vibeeval/propositional-logic
skills/math/mathematical-logic/propositional-logic/SKILL.md
Problem-solving strategies for propositional logic in mathematical logic
$ install --global
skillsauthnpx skillsauth add vibeeval/vibecosystem propositional-logicInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
Security Scan Results
3 of 9 scanners reported clean
Some scanners were skipped, did not run, or reported a non-clean status. Review each row below.
3
Scanners Passed
9
Scanners in report
Clean
TrivyContainer and dependency vulnerability scanner
95%
Clean
SemgrepStatic code analysis for vulnerabilities
95%
Clean
mcp-scan (Snyk)Model Context Protocol security validation
95%
Skipped
Snyk (dep)Open source security scanning
50%
Skipped
Socket.devSupply chain security analysis
50%
Skipped
VirusTotalMulti-engine malware detection
50%
Skipped
CrowdStrikeAdvanced threat intelligence
50%
Skipped
OSV-ScannerOpen Source Vulnerability database check
50%
Skipped
OWASP Dep-Check
50%
Last scanned: Jun 10, 2026, 5:58 AM4.4s1 file scanned
SKILL.md
- name:
- propositional-logic
- description:
- Problem-solving strategies for propositional logic in mathematical logic
- allowed-tools:
- [Bash, Read]
Propositional Logic
When to Use
Use this skill when working on propositional-logic problems in mathematical logic.
Decision Tree
-
Identify Formula Structure
- Classify: tautology, contradiction, or contingent?
- Main connective: AND, OR, IMPLIES, NOT, IFF?
z3_solve.py sat "formula"to check satisfiability
-
Truth Table Method
- For small formulas (<=4 variables): enumerate all valuations
sympy_compute.py truthtable "p & (p -> q) -> q"- Tautology = all T, Contradiction = all F
-
Natural Deduction
- Apply inference rules: Modus Ponens, Modus Tollens
- Conditional proof: assume antecedent, derive consequent
z3_solve.py prove "Implies(And(p, Implies(p,q)), q)"
-
Semantic Tableaux
- Build tree by decomposing formula
- Closed branches = contradictions
- All branches closed = valid argument
Tool Commands
Z3_Sat
uv run python -m runtime.harness scripts/z3_solve.py sat "And(p, Implies(p, q), Not(q))"
Z3_Tautology
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(And(p, Implies(p, q)), q)"
Sympy_Truthtable
uv run python -m runtime.harness scripts/sympy_compute.py truthtable "p & (p >> q) >> q"
Z3_Modus_Ponens
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(And(p, Implies(p,q)), q)"
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
Related Skills
vibeeval/workflow-router
development
VerifiedTrustedCommunity
Goal-based workflow orchestration - routes tasks to specialist agents based on user goals
500SKILL.mdUpdated Jun 11, 2026
vibeeval/wiring
tools
VerifiedTrustedCommunity
Wiring Verification
500SKILL.mdUpdated Jun 11, 2026
vibeeval/websocket-patterns
development
VerifiedTrustedCommunity
Connection management, room patterns, reconnection strategies, message buffering, and binary protocol design.
500SKILL.mdUpdated Jun 11, 2026
vibeeval/vp-engineering
testing
VerifiedTrustedCommunity
VP Engineering perspective - org design (team topologies), process improvement, cross-team dependencies, engineering culture, OKRs, incident management maturity, platform strategy, DX optimization, release management at scale
500SKILL.mdUpdated Jun 11, 2026