Odonto logic

Converting logic expressed in formal or tabular forms into JavaScript involves mapping the logical conditions and outcomes into code using conditional statements, loops, and functions. I’ll break this down using common logic representations such as truth tables, if-then logic, and matrix representations.

Example 1: Truth Table Logic to JavaScript

A truth table expresses the outcomes of logical operators (AND, OR, NOT, etc.) for every possible input combination. You can convert this into JavaScript using if, else if, and else statements.

Example Truth Table

This table can be described as a logical AND, where both inputs A and B need to be 1 for the output to be 1.

```JavaScript Code

function logicAND(a, b) { if (a === 1 && b === 1) { return 1; // Output is 1 when both A and B are 1 } else { return 0; // Output is 0 in all other cases } }

// Test console.log(logicAND(1, 1)); // Outputs 1 console.log(logicAND(1, 0)); // Outputs 0

Example 2: Conditional Logic (If-Then Rules)

In formal logic (if-then rules), you can represent statements like:

If A is true, then do X.

If B is true, then do Y.


This is straightforward to translate into JavaScript using conditional statements.

Example Rule:

If the temperature is greater than 30°C, then turn on the fan.

If the temperature is less than 10°C, then turn on the heater.



```JavaScript Code

function controlTemperature(temp) {
    if (temp > 30) {
        return 'Turn on the fan';
    } else if (temp < 10) {
        return 'Turn on the heater';
    } else {
        return 'Temperature is normal';
    }
}

// Test
console.log(controlTemperature(35)); // Outputs: Turn on the fan
console.log(controlTemperature(5));  // Outputs: Turn on the heater

Example 3: Matrix Representation to JavaScript

A matrix form often represents data in grids (or arrays). In JavaScript, you can use nested arrays (or 2D arrays) to represent such matrices. Operations on matrices (like accessing elements, summing rows/columns) can be done using loops.

Example Matrix:

Matrix form for caries diagnosis: | Location | Probe | Diagnosis | |-------------|-------------|---------------| | Cervical | Chalky | Restoration | | Cervical | Grossly | Extraction | | Proximal | Chalky | Restoration |

```JavaScript Matrix Representation:

const cariesDiagnosis = [ { location: 'Cervical', probe: 'Chalky', diagnosis: 'Restoration' }, { location: 'Cervical', probe: 'Grossly', diagnosis: 'Extraction' }, { location: 'Proximal', probe: 'Chalky', diagnosis: 'Restoration' } ];

// Test console.log(getDiagnosis('Cervical', 'Chalky')); // Outputs: Restoration console.log(getDiagnosis('Cervical', 'Grossly')); // Outputs: Extraction

Example 4: Converting Formal Logic Symbols to JavaScript

If you have formal logic representations with operators like ∧ (AND), ∨ (OR), or ¬ (NOT), you can map these to JavaScript as follows:

Example:

If A ∧ B → C, it means "if both A and B are true, then C is true."

```js
function implies(a, b) {
    if (a && b) {
        return true;  // A ∧ B → C
    } else {
        return false;
    }
}

// Test
console.log(implies(true, true));  // Outputs true
console.log(implies(true, false)); // Outputs false

Example 5: Complex Table with Multiple Conditions

Let’s take a more complex table and convert it to code.

```JavaScript Code

// Test console.log(complexLogic(true, false, true)); // Outputs: X console.log(complexLogic(false, true, true)); // Outputs: Y

``` Summary of Conversions:

Tables/Matrix: Can be translated into arrays or objects with lookup functions.

Truth Tables: Translate using if, else if, else, and logical operators like &&, ||, !.

Formal Logic (if-then): Use conditional (if) statements in JavaScript to implement logical implications.

By structuring your formal or tabular logic into conditions and using arrays or objects, you can directly convert formal representations into JavaScript code.