Boolean Logic

TRUE and FALSE values are combined using the operators AND, OR, NOT, and IMPLIES.

Example: XOR Function

§ xor

GIVEN x IS A BOOLEAN, y IS A BOOLEAN
GIVETH A BOOLEAN
DECIDE xor x y IS
     x AND NOT y
  OR NOT x AND y

Inert Elements: Grammatical Scaffolding

Legal documents often contain phrases that provide context or readability but don't affect the logical outcome. L4 supports inert elements—bare string literals in boolean context that serve as grammatical scaffolding.

How Inert Elements Work

When a string literal (in double quotes) appears as a direct operand of AND or OR, it becomes an inert element with context-aware evaluation:

• In AND context: Evaluates to TRUE (the identity for AND)

• In OR context: Evaluates to FALSE (the identity for OR)

This follows the mathematical principle of monoid identities: the value that, when combined with any other value using the operation, returns that other value unchanged.

Example: Contract Validity

GIVEN `parties have capacity` IS A BOOLEAN
      `consideration present` IS A BOOLEAN
DECIDE `contract valid` IF
        "notwithstanding any provision to the contrary"
    AND `parties have capacity`
    AND `consideration present`

The string "notwithstanding any provision to the contrary" evaluates to TRUE in this AND chain, so the result depends only on the actual boolean parameters.

Example: Legal Conditions with OR

GIVEN `is over 21` IS A BOOLEAN
      `is married` IS A BOOLEAN
      `has parental consent` IS A BOOLEAN
DECIDE `person qualifies` IF
        "whether in sickness or in health"
    ... `is over 21`
    AND     `is married`
        OR  `has parental consent`
        OR  "or any other qualifying circumstance"

Here:

• "whether in sickness or in health" is in AND context → evaluates to TRUE

• "or any other qualifying circumstance" is in OR context → evaluates to FALSE

The inert strings don't change the logical outcome but make the rule more readable and closer to natural legal language.

Asyndetic Conjunction (...)

L4 supports asyndetic conjunction—continuing an AND chain without repeating the conjunction keyword. The ellipsis (...) is the syntax for this feature; asyndetic conjunction is the semantics (what it means).

An asyndeton is a rhetorical device where conjunctions are deliberately omitted, as in "I came, I saw, I conquered" (instead of "I came and I saw and I conquered").

DECIDE `rule applies` IF
        "subject to the following conditions"
    ... `condition one`
    ... `condition two`
    AND `condition three`

This is equivalent to:

DECIDE `rule applies` IF
        "subject to the following conditions"
    AND `condition one`
    AND `condition two`
    AND `condition three`

Real-World Example: Singapore Penal Code Section 415

The inert elements feature enables direct encoding of complex legal structures like criminal statutes:

GIVEN `deceives` IS A BOOLEAN
      `fraudulent` IS A BOOLEAN
      `dishonest` IS A BOOLEAN
      `delivers` IS A BOOLEAN
DECIDE `commits cheating` IF
    "by deceiving any person"
    ... `deceives`
    AND "and"
    AND     "fraudulently or dishonestly induces"
            ... `fraudulent`
            OR  `dishonest`
        ... "the person so deceived to"
        AND `delivers`

The strings like "by deceiving any person" and "the person so deceived to" preserve the original statutory language while the boolean parameters (deceives, fraudulent, etc.) carry the actual logical content.

When to Use Inert Elements

Use inert elements when you want to:

1. Preserve original legal language - Keep statutory or contractual phrases visible in the formalization

2. Improve readability - Add context that helps readers understand the rule's purpose

3. Document intent - Leave markers indicating where certain conditions belong, even if not yet fully specified

4. Create isomorphic representations - Make L4 code that closely mirrors the structure of the source legal document

Asyndetic Disjunction (..)

For symmetry, L4 also supports asyndetic disjunction—implicit OR using the two-dot ellipsis (..):

DECIDE `qualifies` IF
        `has license`
    ..  `has permit`
    OR  `has exemption`

This is equivalent to:

DECIDE `qualifies` IF
        `has license`
    OR  `has permit`
    OR  `has exemption`

Syntax	Name	Semantics
...	Three-dot ellipsis	Asyndetic conjunction (implicit AND)
..	Two-dot ellipsis	Asyndetic disjunction (implicit OR)

Important Notes

• Inert elements only work in boolean context (direct operands of AND/OR)

• A bare string in non-boolean context (e.g., in an EQUALS comparison) remains a string

• Use ... (three dots) for AND continuation, .. (two dots) for OR continuation