DAG Path Addressing for Generalization Hierarchy Propositions
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Solution Overview
Problem
The inefficiency in storing and processing propositions expressed in Conceptual Graph Interchange Format (CGIF) and other logic languages due to the requirement of many variable names, which limits storage and processing efficiency in applications like generalization hierarchies, data-flow diagrams, and conceptual graphs.
Innovation Solution
DAG Path Addressing allows names to be factored out by providing unique address ranges for nodes in Directed Acyclic Graphs (DAGs), enabling efficient referencing and correlation of instances within hierarchies, and simplifying the representation and processing of propositions by using binding lists.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If propositions are expressed in CGIF or other logic languages, then propositions can be formally represented, but storage and processing efficiency deteriorates due to the requirement of many variable names
Solution Approach 1:
The patent extracts variable names from the logical structure of propositions and stores them separately in binding lists. Each proposition is represented by its core logical form without embedded variable names, which are instead referenced through bindings. This separation eliminates the redundancy of repeating variable names throughout the proposition structure, thereby improving storage efficiency and processing speed while maintaining formal representation.
Solution Approach 2:
The binding list structure serves multiple functions: it stores variable name bindings, enables efficient lookup of variable references, and supports the formal representation of propositions. By creating a universal binding mechanism that works across different proposition types and logical languages, the system achieves both formal correctness and processing efficiency without requiring separate solutions for different cases.
2Loss of information
If variable names are included in proposition expressions, then propositions can be clearly identified, but device complexity increases due to the need to manage many variable names
Solution Approach 1:
Variable names are extracted from the proposition expression and stored in separate binding lists. The proposition itself contains only the essential logical structure and references, while the binding list holds the actual variable name mappings. This extraction reduces the complexity of proposition management while preserving complete identification information through the binding references.
Solution Approach 2:
The binding list acts as an intermediary between the simplified proposition structure and the full variable name information. Instead of embedding variable names directly in propositions (which increases complexity), the system uses bindings as mediators that link proposition references to their corresponding variable names, thereby maintaining clear identification without increasing structural complexity.
3Reliability
If names are embedded in DFD descriptions using UML, then DFDs can be fully described, but storage and processing efficiency deteriorates
Solution Approach 1:
The patent extracts variable names from DFD descriptions and stores them in binding lists associated with the DAG representation. The DFD structure itself contains only the essential flow and transformation information without redundant variable name repetitions. This extraction maintains complete DFD description while improving storage efficiency and processing speed by eliminating name embedding overhead.
4Measurement precision
If variable names are used in CG descriptions, then conceptual graphs can be precisely expressed, but processing efficiency deteriorates independent of names or values
Solution Approach 1:
Variable names are extracted from conceptual graph expressions and stored in binding lists. The conceptual graph structure retains precise meaning through its logical form and relationships, while variable name management is handled separately through bindings. This separation maintains expression precision while improving processing efficiency by eliminating the overhead of embedded variable names during graph operations.
Data Source
AI summary
A memory for storing a directed acyclic graph (DAG) for access by an application being executed by one or more processors of a computing device is described. The DAG includes a plurality of nodes, wherein each node represents a data point within the DAG. The DAG further includes a plurality of directional edges. Each directional edge connects a pair of the nodes and represents a covering-covered relationship between two nodes. Each node comprises a subgraph consisting of the respective node and all other nodes reachable via a covering path that comprises a sequence of covering and covered nodes. Each node comprises a set of node parameters including at least an identifier and an address range. Each node and the legal address specify a cover path. Utilizing DAG Path Addressing with bindings the memory can be organized to store a generalization hierarchy of logical propositions.