Tyche 0.1.0

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 represent and reason about aleatoric information. The system includes syntax for describing aleatoric information (in tyche.language), Aleatoric knowledge bases are a generalisation of description logic knowledge bases, where concepts and roles are aleatoric, in that they are assumed to be determined by the role of a die. This allows fine-grained modelling of probabilistic belief systems, with a rigorous mathematical foundation.

The tyche package consists of the following modules:

• language. This is the aleatoric description logic langauge module for representing formulas, and performing basic transformations. It consists of the following classes:
  • the logical operators Concept, Conditional, Expectation and LeastFixedPoint
  • and the role operators Role, Test, Iterate, and Combine
  • Proof, theorem proving utilities.
• logic. This is the aleatoric description logic module for reasoning. It consists of the classes:
  • Axiom, a class for representing intensional beliefs, or TBooks.
  • Assertion, a class for representing extensional beliefs, or ABooks.
  • Theory, a class for inference given axioms and assertions, satisfiability and consistency checking
  • this class will have multiple utility classes to support the extensive algorithms required for satisfiability testing
• models. This is the module for representing interpretations of an aleatoric theory, which is essentially a belief model for decision support. It provides a framework for writing python classes that represent aleatoric information constrained by aleatoric theories. It also permits learning and database synchronisation operations, and consists of the classes:
  • Distribution, various classes for representing distributions over fields that an individual can have
  • Individual, for representing aleatoric individuals. These may be subclassed and decorated with aleatoric concepts, roles and axioms.
  • BeliefBase, a module for synchronising individuals with databases, checking consistency with theories, handling queries, and performing learning operations given observations.
  • SqlAleatory a wrapper for sqlalchemy to handle aleatoric information.

The Tyche project also consists of the package test which will contain unit tests as they are written, and an examples directory containing prototypes of python classes that use the tyche package.

This page will be updated as these modules and packages are fleshed out.