Logic Puzzle Solver
Conclusion: -
Understanding Formal Logic
What is Formal Logic?
Formal logic is a systematic study of valid inference and reasoning patterns using formal languages.
Key Components:
- Propositions: Basic statements that are true or false
- Logical Operators: AND, OR, NOT, IMPLIES, etc.
- Truth Tables: Systematic evaluation of logical expressions
- Logical Equivalences: Different expressions with same truth values
Types of Logic
- Propositional Logic:
- Basic true/false statements
- Boolean operations
- Truth tables
- Logical equivalences
- Predicate Logic:
- Quantifiers (∀, ∃)
- Variables and predicates
- Domain of discourse
- First-order logic
- Temporal Logic:
- Time-dependent statements
- Modal operators
- Linear time logic
- Branching time logic
Advanced Concepts
Normal Forms
Conjunctive Normal Form (CNF)
Disjunctive Normal Form (DNF)
Prenex Normal Form
Proof Systems
Natural Deduction
Resolution
Sequent Calculus
Decision Procedures
SAT Solving
Model Checking
Automated Theorem Proving
Applications
Program Verification
Circuit Design
AI Reasoning
Logical Inference Rules
Basic Rules
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Derived Rules
Disjunctive Syllogism
Resolution
Cut Rule
Equivalences
De Morgan's Laws
Distribution
Double Negation
Quantifier Rules
Universal Instantiation
Existential Generalization
Skolemization