Idempotence Duplicate Term Collapser Checker (P∧P=P)
Collapse equal identifier operands under conjunction or disjunction using idempotence.
Description
Idempotence collapses an operand combined with itself under AND or OR.
Idempotence collapses an operand combined with itself under AND or OR. Different atom names do not qualify for this syntactic simplification.1
The tool returns applicable, simplified. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Idempotence Duplicate Term Collapser Checker (P∧P=P)
Use this for the following task: Collapse equal identifier operands under conjunction or disjunction using idempotence. Prepare the specified logical encoding before running the check or transformation.
How to use Idempotence Duplicate Term Collapser Checker (P∧P=P) and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter operator, left, right according to the field table, then run the tool.
- Read applicable, simplified. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| operator | Boolean operator | string; choices "and", "or" | Required |
| left | Left | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| right | Right | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Choose and or or and enter two identifiers. If they match exactly, return applicable=true and that identifier; otherwise render the original binary expression.
P AND P = P; P OR P = P The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| applicable | Idempotence applies | boolean |
| simplified | Resulting propositional formula | string (propositional-formula) |
{
"input": {
"operator": "and",
"left": "p",
"right": "p"
},
"output": {
"applicable": true,
"simplified": "p"
}
}Limitations and assumptions
Operands are case-sensitive identifier atoms, not complete expressions. The tool does not parse a proof or determine whether the premises are true.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Absorption Law Simplifier (P∨(P∧Q)=P) when you need its operation: Simplify either classical absorption-law form for two identifier atoms. Choose Complement Law Contradiction Tautology Pair Checker for the complementary operation: Check for complementary signed identifier literals and apply their conjunction or disjunction law.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- Absorption Law Simplifier (P∨(P∧Q)=P)
Simplify either classical absorption-law form for two identifier atoms.
- Complement Law Contradiction Tautology Pair Checker
Check for complementary signed identifier literals and apply their conjunction or disjunction law.