Description
Evaluate classical material implication for two supplied Boolean truth values.
A logical calculation operates on a stated representation: truth values, token lists, counts, or an explicitly supplied relation. Checking one assignment, pair, trace, or witness is different from proving a formula or validating an entire argument. Empty domains, duplicate tokens, and scope conventions can change the result.
Evaluate classical material implication for two supplied Boolean truth values.
When to use this tool
Use Implication Truth Gap when you need this exact local truth, count, token, relation, or witness check within a larger logic workflow.
How to use the tool and how it works
- Enter antecedent, consequent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read implication, counterexample. Inspect implication, counterexample before interpreting the associated values.
Return implication=NOT antecedent OR consequent and counterexample=antecedent AND NOT consequent.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| antecedent | Antecedent | Required. Boolean. |
| consequent | Consequent | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| implication | Implication | Required. Boolean. |
| counterexample | Counterexample | Required. Boolean. |
{
"input": {
"antecedent": true,
"consequent": false
},
"output": {
"implication": false,
"counterexample": true
}
}Limitations and assumptions
- This is the classical material-implication truth table for one assignment. A true implication at one row does not prove entailment across all assignments.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use a parser, scope-aware representation, model checker, or proof procedure when the supplied token or witness representation is insufficient. A local passing check should not be promoted to global validity.
References
Similar or alternative tools
- Alpha Equivalence Bound Variable Pair
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- Argument Assumption Scope Depth
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