Logic Derivation Calculator

Logic Derivation Calculator

This calculator helps you determine the truth value of a complex logical expression based on the truth values of its atomic propositions (P, Q, R).

True False

True False

True False

Supported operators: AND, OR, NOT. Use P, Q, R for propositions. Parentheses are supported.

function calculateLogicDerivation() { var pValue = document.getElementById('propP').value === 'true'; var qValue = document.getElementById('propQ').value === 'true'; var rValue = document.getElementById('propR').value === 'true'; var expression = document.getElementById('logicalExpression').value; if (!expression.trim()) { document.getElementById('result').innerHTML = 'Please enter a logical expression.'; return; } // Step 1: Replace proposition variables with their boolean values var processedExpression = expression.toUpperCase(); // Convert to uppercase for consistent operator matching processedExpression = processedExpression.replace(/\bP\b/g, pValue); processedExpression = processedExpression.replace(/\bQ\b/g, qValue); processedExpression = processedExpression.replace(/\bR\b/g, rValue); // Step 2: Replace logical operators with JavaScript equivalents processedExpression = processedExpression.replace(/\bNOT\b/g, '!'); processedExpression = processedExpression.replace(/\bAND\b/g, '&&'); processedExpression = processedExpression.replace(/\bOR\b/g, '||'); // Step 3: Basic sanitization to prevent arbitrary code execution // Allowed characters: true, false, !, &&, ||, (, ), whitespace // This regex ensures only boolean literals, logical operators, parentheses, and spaces are present. var allowedPattern = /^[trueFALSE!&|()\s]*$/; if (!allowedPattern.test(processedExpression)) { document.getElementById('result').innerHTML = 'Invalid characters or unsupported operators in the expression. Only P, Q, R, AND, OR, NOT, and parentheses are allowed.'; return; } var derivedTruthValue; try { // Step 4: Evaluate the expression derivedTruthValue = eval(processedExpression); if (typeof derivedTruthValue !== 'boolean') { throw new Error('Expression did not evaluate to a boolean value. Please check your syntax.'); } document.getElementById('result').innerHTML = '

Derived Truth Value: ' + (derivedTruthValue ? 'True' : 'False') + '

'; } catch (e) { document.getElementById('result').innerHTML = 'Error evaluating expression: ' + e.message + '. Please check your syntax.'; } }

Understanding Logic Derivation

Logic derivation is the process of determining the truth value of a complex logical statement based on the truth values of its simpler, atomic components. In propositional logic, we use propositions (statements that can be either true or false) and logical connectives to build more intricate expressions. This calculator helps you perform this derivation for various scenarios.

Key Concepts:

• Proposition: A declarative sentence that is either true or false, but not both. In this calculator, P, Q, and R represent atomic propositions.
• Truth Value: The status of a proposition being either True or False.
• Logical Connectives: Symbols or words used to combine propositions into more complex statements.
  • AND (Conjunction): Represented by '∧' or 'AND'. The statement 'P AND Q' is true only if both P and Q are true.
  • OR (Disjunction): Represented by '∨' or 'OR'. The statement 'P OR Q' is true if at least one of P or Q is true (inclusive OR).
  • NOT (Negation): Represented by '¬' or 'NOT'. The statement 'NOT P' is true if P is false, and false if P is true.
  • Parentheses (): Used to group parts of an expression and dictate the order of operations, similar to algebra.

How to Use the Calculator:

1. Set Truth Values: Choose 'True' or 'False' for propositions P, Q, and R based on your scenario.
2. Enter Logical Expression: Type your logical expression into the provided text field.
   • Use 'P', 'Q', 'R' for your propositions.
   • Use 'AND', 'OR', 'NOT' for logical connectives. (Case-insensitive, e.g., 'and' or 'AND' both work).
   • Use parentheses '()' to specify the order of operations.
3. Calculate: Click the 'Calculate Truth Value' button to see the derived truth value of your expression.

Examples of Logical Expressions:

Let's assume P is True, Q is False, and R is True for these examples:

• Expression: P AND Q
  • Input: P=True, Q=False, R=True
  • Calculation: True AND False → False
  • Derived Truth Value: False
• Expression: NOT P OR R
  • Input: P=True, Q=False, R=True
  • Calculation: NOT True OR True → False OR True → True
  • Derived Truth Value: True
• Expression: (P OR Q) AND NOT R
  • Input: P=True, Q=False, R=True
  • Calculation: (True OR False) AND NOT True → True AND False → False
  • Derived Truth Value: False
• Expression: NOT (P AND NOT Q)
  • Input: P=True, Q=False, R=True
  • Calculation: NOT (True AND NOT False) → NOT (True AND True) → NOT True → False
  • Derived Truth Value: False

This tool is ideal for students of logic, philosophy, computer science, or anyone needing to quickly evaluate complex logical statements.