Abstract syntax tree for logic expressions

Build an AST (JSON object) from a logic expression string

Input

 const logicExpression = 'a AND b OR c';

Processing

 const bracketTree = new BracketTree(logicExpression);
const logicTree = new LogicTree(bracketTree.nodes, bracketTree.text).getAst();

Output

 console.log(logicTree);
{
name: 'node0',
content: 'a AND b OR c',
orParams: [{
text: 'a AND b',
andParams: [{ name: 'a' }, { name: 'b' }]
}, {
text: 'c',
andParams: [{ name: 'c' }]
}]
}

Logical operators

• Logical negation NOT
• Logical conjunction AND
  • Logical NAND
• Logical disjunction OR
  • Logical NOR
  • Logical exclusive disjunction XOR
  • Logical equality XNOR

Logical truth table

a	b	AND	OR	NAND	NOR	XOR	XNOR
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Different syntax in programming and natural languages

Language	Negation	Conjunction	Disjunction	XOR
C++	!	&&	||	^
Fortran	.NOT.	.AND.	.OR.	.XOR.
Java	!	&&	||	^
Pascal	not	and	or	xor
PL/I	¬	&	|	^
Prolog	+	,	;
Turbo Basic	NOT	AND	OR	XOR
SQL	NOT	AND	OR
English	not	and	or	either
Russian	не	и	или	либо

https://en.wikipedia.org/wiki/Logical_connective

From boolean expression to logic tree

Input boolean expression: (true OR false) AND NOT(false) OR true OR false

1. Create a binary boolean expression tree

2. Skip logical negation operator (NOT, ~)

• A negation operator is unary. It applicable for one node only.
• Put it as a property of the corresponding node of the tree: node.isNegation = true

3. Transform all binary logical operators to basic: conjunction and disjunction

• a NAND b == NOT(A AND B)
• a XOR b == (a OR b) AND (a NAND b)
• a XNOR b == NOT(a XOR b)

4. Order of precedence (priority) for basic syntax operators

Syntax	Precedence
parenthesis	1
NOT	2
AND	3
OR	4

5. Define own relations between basic logical binary operators

• AND can contain only ORs (1 to many)
• OR can contain only ANDs (1 to many)

6. Build an abstract syntax tree, using rules above

 // input
(a OR b) AND NOT(c) OR d OR e
// output
{
name: 'node0',
content: '(a OR b) AND NOT(c) OR d OR e',
orParams: [{
text: '(a OR b) AND NOT(c)',
andParams: [{
name: 'node0',
content: 'a OR b',
orParams: [{
text: 'a',
andParams: [{ name: 'a' }]
}, {
text: 'b',
andParams: [{ name: 'b' }]
}]
}, {
name: 'c',
isNegation: true
}]
}, {
text: 'd',
andParams: [{ name: 'd' }]
}, {
text: 'e',
andParams: [{name: 'e' }]
}]
}

Where:

• nodeX - specific name for a parameter, which contains a group of other parameters, where X - order number of a node in a list of operators
• isNegation - adds Logical negation (NOT) to the corresponding parameter

7. Use this logic tree for any business purposes

• calculate a result of a logic expression: a>3 AND a<5 == false // (if a = 8)
• build a presentational string, using any syntax (SQL, JAVA, PASCAL, etc.): a AND b OR NOT c --> a && b || !c
• draw a tree diagram for any logic expression
• build a decision tree
• etc.