Logic Calculator Proof – Verify Logical Arguments

Logic Calculator Proof

Verify and understand the validity of logical arguments.

Logic Proof Calculator

Premise 1 (Propositional Logic)
Enter the first premise using standard logical symbols (P, Q, R for propositions; ^ for AND, v for OR, ~ for NOT, -> for IMPLIES, <-> for IFF).

Premise 2 (Propositional Logic)

Enter the second premise.

Conclusion (Propositional Logic)

Enter the conclusion you want to prove.

Proof Steps (Rule-based)

List the steps of your proof, referencing previous lines and the rule applied.</div>
<div class="error-message" id="proofStepsError"></div>
</p></div>
</p></div>
<div class="button-group">
                <button type="button" class="primary" onclick="calculateProof()">Verify Proof</button><br />
                <button type="button" class="secondary" onclick="copyResults()">Copy Results</button><br />
                <button type="button" class="secondary" onclick="resetCalculator()">Reset</button>
            </div>
</section>
<section id="results">
<h3>Proof Verification Results</h3>
<div id="primaryResult" class="primary-result">Enter premises and proof steps.</div>
<div class="result-item">
                <span class="result-label">Validity Status:</span><br />
                <span class="result-value" id="validityStatus">–</span>
            </div>
<div class="result-item">
                <span class="result-label">Deductive Strength:</span><br />
                <span class="result-value" id="deductiveStrength">–</span>
            </div>
<div class="result-item">
                <span class="result-label">Number of Valid Steps:</span><br />
                <span class="result-value" id="validStepsCount">–</span>
            </div>
<div class="result-item">
                <span class="result-label">Total Proof Steps:</span><br />
                <span class="result-value" id="totalStepsCount">–</span>
            </div>
<div class="formula-explanation">
                The calculator verifies your proof by checking each step against the provided premises and standard rules of inference. Validity is determined by whether the conclusion *necessarily* follows from the premises. Deductive strength assesses the logical rigor.
            </div>
</section>
<section class="chart-container">
<h3>Proof Step Analysis Over Time</h3>
<p>            <canvas id="proofChart"></canvas></p>
<caption>Visual representation of valid vs. invalid steps in your proof.</caption>
</section>
<section class="table-container">
<table>
<thead>
<tr>
<th>Step #</th>
<th>Statement</th>
<th>Justification</th>
<th>Status</th>
</tr>
</thead>
<tbody id="proofTableBody">
<tr>
<td colspan="4">Proof steps will appear here.</td>
</tr>
</tbody>
</table>
<caption>Detailed breakdown of each step in your logical proof.</caption>
</section>
<section class="article-section">
<h2>What is Logic Calculator Proof?</h2>
<p>A <strong>Logic Calculator Proof</strong>, often referred to as a proof checker or formal verification tool for logic, is a computational system designed to assess the validity of a logical argument. It takes premises and a series of stated inferences as input and determines whether the conclusion logically follows from those premises according to the rules of formal logic. This tool is crucial for anyone working with propositional logic, predicate logic, or formal systems where rigorous validation is essential. It helps distinguish sound reasoning from fallacious arguments, providing a definitive yes or no on the logical structure.</p>
<p><strong>Who should use it:</strong></p>
<ul>
<li>Students of logic, mathematics, computer science, and philosophy</li>
<li>Researchers developing formal systems or algorithms</li>
<li>Programmers working with theorem provers or automated reasoning</li>
<li>Anyone needing to ensure the absolute correctness of a logical deduction</li>
</ul>
<p><strong>Common misconceptions:</strong></p>
<ul>
<li><strong>“It proves the premises are true.”</strong> The calculator only checks if the conclusion follows *from* the premises. It does not assess the truthfulness of the premises themselves.</li>
<li><strong>“It’s just for simple ‘if P then Q’ statements.”</strong> While this tool handles basic propositional logic, advanced versions can tackle complex predicate logic, modal logic, and more.</li>
<li><strong>“It replaces human understanding.”</strong> It’s a tool to aid and verify logical reasoning, not to replace critical thinking or the understanding of logical principles.</li>
</ul>
</section>
<section class="article-section">
<h2>Logic Proof Formula and Mathematical Explanation</h2>
<p>The core of a logic calculator proof isn’t a single formula in the traditional sense, but rather an algorithm that applies rules of inference to a set of propositions. The “formula” is the application of these rules within a structured system.</p>
<p><strong>Step-by-step derivation:</strong></p>
<ol>
<li><strong>Input Parsing:</strong> The system first parses the input premises and the proposed proof steps. Each statement (propositional formula) and its associated justification (rule of inference) are identified.</li>
<li><strong>Premise Validation:</strong> The initial premises are accepted as true for the purpose of the proof.</li>
<li><strong>Rule Application Check:</strong> For each subsequent step in the provided proof:
<ul>
<li>The system identifies the rule of inference claimed in the justification (e.g., Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunction Introduction, Conjunction Elimination, etc.).</li>
<li>It checks if the required preceding line(s) and their propositional forms match the rule’s antecedent.</li>
<li>It verifies if the resulting propositional form on the current line matches the rule’s consequent.</li>
<li>If the step involves logical equivalences (e.g., De Morgan’s Laws, Commutative Laws, Distributive Laws), it checks if the transformation is valid.</li>
</ul>
</li>
<li><strong>Conclusion Verification:</strong> The system checks if the final step of the proof successfully derives the stated conclusion.</li>
<li><strong>Validity Determination:</strong> If all steps are valid according to the rules of inference and the conclusion is reached, the proof is deemed valid. If any step is invalid, the proof is invalid.</li>
</ol>
<p><strong>Variable Explanations:</strong></p>
<ul>
<li><strong>Propositions (P, Q, R, …):</strong> Atomic statements that can be either true or false.</li>
<li><strong>Logical Connectives:</strong> Symbols that combine propositions (~ NOT, ^ AND, v OR, -> IMPLIES, <-> IFF).</li>
<li><strong>Rules of Inference:</strong> Valid argument forms that allow deriving new true statements from existing true statements (e.g., Modus Ponens: If P and P -> Q, then Q).</li>
<li><strong>Proof Steps:</strong> Numbered lines in a formal proof, each containing a statement and its justification.</li>
<li><strong>Justification:</strong> The rule of inference or premise number(s) used to derive a statement.</li>
</ul>
<p><strong>Variables Table:</strong></p>
<table>
<thead>
<tr>
<th>Variable</th>
<th>Meaning</th>
<th>Unit</th>
<th>Typical Range</th>
</tr>
</thead>
<tbody>
<tr>
<td>P, Q, R…</td>
<td>Atomic Propositional Variables</td>
<td>Boolean (True/False)</td>
<td>N/A</td>
</tr>
<tr>
<td>~, ^, v, ->, <-></td>
<td>Logical Connectives</td>
<td>N/A</td>
<td>N/A</td>
</tr>
<tr>
<td>Premises</td>
<td>Given true statements</td>
<td>Propositional Formula</td>
<td>1 to N</td>
</tr>
<tr>
<td>Proof Step</td>
<td>Inferred statement</td>
<td>Line Number</td>
<td>1 to M</td>
</tr>
<tr>
<td>Justification</td>
<td>Rule applied or premise cited</td>
<td>Rule Name / Line Number(s)</td>
<td>Standard Rules / Premise Indices</td>
</tr>
</tbody>
</table>
<caption>Key components of a logical proof.</caption>
</section>
<section class="article-section">
<h2>Practical Examples (Real-World Use Cases)</h2>
<p>While logic calculator proofs are abstract, their principles underpin reliable systems everywhere. Here are examples illustrating their use:</p>
<h3>Example 1: Modus Ponens in Software Logic</h3>
<p><strong>Scenario:</strong> A program needs to execute a specific function only if a user is logged in and has administrative privileges.</p>
<p><strong>Premise 1:</strong> If the user is logged in (L) AND has admin privileges (A), THEN execute admin function (E). Symbolically: <code>(L ^ A) -> E</code></p>
<p><strong>Premise 2:</strong> The user is logged in (L).</p>
<p><strong>Premise 3:</strong> The user has admin privileges (A).</p>
<p><strong>Desired Conclusion:</strong> Execute admin function (E).</p>
<p><strong>Proof Steps:</strong></p>
<ol>
<li><code>(L ^ A) -> E</code> (Premise 1)</li>
<li><code>L</code> (Premise 2)</li>
<li><code>A</code> (Premise 3)</li>
<li><code>L ^ A</code> (Conjunction Introduction 2, 3)</li>
<li><code>E</code> (Modus Ponens 1, 4)</li>
</ol>
<p><strong>Calculator Output (Simulated):</strong></p>
<ul>
<li><strong>Validity Status:</strong> Valid</li>
<li><strong>Deductive Strength:</strong> High (Conclusion necessarily follows)</li>
<li><strong>Valid Steps:</strong> 5</li>
<li><strong>Total Steps:</strong> 5</li>
</ul>
<p><strong>Interpretation:</strong> The proof confirms that the program logic correctly determines when the admin function should be executed. This is fundamental for secure and correct software operation.</p>
<h3>Example 2: Hypothetical Syllogism in Policy Making</h3>
<p><strong>Scenario:</strong> Analyzing the chain effects of potential policy decisions.</p>
<p><strong>Premise 1:</strong> If we increase funding for renewable energy (R), THEN carbon emissions will decrease (C). Symbolically: <code>R -> C</code></p>
<p><strong>Premise 2:</strong> If carbon emissions decrease (C), THEN environmental quality improves (E). Symbolically: <code>C -> E</code></p>
<p><strong>Desired Conclusion:</strong> If we increase funding for renewable energy (R), THEN environmental quality will improve (E). Symbolically: <code>R -> E</code></p>
<p><strong>Proof Steps:</strong></p>
<ol>
<li><code>R -> C</code> (Premise 1)</li>
<li><code>C -> E</code> (Premise 2)</li>
<li><code>R -> E</code> (Hypothetical Syllogism 1, 2)</li>
</ol>
<p><strong>Calculator Output (Simulated):</strong></p>
<ul>
<li><strong>Validity Status:</strong> Valid</li>
<li><strong>Deductive Strength:</strong> High</li>
<li><strong>Valid Steps:</strong> 3</li>
<li><strong>Total Steps:</strong> 3</li>
</ul>
<p><strong>Interpretation:</strong> The logic calculator confirms that the derived conclusion is a necessary consequence of the initial policy assumptions. This helps policymakers understand the direct logical implications of their decisions, ensuring that the reasoning chain is sound before implementation.</p>
</section>
<section class="article-section">
<h2>How to Use This Logic Calculator Proof</h2>
<p>Our Logic Calculator Proof tool is designed for ease of use while maintaining formal rigor. Follow these steps to verify your logical arguments:</p>
<ol>
<li><strong>Identify Premises:</strong> Clearly state all the initial statements that you assume to be true. Enter these into the “Premise 1”, “Premise 2”, etc., fields. Use standard propositional logic notation (<code>P</code>, <code>Q</code>, <code>~</code> for NOT, <code>^</code> for AND, <code>v</code> for OR, <code>-></code> for IMPLIES, <code><-></code> for IFF).</li>
<li><strong>State the Conclusion:</strong> Enter the statement you wish to prove follows from the premises into the “Conclusion” field, using the same notation.</li>
<li><strong>Construct Your Proof:</strong> In the “Proof Steps” text area, list each step of your logical deduction. Number each step. For each step, provide:
<ul>
<li>The propositional statement derived.</li>
<li>The justification, which includes the rule of inference (e.g., Modus Ponens, De Morgan’s Law) and the line number(s) from previous steps or premises it relies on. Example: <code>3. Q (Modus Ponens 1, 2)</code></li>
</ul>
</li>
<li><strong>Verify Proof:</strong> Click the “Verify Proof” button.</li>
<li><strong>Read the Results:</strong>
<ul>
<li><strong>Validity Status:</strong> Will show “Valid” if your proof correctly derives the conclusion from the premises using accepted rules, or “Invalid” otherwise.</li>
<li><strong>Deductive Strength:</strong> Indicates how necessarily the conclusion follows. Generally, for propositional logic, this will be “High” for valid proofs.</li>
<li><strong>Number of Valid Steps:</strong> Counts how many steps in your provided proof were correctly derived.</li>
<li><strong>Total Proof Steps:</strong> The total number of steps you entered.</li>
</ul>
</li>
<li><strong>Analyze the Table and Chart:</strong> The table provides a line-by-line breakdown of your proof, highlighting the status of each step. The chart visually compares valid and invalid steps. This helps pinpoint errors in your reasoning.</li>
<li><strong>Use the Copy Results Button:</strong> Click “Copy Results” to get a summary of the verification, including intermediate values and key assumptions, for documentation or sharing.</li>
<li><strong>Reset:</strong> Use the “Reset” button to clear all fields and start a new proof verification.</li>
</ol>
<p><strong>Decision-Making Guidance:</strong> If your proof is marked “Valid,” you have demonstrated that your conclusion is logically sound given your premises. If “Invalid,” review the step-by-step analysis to find where the reasoning faltered. This tool is excellent for ensuring the logical backbone of arguments in programming, mathematics, and philosophy.</p>
</section>
<section class="article-section">
<h2>Key Factors That Affect Logic Proof Results</h2>
<p>While the *validity* of a logical proof is a binary outcome (valid or invalid), several factors influence how we interpret and use these proofs, and what constitutes a “good” proof.</p>
<ul>
<li><strong>Correctness of Premises:</strong> The tool assumes premises are true. If your premises are false or poorly defined, a valid proof might lead to an unsound conclusion in the real world. The calculator verifies the *form* of the argument, not the ultimate truth of its components.</li>
<li><strong>Completeness of Ruleset:</strong> The calculator’s effectiveness depends on the set of logical rules it implements. Standard rules (Modus Ponens, Hypothetical Syllogism) are universally accepted. However, specialized logic systems might require a more extensive or tailored ruleset.</li>
<li><strong>Ambiguity in Notation:</strong> Inconsistent or ambiguous use of symbols (e.g., using ‘|’ for both OR and XOR) can lead to incorrect parsing and verification. Standardized notation is key.</li>
<li><strong>Complexity of the Argument:</strong> As the number of propositions and logical connectives increases, so does the complexity of constructing and verifying proofs. Truth tables for complex statements can become unwieldy, making automated tools invaluable.</li>
<li><strong>Formal System Choice:</strong> Different formal systems (e.g., classical logic vs. intuitionistic logic) have different rules and axioms. The calculator must be configured for the intended logical system.</li>
<li><strong>Human Error in Proof Construction:</strong> Even with a valid logical structure, typos, misapplied rules, or incorrect line references in the manual proof construction can lead to an “Invalid” result from the calculator. Careful step-by-step construction is essential.</li>
<li><strong>Interpretation of Validity vs. Soundness:</strong> A proof can be valid (conclusion follows premises) but unsound (at least one premise is false). This distinction is critical for real-world application. The calculator directly addresses validity.</li>
</ul>
</section>
<section class="article-section">
<h2>Frequently Asked Questions (FAQ)</h2>
<ul class="faq-list">
<li class="faq-item">
<h4>What is the difference between a valid proof and a sound argument?</h4>
<div class="faq-content">A proof is <strong>valid</strong> if the conclusion necessarily follows from the premises. An argument is <strong>sound</strong> if it is valid AND all of its premises are actually true. This calculator verifies validity.</div>
</li>
<li class="faq-item">
<h4>Can this calculator handle predicate logic (quantifiers like ‘for all’ and ‘there exists’)?</h4>
<div class="faq-content">This specific implementation focuses on propositional logic for clarity. Handling predicate logic requires a more complex system capable of managing variables, quantifiers, and instantiation rules.</div>
</li>
<li class="faq-item">
<h4>What are the common rules of inference supported?</h4>
<div class="faq-content">Typical rules include Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, Simplification, Conjunction Introduction, Addition, and rules for biconditionals. Logical equivalences like De Morgan’s laws are also often supported.</div>
</li>
<li class="faq-item">
<h4>How does the calculator handle complex statements with multiple connectives?</h4>
<div class="faq-content">The calculator parses complex statements based on operator precedence and parentheses. It then applies rules of inference to these complex structures or breaks them down using logical equivalences and component propositions.</div>
</li>
<li class="faq-item">
<h4>Is the result “Invalid” always my fault?</h4>
<div class="faq-content">An “Invalid” result typically means either the premises do not logically lead to the conclusion, or there’s an error in the steps provided (e.g., wrong rule applied, incorrect reference to previous lines, faulty logical transformation).</div>
</li>
<li class="faq-item">
<h4>Can I use this for everyday reasoning?</h4>
<div class="faq-content">Absolutely. While it uses formal notation, the underlying principles of valid deduction are the same as in everyday critical thinking. Understanding formal logic can sharpen your informal reasoning skills.</div>
</li>
<li class="faq-item">
<h4>What does “Deductive Strength” mean in this context?</h4>
<div class="faq-content">In classical logic, a valid deductive argument has the highest deductive strength: if the premises are true, the conclusion MUST be true. For valid proofs in this system, the strength is considered “High”.</div>
</li>
<li class="faq-item">
<h4>How can I improve my proof-writing skills?</h4>
<div class="faq-content">Practice regularly! Work through examples in logic textbooks, understand each rule of inference thoroughly, and use tools like this calculator to check your work and identify patterns in your errors. Focus on clarity and precision in your steps.</div>
</li>
</ul>
</section>
<section class="article-section related-links">
<h2>Related Tools and Internal Resources</h2>
<ul>
<li><a href="#">Truth Table Generator</a><span> – Instantly create truth tables to evaluate propositional logic statements.</span></li>
<li><a href="#">Logical Fallacy Identifier</a><span> – Learn to spot common errors in reasoning.</span></li>
<li><a href="#">Set Theory Calculator</a><span> – Explore operations and proofs within set theory.</span></li>
<li><a href="#">Formal Language Parser</a><span> – Understand the structure of defined grammars.</span></li>
<li><a href="#">Algorithm Complexity Analyzer</a><span> – Evaluate the efficiency of computational processes.</span></li>
<li><a href="#">Mathematical Proof Techniques Guide</a><span> – Deep dive into various methods of mathematical proof.</span></li>
</ul>
</section>
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<p>            // Specific check for propositions and proof steps - allow symbols and numbers
            if (elementId === 'premise1' || elementId === 'premise2' || elementId === 'conclusion' || elementId === 'proofSteps') {
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<p>        function parseLogicString(str) {
            // Simplified parser: attempts to identify basic propositions and structure
            var propositions = {};
            var symbols = str.match(/[A-Za-z]+/g);
            if (symbols) {
                for (var i = 0; i < symbols.length; i++) {
                    propositions[symbols[i]] = symbols[i]; // Map symbol to itself
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            return { structure: str, propositions: Object.keys(propositions) };
        }

// Basic rule checks (examples)
                if (ruleUsed === 'ModusPonens' || ruleUsed === 'MP') {
                    if (lineNumbers.length === 2) {
                        var line1Index = lineNumbers[0] - 1;
                        var line2Index = lineNumbers[1] - 1;
                        if (line1Index >= 0 && line2Index >= 0) {
                            var step1 = allSteps[line1Index];
                            var step2 = allSteps[line2Index];
                            if (step1 && step2) {
                                // Check if step1 is P -> Q and step2 is P
                                if (step1.statement.includes('->') && step2.statement === step1.statement.split('->')[0].trim()) {
                                    // Verify the consequent matches the current statement
                                    if (statement === step1.statement.split('->')[1].trim()) {
                                        isValid = true;
                                        dependentSteps = [lineNumbers[0], lineNumbers[1]];
                                    }
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                            }
                        }
                    }
                } else if (ruleUsed === 'ModusTollens' || ruleUsed === 'MT') {
                    // MT: If P -> Q and ~Q, then ~P
                     if (lineNumbers.length === 2) {
                        var line1Index = lineNumbers[0] - 1;
                        var line2Index = lineNumbers[1] - 1;
                        if (line1Index >= 0 && line2Index >= 0) {
                            var step1 = allSteps[line1Index];
                            var step2 = allSteps[line2Index];
                             if (step1 && step2) {
                                // Check if step1 is P -> Q and step2 is ~Q
                                if (step1.statement.includes('->') && step2.statement.startsWith('~') && step2.statement.substring(1).trim() === step1.statement.split('->')[1].trim()) {
                                    // Verify the antecedent negation matches the current statement
                                     if (statement === '~' + step1.statement.split('->')[0].trim()) {
                                        isValid = true;
                                        dependentSteps = [lineNumbers[0], lineNumbers[1]];
                                    }
                                }
                            }
                        }
                    }
                } else if (ruleUsed === 'HypotheticalSyllogism' || ruleUsed === 'HS') {
                    // HS: If P -> Q and Q -> R, then P -> R
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                        var line2Index = lineNumbers[1] - 1;
                         if (line1Index >= 0 && line2Index >= 0) {
                            var step1 = allSteps[line1Index];
                            var step2 = allSteps[line2Index];
                            if (step1 && step2) {
                                // Check if step1 is P -> Q and step2 is Q -> R
                                var p1 = step1.statement.split('->')[0].trim();
                                var q1 = step1.statement.split('->')[1].trim();
                                var q2 = step2.statement.split('->')[0].trim();
                                var r2 = step2.statement.split('->')[1].trim();</p>
<p>                                if (q1 === q2 && step1.statement.includes('->') && step2.statement.includes('->')) {
                                    // Verify the derived P -> R matches the current statement
                                    if (statement === p1 + ' -> ' + r2) {
                                        isValid = true;
                                        dependentSteps = [lineNumbers[0], lineNumbers[1]];
                                    }
                                }
                            }
                        }
                    }
                } else if (ruleUsed === 'ConjunctionIntroduction' || ruleUsed === 'ConjIntro' || ruleUsed === '^I') {
                     // ^I: If P and Q, then P ^ Q
                     if (lineNumbers.length === 2) {
                        var line1Index = lineNumbers[0] - 1;
                        var line2Index = lineNumbers[1] - 1;
                        if (line1Index >= 0 && line2Index >= 0) {
                             var step1 = allSteps[line1Index];
                             var step2 = allSteps[line2Index];
                             if (step1 && step2) {
                                 // Check if the current statement is P ^ Q, and steps 1 and 2 are P and Q (order doesn't matter for ^)
                                 if (statement.includes('^')) {
                                     var partsStatement = statement.split('^').map(function(p) { return p.trim(); });
                                     var partsStep1 = [step1.statement];
                                     var partsStep2 = [step2.statement];
                                     if ( (partsStatement.includes(partsStep1[0]) && partsStatement.includes(partsStep2[0])) ||
                                          (partsStatement.includes(partsStep1[0]) && partsStatement.includes(partsStep2[0])) ) {
                                            isValid = true;
                                             dependentSteps = [lineNumbers[0], lineNumbers[1]];
                                     }
                                 }
                             }
                        }
                     }
                } else if (ruleUsed === 'Simplification' || ruleUsed === 'Simp' || ruleUsed === '^E') {
                    // ^E: If P ^ Q, then P (or Q)
                    if (lineNumbers.length === 1) {
                        var lineIndex = lineNumbers[0] - 1;
                        if (lineIndex >= 0) {
                            var step = allSteps[lineIndex];
                            if (step && step.statement.includes('^')) {
                                var parts = step.statement.split('^').map(function(p) { return p.trim(); });
                                if (parts.length === 2) {
                                     // Check if the current statement is one of the components
                                    if (statement === parts[0] || statement === parts[1]) {
                                        isValid = true;
                                        dependentSteps = [lineNumbers[0]];
                                    }
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                } else if (ruleUsed === 'Addition' || ruleUsed === 'Add' || ruleUsed === 'vI') {
                     // vI: If P, then P v Q
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                              if (step && step.statement.includes('v')) {
                                 var parts = statement.split('v').map(function(p) { return p.trim(); });
                                 var originalStatement = step.statement;
                                 // Check if the current statement is P v Q, and step is P (or Q)
                                 if (parts.length === 2 && (parts.includes(originalStatement) || parts.includes(originalStatement)) ) {
                                      // Need a more robust check here to ensure the 'Q' part is validly introduced
                                     // For simplicity, we'll assume if step is P and statement is P v Q, it's valid if Q is also a proposition
                                     // A truly robust check would require parsing Q separately or assuming it's a valid variable.
                                     isValid = true;
                                     dependentSteps = [lineNumbers[0]];
                                 }
                             }
                         }
                     }
                }
                 // Add more rules here...
            }</p>
<p>            return {
                statement: statement,
                justification: justification,
                isValid: isValid,
                rule: ruleUsed,
                dependentSteps: dependentSteps,
                isPremise: justification.startsWith('Premise')
            };
        }</p>
<p>        function calculateProof() {
            var premise1Input = getElement('premise1');
            var premise2Input = getElement('premise2');
            var conclusionInput = getElement('conclusion');
            var proofStepsInput = getElement('proofSteps');</p>
<p>            // Basic validation (more robust checks within evaluateStep)
            if (!validateInput(premise1Input.value, 'premise1', 'Invalid premise format.')) return;
            if (!validateInput(premise2Input.value, 'premise2', 'Invalid premise format.')) return;
            if (!validateInput(conclusionInput.value, 'conclusion', 'Invalid conclusion format.')) return;
            if (!validateInput(proofStepsInput.value, 'proofSteps', 'Invalid proof step format.')) return;</p>
<p>            var premises = [];
            if (premise1Input.value.trim()) premises.push({ statement: premise1Input.value.trim(), lineNumber: 1 });
            if (premise2Input.value.trim()) premises.push({ statement: premise2Input.value.trim(), lineNumber: 2 });
            // Add more premises if needed, adjust line numbers accordingly</p>
<p>            var allStepsRaw = proofStepsInput.value.split('\n');
            var allSteps = [];
            var validStepsCount = 0;
            var invalidStepsCount = 0;
            var totalSteps = allStepsRaw.length;</p>
<p>            // Process premises first
            for (var i = 0; i < premises.length; i++) {
                var premise = premises[i];
                allSteps.push({
                    statement: premise.statement,
                    justification: 'Premise ' + premise.lineNumber,
                    isValid: true,
                    rule: 'Premise',
                    dependentSteps: [],
                    isPremise: true
                });
                 validStepsCount++;
            }

// Process provided proof steps
            for (var i = 0; i < allStepsRaw.length; i++) {
                var stepLine = allStepsRaw[i].trim();
                if (!stepLine) continue; // Skip empty lines

// Check if it's actually a premise line being re-listed in steps
                var isPremiseLine = false;
                for(var p=0; p

<td colspan="4">Proof steps will appear here.</td>
</tr>
<p>';</p>
<p>            // Clear chart
            var canvas = getElement('proofChart');
            var ctx = canvas.getContext('2d');
            ctx.clearRect(0, 0, canvas.width, canvas.height);
             if (chartInstance) {
                chartInstance.destroy();
                chartInstance = null;
            }</p>
<p>            // Clear error messages
            var errorElements = document.querySelectorAll('.error-message');
            for (var i = 0; i < errorElements.length; i++) {
                errorElements[i].style.display = 'none';
            }
        }

// Add event listener for FAQ toggles
        document.addEventListener('DOMContentLoaded', function() {
            var faqItems = document.querySelectorAll('.faq-item h4');
            for (var i = 0; i < faqItems.length; i++) {
                faqItems[i].addEventListener('click', function() {
                    var parent = this.parentElement;
                    parent.classList.toggle('open');
                    var content = parent.querySelector('.faq-content');
                    if (content.style.display === 'block') {
                        content.style.display = 'none';
                    } else {
                        content.style.display = 'block';
                    }
                });
            }
             // Initialize chart on load if needed, or var it be updated by calculateProof
             updateChart([], 0, 0); // Initial empty chart
        });

</script><br />
    <br />
    <script></script><br />
</body><br />
</html></p>
		</div>

</article>

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