Logic-Based Verification
In contrast to probabilistic neural networks, Formal Logic provides a binary verification system. Statements are processed as true, false, or unprovable, serving as a foundation for auditable computation.
Core Frameworks
- First-Order Logic (FOL): Foundational language for representing discrete objects and relational structures.
- Description Logic (DL): Efficient sub-languages of FOL used for modeling knowledge domains (e.g., OWL in the Semantic Web).
- Satisfiability Modulo Theories (SMT): Determining the satisfiability of formulas relative to specific background theories such as linear arithmetic or bit-vectors.
Automated Solvers
Industrial-grade solvers are utilized to verify logical consistency in agent workflows:
- Z3 Solver (Microsoft Research): High-performance SMT solver used for hardware/software verification and constraint solving.
- CVC5: An automated theorem prover for SMT and related logical problems.
Related Logical Paradigms
- Answer Set Programming (ASP): A form of declarative programming oriented towards difficult search problems, widely used in planning and configuration tasks.
- The SAT Solver Heritage: Modern SMT solvers are built on decades of research into the Boolean Satisfiability Problem (SAT), with foundational algorithms like DPLL and CDCL.
- Modal Logic: Used for reasoning about necessity, possibility, and temporal sequences in multi-agent environments.
- Higher-Order Logic (HOL): A more expressive but computationally harder fragment of logic used for foundational mathematical verification.
Strategic Role
The objective is to translate LLM-proposed reasoning chains into formal logic representations. By passing these representations to SMT solvers, it is possible to verify that actions do not violate defined logical or physical invariants, ensuring a higher level of system reliability.