Absorption Law Simplifier (P∨(P∧Q)=P)
Simplify either classical absorption-law form for two identifier atoms.
Description
Absorption removes a nested combination that adds no new truth condition to its repeated leading atom.
Absorption removes a nested combination that adds no new truth condition to its repeated leading atom. It holds with either AND outside OR or OR outside AND.1
The tool returns original, rewritten. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Absorption Law Simplifier (P∨(P∧Q)=P)
Use this for the following task: Simplify either classical absorption-law form for two identifier atoms. Prepare the specified logical encoding before running the check or transformation.
How to use Absorption Law Simplifier (P∨(P∧Q)=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 outerOperator, p, q according to the field table, then run the tool.
- Read original, rewritten. 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 |
|---|---|---|---|
| outerOperator | Outer Boolean operator | string; choices "and", "or" | Required |
| p | P | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| q | Q | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Choose the outer operation and supply atom identifiers p and q. Use the other operation inside, render the original and return p as its equivalent rewrite.
P OR (P AND Q)=P; P AND (P OR Q)=P The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| original | Original propositional formula | string (propositional-formula) |
| rewritten | Equivalent propositional formula | string (propositional-formula) |
{
"input": {
"outerOperator": "or",
"p": "p",
"q": "q"
},
"output": {
"original": "(p || (p && q))",
"rewritten": "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 Idempotence Duplicate Term Collapser Checker (P∧P=P) when you need its operation: Collapse equal identifier operands under conjunction or disjunction using idempotence. Choose Distributivity OR-over-AND Expansion Applier for the complementary operation: Distribute disjunction over conjunction for three identifier atoms.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- Idempotence Duplicate Term Collapser Checker (P∧P=P)
Collapse equal identifier operands under conjunction or disjunction using idempotence.
- Distributivity OR-over-AND Expansion Applier
Distribute disjunction over conjunction for three identifier atoms.