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
• Reasoning with Relation Algebras: Subalgebras, Consistency, and Tractability
  • A Primer for the Notebook, Subalgebras of Allen’s Algebra
  • Table of Contents
  • Setting Up
  • 1. RelSets, Disjunctions and Conjunctions
  • 2. The Three Operations: Intersection, Converse, Composition
  • 3. Subalgebras, Closure, and Generators
  • 4. Intervals Are Made of Points: Convex, Pointisable and ORD-Horn RelSets
  • 5. Consistency and Inconsistency
  • 6. Path Consistency, and Networks that are Path Consistent but Inconsistent
  • 7. Complexity: Decidability, NP-hard, NP-complete, Tractable, Maximal
  • 8. Searching for Tractable Subalgebras: Refuted Subalgebras
  • Glossary
  • Exercises
  • References
• Subalgebras of Allen’s Algebra Defined by Point Relations
  • Table of Contents
  • Imports and the Algebra
  • Relations are Orderings of End Points
  • Three Families of Relation Sets
  • Checking that the Families are Subalgebras
  • Generating the ORD-Horn Subalgebra
  • Looking for Tractable Subalgebras Beyond H
  • The Point Algebra
  • References

Constraint Networks

• Temporal Reasoning about Time Intervals and Time Points
  • Algebra
  • Network
  • Propagation
  • Summary
• 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

• 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

API Reference

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

Annotated Bibliography

• Annotated Bibliography
  • 1. Categories
  • 2. About the Links
  • 3. Annotated Entries by Category
  • 4. All Works in Chronological Order

Project Info

• License