a5c-ai/formal-logic-analysis

Formal Logic Analysis Skill

Apply formal logic systems to analyze, formalize, and evaluate arguments with rigorous symbolic methods.

Overview

The Formal Logic Analysis skill enables systematic application of propositional, predicate, and modal logic systems to formalize arguments, construct proofs, evaluate validity, and assess soundness using symbolic notation, truth tables, and proof procedures.

Capabilities

Propositional Logic

• Translate natural language arguments into propositional form
• Construct truth tables for validity assessment
• Apply natural deduction rules
• Identify logical equivalences and tautologies
• Evaluate argument validity through truth-functional analysis

Predicate Logic

• Formalize arguments with quantifiers and predicates
• Apply universal and existential instantiation/generalization
• Construct formal proofs in first-order logic
• Analyze logical relations and inferences
• Handle multiple quantification and scope issues

Modal Logic

• Apply necessity and possibility operators
• Analyze arguments involving modality
• Work with different modal systems (K, T, S4, S5)
• Evaluate modal validity
• Apply modal logic to philosophical arguments

Proof Construction

• Build natural deduction proofs
• Apply inference rules systematically
• Construct indirect proofs
• Use conditional proof techniques
• Verify proof correctness

Usage Guidelines

When to Use

• Formalizing philosophical arguments
• Testing argument validity
• Analyzing logical structure
• Teaching formal reasoning
• Evaluating philosophical positions

Best Practices

• Translate arguments carefully and completely
• Check translations against original meaning
• Use appropriate logical system for the argument type
• Document proof steps clearly
• Verify validity independently when possible

Integration Points

• Argument Mapping and Reconstruction skill
• Fallacy Detection and Analysis skill
• Philosophical Writing and Argumentation skill
• Conceptual Analysis skill

References

• Formal Logic Analysis process
• Modal Logic Application process
• Argument Reconstruction and Analysis process
• Logic Analyst Agent