Description
Classical material implication for one supplied truth assignment.
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.
Classical material implication for one supplied truth assignment.
When to use this tool
Use Propositional Conditional Counterexample Row 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 conditional, counterexample. Inspect conditional, counterexample before interpreting the associated values.
Return conditional=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 |
|---|---|---|
| conditional | Conditional | Required. Boolean. |
| counterexample | Counterexample | Required. Boolean. |
{
"input": {
"antecedent": true,
"consequent": false
},
"output": {
"conditional": false,
"counterexample": true
}
}Limitations and assumptions
- This is material implication for one classical Boolean assignment, not causal implication, relevance, or a proof that an arbitrary argument is valid.
- 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
- Implication Truth Gap
Evaluate classical material implication for two supplied Boolean truth values.
- Argument Validity Countermodel One Assignment
Identify a countermodel in one assignment; a non-countermodel does not establish global argument validity.