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temporal-logic-translator skill

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This skill translates temporal logic formalisms and guides property specification, enabling precise formal verification and translations between LTL, CTL, and

npx playbooks add skill a5c-ai/babysitter --skill temporal-logic-translator

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---
name: temporal-logic-translator
description: Translate between temporal logic formalisms and generate property specifications
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - Grep
metadata:
  specialization: computer-science
  domain: science
  category: formal-verification
  phase: 6
---

# Temporal Logic Translator

## Purpose

Provides expert guidance on temporal logic specification and translation between formalisms.

## Capabilities

- LTL to Buchi automata
- CTL to CTL* comparison
- Natural language to temporal logic
- Property pattern templates
- Formula equivalence checking
- Negation normal form conversion

## Usage Guidelines

1. **Property Identification**: Identify desired system properties
2. **Formalization**: Express in appropriate temporal logic
3. **Translation**: Convert between formalisms if needed
4. **Pattern Matching**: Use property pattern templates
5. **Verification**: Check formula equivalence

## Tools/Libraries

- Spot
- GOAL
- LTL2BA
- NuSMV

Overview

This skill provides expert translation and specification generation for temporal logics used in system verification. It helps convert informal requirements into formal LTL/CTL/CTL* expressions, translate between formalisms, and generate automata when needed. The focus is on producing verifiable property specifications and assisting automated workflows.

How this skill works

The skill inspects natural-language requirements or existing formulas and maps them to temporal-logic patterns and templates. It can translate LTL to Büchi automata, compare CTL and CTL* formulations, convert formulas to negation normal form, and check equivalence between expressions. It leverages known toolchains and pattern libraries to produce concise, machine-checkable properties for model checkers and orchestration tools.

When to use it

  • You need formal properties from informal requirements for model checking.
  • Translating between LTL, CTL, and automata representations for verification tools.
  • Generating property templates for recurring design patterns (safety, liveness, response).
  • Checking whether two temporal formulas are equivalent or one implies another.
  • Preparing properties for integration with verification pipelines (NuSMV, Spot, LTL2BA).

Best practices

  • Start with clear, atomic requirements and identify scope (system vs environment).
  • Map each requirement to a single pattern (safety, liveness, response) before formalizing.
  • Prefer small, modular formulas; compose properties rather than monolithic expressions.
  • Validate generated formulas with small model checks and sanity cases before full verification.
  • Keep both the natural-language intent and the formal formula together for traceability.

Example use cases

  • Translate a textual requirement like “requests are eventually granted” into an LTL response formula and produce a Büchi automaton for a model checker.
  • Convert a CTL property to a CTL* expression to reason about path vs state quantification differences.
  • Use pattern templates to quickly generate a suite of safety and liveness properties for a new component.
  • Check equivalence of two independently written formulas to avoid redundant or conflicting properties.
  • Transform formulas into negation normal form before passing them into automated tools that require NNF.

FAQ

Which formalisms does the skill support?

Primary support includes LTL, CTL, CTL*, and Büchi automata representations; translations and comparisons between these are provided.

Can it generate artifacts compatible with model checkers?

Yes. Outputs are designed to integrate with common tools and pipelines such as Spot, LTL2BA, GOAL, and NuSMV, with options to produce automata or formatted property files.