoning: arXiv link

Structure

The tyche package consists of the following main modules:

• language. This is the aleatoric description logic language module for representing sentences. The language module also contains the representation used for the value of roles.
• individuals. This is the ontological knowledge base individuals module for representing ontologies of individuals, the probabilistic beliefs about them (concepts), and the probabilistic relationships between them (roles). The individuals module also contains classes and functions that may be used to learn from aleatoric description logic observations.
• distributions. This module contains utility classes for representing and manipulating probability distributions. These distributions may be used to convert continuous quantities into probabilities, and to learn the probability distributions from aleatoric description logic observations.

The Tyche project also consists of the package test that contains unit tests for the functionality of Tyche, and the package examples that contains example uses of Tyche.

License

Tyche is licensed under the MIT License.