Description
Compose formal modus ponens, modus tollens, and hypothetical syllogism cards with fresh illustrative atoms and controlled invalid conclusions, delegating rule keys.
A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.
Compose formal modus ponens, modus tollens, and hypothetical syllogism cards with fresh illustrative atoms and controlled invalid conclusions, delegating rule keys.
When to use this tool
Use this generator to create reproducible inference rule proof cards cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply rules, count, invalidCount in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read cards. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.
Construct modus ponens, modus tollens, or hypothetical-syllogism cards using fresh symbolic atoms. Build exactly invalidCount cards with an unrelated conclusion, delegate the corresponding rule checks, and shuffle the finished cards.1
Delegated operations used for this result: modus ponens step validator; modus tollens step validator. Their calculation or parsing conventions apply to the corresponding result fields.2, 3
| Input field | Meaning and units | Accepted input |
|---|---|---|
| rules | Rules | Required. Array of Text; one of "modus-ponens", "modus-tollens", "hypothetical-syllogism".; minimum items 1; maximum items 3. |
| count | Requested count; the mechanics explain whether one draw expands into several returned records. | Required. Safe integer; minimum 1; maximum 64. |
| invalidCount | Invalid Count | Required. Safe integer; minimum 0; maximum 64. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cards | Cards | Required. Array of Object; no unknown keys.; minimum items 1; maximum items 64. |
| cards[].rule | Rule | Required. Text; one of "modus-ponens", "modus-tollens", "hypothetical-syllogism". |
| cards[].premises | Premises | Required. Array of Text; maximum UTF-16 length 100.; minimum items 2; maximum items 2. |
| cards[].conclusion | Conclusion | Required. Text; maximum UTF-16 length 100. |
| cards[].matchesRule | Matches Rule | Required. Boolean. |
| randomness | Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional numeric replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"rules": [
"modus-ponens",
"modus-tollens",
"hypothetical-syllogism"
],
"count": 2,
"invalidCount": 1,
"seed": 42
},
"output": {
"cards": [
{
"rule": "modus-tollens",
"premises": [
"(p1 -> q1)",
"!q1"
],
"conclusion": "!x1",
"matchesRule": false
},
{
"rule": "modus-tollens",
"premises": [
"(p2 -> q2)",
"!q2"
],
"conclusion": "!p2",
"matchesRule": true
}
],
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- This tests one selected inference pattern rather than arbitrary validity or a complete proof. invalidCount cannot exceed count and answer-bearing validation should be separated from student prompts.
- A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
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