Theorem proving is the activity of establishing the truth of mathematical or logical statements by constructing rigorous, step-by-step deductions from axioms and inference rules. Automated theorem proving uses software to search for or verify such proofs, while interactive theorem proving combines machine checking with human guidance. It underpins formal verification of hardware, software and protocols, as well as the mechanisation of mathematics.
Overview
- Theorem Proving is situated within the artificial-intelligence domain and is defined as a subclass of Automated Reasoning.
- It connects to the wider knowledge graph through 18 typed relations spanning structural, functional and contrastive predicates.
- As a established concept, it represents established knowledge with stable terminology and well-understood boundaries.
Key aspects
- Relationship to Automated Reasoning situates this concept within its operational and conceptual context.
- Relationship to Mathematical Logic situates this concept within its operational and conceptual context.
- Relationship to Formal Methods situates this concept within its operational and conceptual context.
- Relationship to Logic situates this concept within its operational and conceptual context.
- Relationship to Inference situates this concept within its operational and conceptual context.
Mechanisms
- The concept is realised through its constituent parts and the standards, methods and dependencies enumerated in its relations.
- It both requires upstream capabilities and enables downstream capabilities, forming part of a directed chain of dependencies in the graph.
Applications
- Practical use of Theorem Proving appears wherever its enabled and supported concepts are deployed.
- It is referenced by existing classes in the graph, anchoring those edges to a defined, rooted node.