SpecLogician

SpecLogician is an AI framework for data-driven formal program specification synthesis, verification, and analysis.

It replaces monolithic “spec-first” formal modeling with an incremental, scenario-driven approach that works naturally with LLM-powered and agentic tools—while keeping correctness grounded in machine-checkable formal logic.

  • Website: www.speclogician.dev
  • Core idea: build a formal model from symbolic given / when / then scenarios, linked to a rich domain model (predicates, transitions, state/action types, and auxiliary logic).

1) The challenge: scaling formal methods via LLM-powered automation

  • Automatically applying formal methods to large software systems using LLM-powered and agentic tools remains a fundamental challenge
  • Traditional formal modeling approaches require building large, monolithic formal models upfront
  • There is no single canonical way to formalize a complex software system
  • As a result, formalization becomes as much an art as a science, relying heavily on expert judgment
  • These characteristics fundamentally limit automation:
    • LLMs struggle to generate or maintain large, globally consistent formal models
    • Small local changes often require understanding the entire model
    • Monolithic models are brittle under iterative, agent-driven workflows

2) SpecLogician’s core idea

  • SpecLogician is an AI framework for data-driven formal program specification synthesis, verification, and analysis
  • It replaces monolithic specifications with incrementally constructed formal logic
  • The core logic is built from symbolic given / when / then scenarios
  • Scenarios are:
    • composable
    • declarative
    • local in scope
  • Scenarios are connected to a domain model of arbitrary complexity
  • The domain model captures:
    • predicates
    • transitions
    • state/action structure
    • auxiliary and domain-specific logic

3) Why this structure works well with LLMs

  • LLM-powered tools are used to:
    • propose new scenarios
    • refine existing scenarios
    • generate structured deltas (add / remove / edit)
  • LLMs operate on small, well-scoped artifacts, not entire formal models
  • Each change is:
    • explicit
    • typed
    • machine-checkable
  • This aligns naturally with how LLMs perform best:
    • local reasoning
    • incremental edits
    • structured outputs (JSON, CLI commands)

4) Agentic reasoning loop (formal reasoning as the backbone)

  • SpecLogician sits at the center of an agentic reasoning loop
  • In this loop:
    • CodeLogician / ImandraX translate source code into formal models and reasoning artifacts
    • LLM-powered agentic CLIs propose scenario additions, edits, and removals as structured deltas
    • Software mapping tools (e.g. CodeMaps from cognition.ai) provide high-level program structure and navigation context
  • Each agent contributes partial, local insight:
    • code structure
    • behavioral intent
    • execution traces
    • test artifacts
  • SpecLogician:
    • integrates these inputs into a single formal state
    • validates them symbolically
    • delegates global analysis to the ImandraX automated reasoning engine
  • The reasoning engine analyzes the entire accumulated model after every change
  • This creates a closed-loop workflow:
    • propose → formalize → verify → refine

5) What the resulting formal model enables

  • Systematically identify gaps in design and requirements
  • Precisely understand test coverage and gaps in test coverage
  • Trace:
    • execution logs
    • test cases
    • documentation
    • other artifacts
      back to formal specifications and requirements
  • Automatically generate missing test cases
  • Safely model and verify the impact of changes before they are applied
  • Maintain a single, authoritative source of truth for system behavior

6) Big-picture outcome

  • Transforms LLMs from:
    • probabilistic code generators
      into:
    • reliable collaborators in a verification-driven workflow
  • Makes formal methods:
    • incremental
    • data-driven
    • compatible with LLM-powered automation
    • scalable to real-world software systems
  • Positions SpecLogician as the formal reasoning backbone for modern, agentic software development