Relation Algebras

This section describes the Relation Algebra format and usage found in qualreas.

• Allen’s Algebra of Proper Time Intervals
  • References
  • Dependencies
  • Instantiate an Algebra
  • Algebra Summary
  • Algebra Element Summary
  • Equality Relations
  • Creating Relation Sets
  • Operations on Relation Sets
  • Global Properties of an Algebra of Relations
• Extended Interval Algebras
  • References
  • Dependencies
  • 1. Linear Interval and Point Algebra
  • 2. Right-Branching Interval and Point Algebra
  • 3. Left-Branching Interval and Point Algebra
  • Pick one of the algebras to use for examples
  • Algebra Element Summary
  • Equality Relations
  • Creating Relation Sets
  • Operations on Relation Sets
  • Global Properties of an Algebra of Relations
• Time Point Algebras
  • References
  • The Structures of Linear and Branching Time
  • Linear Point Algebra
  • Right-Branching Point Algebra
  • Left-Branching Point Algebra
  • Right-Binary-Branching Point Algebra
  • Left-Binary-Branching Point Algebra

Constraint Networks

• Temporal Reasoning about Time Intervals and Time Points
  • An Example of Temporal Reasoning
• Region Connection Calculus (RCC)
  • Constraint Network in JSON Format
  • Instantiate the Constraint Network Object
  • Summarize the Network
  • Perform Constraint Propagation
  • Singleton Labelings of a Network
  • Converting Networks to/from Other Formats

Derivation of Algebras

• Deriving Point Algebras
  • Transitivity Table for Linear Time Point Relations
  • Create Linear Point Algebra from Generated Table
  • Transitivity Table for Branching Time Point Relations
  • Transitivity Table for 2-Dimensional Point Relations
  • Create Point Algebras from Generated Tables
• Derive Allen’s Algebra
  • References
  • Dependencies
  • Deriving Allen’s Interval Algebra from Basic Point Algebra
• Derive Extended Interval Algebra
  • References
  • Dependencies
  • Deriving Extended Interval Algebra from Extended Point Algebra
• Derive Left-Binary-Branching Interval Algebra
  • References
  • Dependencies
  • Deriving the Left-Binary-Branching (LBB) Interval Algebra from LBB Point Algebra
• Derive Left-Branching Proper Interval Algebra
  • References
  • Dependencies
  • Deriving the LB Proper Interval Algebra from LB Point Algebra
• Derive Right-Binary-Branching Interval Algebra
  • References
  • Dependencies
  • Deriving the Right-Binary-Branching (RBB) Interval Algebra from RBB Point Algebra
• Derive Right-Branching Proper Interval Algebra
  • References
  • Dependencies
  • Deriving the RB Proper Interval Algebra from RB Point Algebra
• Rectangle Algebra
  • Load the 2D Point Algebra
  • Derive Rectangle Relations
  • Derive the Consistent Networks for Proper Rectangles
  • Assigning Names to the Rectangle Relations

API Reference

• API Reference
  • Qualitative Reasoning Classes
  • TemporalEntity
  • SpatialEntity
  • RelSet
  • Algebra
  • Functions & Etc
  • Network
  • InconsistentNetwork
  • Algebra Derivation Classes
  • FourPointNet
  • SixPointNet
  • Algebra Derivation Functions

Project Info

• License