Datasets:
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Premises:
1. Ugo's alloy is fed by meltwater.
2. If a alloy is signed off by two inspectors, then it is kept under vacuum.
3. If a alloy is not logged in the registry, then it is not tuned to concert pitch.
4. If a alloy is not repainted each spring, then it is not kept under vacuum.
The claimed step does not yet foll... | The premises carry this alloy as far as fed by meltwater but nothing takes fed by meltwater on to signed off by two inspectors, so the chain to repainted each spring is broken at exactly one place. Supplying that link lets every conditional fire in order from fed by meltwater to repainted each spring.
Missing premise:... | null | null |
Premises:
1. If a whale is sealed against salt water, then it is graded for export.
2. Baruch's whale is sealed against salt water.
3. If a whale is not kept under vacuum, then it is not rated for deep pressure.
4. If a whale is logged in the registry, then it is load-bearing.
5. If a whale is graded for export, then i... | The premises carry this whale as far as load-bearing but nothing takes load-bearing on to measured at dawn, so the chain to measured at dawn is broken at exactly one place. Supplying that link lets every conditional fire in order from sealed against salt water to measured at dawn.
Missing premise: if a whale is load-b... | null | null |
Premises:
1. Wale's submarine is rated for deep pressure.
2. If a submarine is not wound by hand, then it is not rated for deep pressure.
3. If a submarine is sealed against salt water, then it is fed by meltwater.
4. If a submarine is not sealed against salt water, then it is not signed off by two inspectors.
5. If a ... | The premises carry this submarine as far as wound by hand but nothing takes wound by hand on to signed off by two inspectors, so the chain to fed by meltwater is broken at exactly one place. Supplying that link lets every conditional fire in order from rated for deep pressure to fed by meltwater.
Missing premise: if a... | null | null |
Premises:
1. If a whale is sealed against salt water, then it is measured at dawn.
2. If a whale is measured at dawn, then it is rated for deep pressure.
3. If a whale is fired above 1200 degrees, then it is rebuilt after the flood.
4. If a whale is not sealed against salt water, then it is not warm-blooded.
5. If a wh... | The conditionals compose into a single chain from repainted each spring through to rated for deep pressure, and the fact supplies repainted each spring for this whale, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link... | null | null |
Premises:
1. Keiko's violin is stamped with a serial number.
2. If a violin is stamped with a serial number, then it is repainted each spring.
3. If a violin is sealed against salt water, then it is magnetically shielded.
The claimed step does not yet follow: exactly one premise is missing. State the single premise th... | The premises carry this violin as far as repainted each spring but nothing takes repainted each spring on to sealed against salt water, so the chain to magnetically shielded is broken at exactly one place. Supplying that link lets every conditional fire in order from stamped with a serial number to magnetically shielde... | null | null |
Premises:
1. If a comet is not stored below freezing, then it is not rebuilt after the flood.
2. Ugo's comet is traced to a single quarry.
3. If a comet is rated for deep pressure, then it is rebuilt after the flood.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that wo... | The premises carry this comet as far as traced to a single quarry but nothing takes traced to a single quarry on to rated for deep pressure, so the chain to stored below freezing is broken at exactly one place. Supplying that link lets every conditional fire in order from traced to a single quarry to stored below freez... | null | null |
Premises:
1. If a loom is grown in shade, then it is load-bearing.
2. If a loom is warm-blooded, then it is sealed against salt water.
3. If a loom is measured at dawn, then it is grown in shade.
4. Esi's loom is measured at dawn.
5. If a loom is audited annually, then it is fired above 1200 degrees.
The claimed step ... | The premises carry this loom as far as load-bearing but nothing takes load-bearing on to audited annually, so the chain to fired above 1200 degrees is broken at exactly one place. Supplying that link lets every conditional fire in order from measured at dawn to fired above 1200 degrees.
Missing premise: if a loom is l... | null | null |
Premises:
1. Baruch's alloy is repainted each spring.
2. If a alloy is audited annually, then it is sealed against salt water.
3. If a alloy is sealed against salt water, then it is stamped with a serial number.
4. If a alloy is not audited annually, then it is not repainted each spring.
Does the claimed step follow f... | The conditionals compose into a single chain from repainted each spring through to stamped with a serial number, and the fact supplies repainted each spring for this alloy, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a... | null | null |
Premises:
1. Tomas's vault is fed by meltwater.
2. If a vault is fed by meltwater, then it is traced to a single quarry.
3. If a vault is traced to a single quarry, then it is signed off by two inspectors.
4. If a vault is grown in shade, then it is repainted each spring.
5. If a vault is signed off by two inspectors, ... | Steps 1 to 3 apply the chain forwards by modus ponens, which is sound. Step 4 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 4. | null | null |
Premises:
1. If a sundial is checked for hairline cracks, then it is grown in shade.
2. Baruch's sundial is checked for hairline cracks.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Baruch's sundial is grown in shade. | The conditional's antecedent is asserted, so its consequent follows. That is modus ponens.
Rule: modus ponens (the step is valid). | null | null |
Premises:
1. If a sundial is rated for deep pressure, then it is rebuilt after the flood.
2. If a sundial is tuned to concert pitch, then it is grown in shade.
3. If a sundial is not measured at dawn, then it is not rebuilt after the flood.
4. Yusuf's sundial is magnetically shielded.
The claimed step does not yet fol... | The premises carry this sundial as far as magnetically shielded but nothing takes magnetically shielded on to rated for deep pressure, so the chain to measured at dawn is broken at exactly one place. Supplying that link lets every conditional fire in order from magnetically shielded to measured at dawn.
Missing premis... | null | null |
Premises:
1. If a submarine is tuned to concert pitch, then it is stored below freezing.
2. Mateo's submarine is not tuned to concert pitch.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Mateo's submarine is not stored below freezing. | Being tuned to concert pitch is sufficient for stored below freezing, not necessary, so denying it settles nothing. That is denying the antecedent.
Rule: denying the antecedent (the step is invalid). | null | null |
Premises:
1. If a lighthouse is not fed by meltwater, then it is not fired above 1200 degrees.
2. Quinn's lighthouse is fired above 1200 degrees.
3. If a lighthouse is fed by meltwater, then it is tuned to concert pitch.
4. If a lighthouse is not stamped with a serial number, then it is not tuned to concert pitch.
Doe... | The conditionals compose into a single chain from fired above 1200 degrees through to stamped with a serial number, and the fact supplies fired above 1200 degrees for this lighthouse, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still ... | null | null |
Premises:
1. All submarines are audited annually.
2. All looms are audited annually.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, every loom is a submarine. | Sharing the property audited annually does not nest one class in the other. That is an undistributed middle.
Rule: undistributed middle (the step is invalid). | null | null |
Premises:
1. Wale's barge is traced to a single quarry.
2. If a barge is not insured against flood, then it is not load-bearing.
3. If a barge is not load-bearing, then it is not traced to a single quarry.
4. If a barge is rated for deep pressure, then it is tuned to concert pitch.
5. If a barge is not mapped by survey... | The premises carry this barge as far as insured against flood but nothing takes insured against flood on to rated for deep pressure, so the chain to tuned to concert pitch is broken at exactly one place. Supplying that link lets every conditional fire in order from traced to a single quarry to tuned to concert pitch.
... | null | null |
Premises:
1. If a monsoon is load-bearing, then it is grown in shade.
2. If a monsoon is grown in shade, then it is measured at dawn.
3. If a monsoon is rated for deep pressure, then it is repainted each spring.
4. Hoang's monsoon is rebuilt after the flood.
The claimed step does not yet follow: exactly one premise is... | The premises carry this monsoon as far as rebuilt after the flood but nothing takes rebuilt after the flood on to load-bearing, so the chain to measured at dawn is broken at exactly one place. Supplying that link lets every conditional fire in order from rebuilt after the flood to measured at dawn.
Missing premise: if... | null | null |
Premises:
1. If a submarine is checked for hairline cracks, then it is rated for deep pressure.
2. If a submarine is rated for deep pressure, then it is traced to a single quarry.
3. If a submarine is tuned to concert pitch, then it is checked for hairline cracks.
4. Rafa's submarine is repainted each spring.
5. If a s... | Steps 1 to 3 apply the chain forwards by modus ponens, which is sound. Step 4 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 4. | null | null |
Premises:
1. If a sundial is stamped with a serial number, then it is traced to a single quarry.
2. If a sundial is traced to a single quarry, then it is logged in the registry.
3. Yusuf's sundial is checked for hairline cracks.
4. If a sundial is checked for hairline cracks, then it is stamped with a serial number.
5.... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. Sofia's orchid is stored below freezing.
2. If a orchid is not checked for hairline cracks, then it is not fired above 1200 degrees.
3. If a orchid is stored below freezing, then it is fired above 1200 degrees.
4. If a orchid is checked for hairline cracks, then it is kept under vacuum.
Does the claimed s... | The conditionals compose into a single chain from stored below freezing through to kept under vacuum, and the fact supplies stored below freezing for this orchid, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Ve... | null | null |
Premises:
1. All mammals are fired above 1200 degrees.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, everything that is fired above 1200 degrees is a mammal. | A universal claim does not convert; things can be fired above 1200 degrees without being mammals. That is illicit conversion.
Rule: illicit conversion (the step is invalid). | null | null |
Premises:
1. If a fern is stamped with a serial number, then it is tuned to concert pitch.
2. Priya's fern is stamped with a serial number.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Priya's fern is tuned to concert pitch. | The conditional's antecedent is asserted, so its consequent follows. That is modus ponens.
Rule: modus ponens (the step is valid). | null | null |
Premises:
1. If a sparrow is not insured against flood, then it is not logged in the registry.
2. Priya's sparrow is checked for hairline cracks.
3. If a sparrow is checked for hairline cracks, then it is stored below freezing.
4. If a sparrow is stored below freezing, then it is tuned to concert pitch.
The claimed st... | The premises carry this sparrow as far as tuned to concert pitch but nothing takes tuned to concert pitch on to logged in the registry, so the chain to insured against flood is broken at exactly one place. Supplying that link lets every conditional fire in order from checked for hairline cracks to insured against flood... | null | null |
Premises:
1. If a orchid is audited annually, then it is measured at dawn.
2. If a orchid is rated for deep pressure, then it is tuned to concert pitch.
3. Tomas's orchid is magnetically shielded.
4. If a orchid is magnetically shielded, then it is audited annually.
5. If a orchid is measured at dawn, then it is rated ... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. If a orchid is fed by meltwater, then it is audited annually.
2. Vera's orchid is fed by meltwater.
3. If a orchid is audited annually, then it is stamped with a serial number.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would make it follow, and say... | The premises carry this orchid as far as stamped with a serial number but nothing takes stamped with a serial number on to graded for export, so the chain to graded for export is broken at exactly one place. Supplying that link lets every conditional fire in order from fed by meltwater to graded for export.
Missing pr... | null | null |
Premises:
1. Lucia's lighthouse is load-bearing.
2. If a lighthouse is fired above 1200 degrees, then it is insured against flood.
3. If a lighthouse is measured at dawn, then it is logged in the registry.
4. If a lighthouse is load-bearing, then it is measured at dawn.
5. If a lighthouse is logged in the registry, the... | Steps 1 to 3 apply the chain forwards by modus ponens, which is sound. Step 4 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 4. | null | null |
Premises:
1. If a submarine is not rebuilt after the flood, then it is not grown in shade.
2. Yusuf's submarine is rated for deep pressure.
3. If a submarine is fired above 1200 degrees, then it is stored below freezing.
4. If a submarine is kept under vacuum, then it is checked for hairline cracks.
5. If a submarine i... | The conditionals compose into a single chain from rated for deep pressure through to rebuilt after the flood, and the fact supplies rated for deep pressure for this submarine, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts a... | null | null |
Premises:
1. Tomas's granite is stored below freezing.
2. If a granite is not grown in shade, then it is not repainted each spring.
3. If a granite is not tuned to concert pitch, then it is not insured against flood.
4. If a granite is not rated for deep pressure, then it is not warm-blooded.
5. If a granite is rated f... | The premises drive this granite towards rebuilt after the flood, not away from it. Nothing in them denies rebuilt after the flood, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. If a vault is not signed off by two inspectors, then it is not warm-blooded.
2. If a vault is checked for hairline cracks, then it is kept under vacuum.
3. If a vault is not checked for hairline cracks, then it is not mapped by survey.
4. If a vault is not mapped by survey, then it is not load-bearing.
5. ... | The premises drive this vault towards kept under vacuum, not away from it. Nothing in them denies kept under vacuum, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. If a kite is graded for export, then it is measured at dawn.
2. If a kite is not insured against flood, then it is not rated for deep pressure.
3. If a kite is not sealed against salt water, then it is not stamped with a serial number.
4. If a kite is not stamped with a serial number, then it is not repain... | The conditionals compose into a single chain from repainted each spring through to measured at dawn, and the fact supplies repainted each spring for this kite, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verdi... | null | null |
Premises:
1. All mammals are measured at dawn.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, everything that is measured at dawn is a mammal. | A universal claim does not convert; things can be measured at dawn without being mammals. That is illicit conversion.
Rule: illicit conversion (the step is invalid). | null | null |
Premises:
1. If a turbine is warm-blooded, then it is fed by meltwater.
2. If a turbine is not warm-blooded, then it is not mapped by survey.
3. Keiko's turbine is mapped by survey.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would make it follow, and say why the... | The premises carry this turbine as far as fed by meltwater but nothing takes fed by meltwater on to signed off by two inspectors, so the chain to signed off by two inspectors is broken at exactly one place. Supplying that link lets every conditional fire in order from mapped by survey to signed off by two inspectors.
... | null | null |
Premises:
1. Omar's beetle is stored below freezing.
2. If a beetle is stored below freezing, then it is fired above 1200 degrees.
3. If a beetle is fired above 1200 degrees, then it is repainted each spring.
4. If a beetle is graded for export, then it is sealed against salt water.
5. If a beetle is not checked for ha... | The premises drive this beetle towards checked for hairline cracks, not away from it. Nothing in them denies checked for hairline cracks, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. Hoang's glacier is tuned to concert pitch.
2. If a glacier is tuned to concert pitch, then it is wound by hand.
3. If a glacier is measured at dawn, then it is load-bearing.
4. If a glacier is traced to a single quarry, then it is stamped with a serial number.
5. If a glacier is not traced to a single quar... | This runs the chain backwards, which affirms the consequent. The premises only say that being tuned to concert pitch forces stamped with a serial number; something can be stamped with a serial number by another route, so nothing follows about it being tuned to concert pitch.
Verdict: the step is invalid. | null | null |
Premises:
1. If a kite is stamped with a serial number, then it is fired above 1200 degrees.
2. If a kite is fired above 1200 degrees, then it is sealed against salt water.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, if a kite is sta... | Two conditionals share a middle term and compose into one. That is a hypothetical syllogism.
Rule: hypothetical syllogism (the step is valid). | null | null |
Premises:
1. If a monsoon is rebuilt after the flood, then it is warm-blooded.
2. Ugo's monsoon is rebuilt after the flood.
3. If a monsoon is warm-blooded, then it is insured against flood.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would make it follow, and sa... | The premises carry this monsoon as far as insured against flood but nothing takes insured against flood on to wound by hand, so the chain to wound by hand is broken at exactly one place. Supplying that link lets every conditional fire in order from rebuilt after the flood to wound by hand.
Missing premise: if a monsoo... | null | null |
Premises:
1. If a nebula is fired above 1200 degrees, then it is rated for deep pressure.
2. If a nebula is not fired above 1200 degrees, then it is not tuned to concert pitch.
3. Omar's nebula is graded for export.
4. If a nebula is graded for export, then it is tuned to concert pitch.
5. If a nebula is kept under vac... | The conditionals compose into a single chain from graded for export through to rated for deep pressure, and the fact supplies graded for export for this nebula, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verd... | null | null |
Premises:
1. Farid's aqueduct is signed off by two inspectors.
2. If a aqueduct is kept under vacuum, then it is measured at dawn.
3. If a aqueduct is audited annually, then it is checked for hairline cracks.
4. If a aqueduct is signed off by two inspectors, then it is kept under vacuum.
5. If a aqueduct is measured at... | The conditionals compose into a single chain from signed off by two inspectors through to fired above 1200 degrees, and the fact supplies signed off by two inspectors for this aqueduct, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it stil... | null | null |
Premises:
1. Either Ada's ledger is signed off by two inspectors or it is insured against flood.
2. Ada's ledger is not signed off by two inspectors.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Ada's ledger is insured against flood. | One disjunct is ruled out, leaving the other. That is a disjunctive syllogism.
Rule: disjunctive syllogism (the step is valid). | null | null |
Premises:
1. If a submarine is warm-blooded, then it is graded for export.
2. If a submarine is fed by meltwater, then it is rebuilt after the flood.
3. If a submarine is load-bearing, then it is fed by meltwater.
4. Ugo's submarine is insured against flood.
5. If a submarine is magnetically shielded, then it is load-b... | The premises carry this submarine as far as insured against flood but nothing takes insured against flood on to magnetically shielded, so the chain to rebuilt after the flood is broken at exactly one place. Supplying that link lets every conditional fire in order from insured against flood to rebuilt after the flood.
... | null | null |
Premises:
1. If a mammal is stored below freezing, then it is kept under vacuum.
2. Nadia's mammal is stored below freezing.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Nadia's mammal is kept under vacuum. | The conditional's antecedent is asserted, so its consequent follows. That is modus ponens.
Rule: modus ponens (the step is valid). | null | null |
Premises:
1. If a sundial is fed by meltwater, then it is audited annually.
2. Celia's sundial is fed by meltwater.
3. If a sundial is not warm-blooded, then it is not audited annually.
4. If a sundial is warm-blooded, then it is signed off by two inspectors.
Does the claimed step follow from the premises by deductive... | The premises drive this sundial towards signed off by two inspectors, not away from it. Nothing in them denies signed off by two inspectors, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. If a whale is magnetically shielded, then it is traced to a single quarry.
2. If a whale is not rebuilt after the flood, then it is not traced to a single quarry.
3. If a whale is graded for export, then it is mapped by survey.
4. If a whale is kept under vacuum, then it is magnetically shielded.
5. Dmitri... | The premises carry this whale as far as wound by hand but nothing takes wound by hand on to kept under vacuum, so the chain to rebuilt after the flood is broken at exactly one place. Supplying that link lets every conditional fire in order from wound by hand to rebuilt after the flood.
Missing premise: if a whale is w... | null | null |
Premises:
1. Keiko's glacier is insured against flood.
2. If a glacier is not fired above 1200 degrees, then it is not grown in shade.
3. If a glacier is fired above 1200 degrees, then it is rebuilt after the flood.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that wou... | The premises carry this glacier as far as insured against flood but nothing takes insured against flood on to grown in shade, so the chain to rebuilt after the flood is broken at exactly one place. Supplying that link lets every conditional fire in order from insured against flood to rebuilt after the flood.
Missing p... | null | null |
Premises:
1. Vera's orchid is fired above 1200 degrees.
2. If a orchid is not stored below freezing, then it is not audited annually.
3. If a orchid is fired above 1200 degrees, then it is audited annually.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would make i... | The premises carry this orchid as far as stored below freezing but nothing takes stored below freezing on to checked for hairline cracks, so the chain to checked for hairline cracks is broken at exactly one place. Supplying that link lets every conditional fire in order from fired above 1200 degrees to checked for hair... | null | null |
Premises:
1. If a barge is not rated for deep pressure, then it is not measured at dawn.
2. If a barge is not graded for export, then it is not repainted each spring.
3. Keiko's barge is repainted each spring.
4. If a barge is not signed off by two inspectors, then it is not graded for export.
5. If a barge is signed o... | The conditionals compose into a single chain from repainted each spring through to kept under vacuum, and the fact supplies repainted each spring for this barge, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Ver... | null | null |
Premises:
1. If a orchid is warm-blooded, then it is traced to a single quarry.
2. If a orchid is not measured at dawn, then it is not kept under vacuum.
3. If a orchid is not rated for deep pressure, then it is not traced to a single quarry.
4. Hoang's orchid is warm-blooded.
5. If a orchid is repainted each spring, t... | The chain is interrupted: no premise carries rated for deep pressure to kept under vacuum, and the spare conditionals join properties that are not on the chain, so the derivation stops before measured at dawn and the conclusion does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. If a beetle is not fired above 1200 degrees, then it is not fed by meltwater.
2. If a beetle is grown in shade, then it is kept under vacuum.
3. Keiko's beetle is fed by meltwater.
4. If a beetle is not repainted each spring, then it is not audited annually.
The claimed step does not yet follow: exactly o... | The premises carry this beetle as far as fired above 1200 degrees but nothing takes fired above 1200 degrees on to grown in shade, so the chain to kept under vacuum is broken at exactly one place. Supplying that link lets every conditional fire in order from fed by meltwater to kept under vacuum.
Missing premise: if a... | null | null |
Premises:
1. If a fern is audited annually, then it is graded for export.
2. Ines's fern is audited annually.
3. If a fern is rebuilt after the flood, then it is signed off by two inspectors.
4. If a fern is signed off by two inspectors, then it is sealed against salt water.
5. If a fern is graded for export, then it i... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. All comets are warm-blooded.
2. All looms are warm-blooded.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, every loom is a comet. | Sharing the property warm-blooded does not nest one class in the other. That is an undistributed middle.
Rule: undistributed middle (the step is invalid). | null | null |
Premises:
1. Celia's sundial is magnetically shielded.
2. If a sundial is magnetically shielded, then it is repainted each spring.
3. If a sundial is stamped with a serial number, then it is fed by meltwater.
4. If a sundial is repainted each spring, then it is rebuilt after the flood.
5. If a sundial is rebuilt after ... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. If a alloy is magnetically shielded, then it is graded for export.
2. If a alloy is not traced to a single quarry, then it is not measured at dawn.
3. Keiko's alloy is sealed against salt water.
4. If a alloy is not tuned to concert pitch, then it is not wound by hand.
5. If a alloy is sealed against salt ... | The premises carry this alloy as far as tuned to concert pitch but nothing takes tuned to concert pitch on to magnetically shielded, so the chain to graded for export is broken at exactly one place. Supplying that link lets every conditional fire in order from sealed against salt water to graded for export.
Missing pr... | null | null |
Premises:
1. Rafa's submarine is kept under vacuum.
2. If a submarine is magnetically shielded, then it is mapped by survey.
3. If a submarine is kept under vacuum, then it is stamped with a serial number.
4. If a submarine is stamped with a serial number, then it is magnetically shielded.
5. If a submarine is mapped b... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. Esi's aqueduct is signed off by two inspectors.
2. If a aqueduct is rebuilt after the flood, then it is traced to a single quarry.
3. If a aqueduct is measured at dawn, then it is rebuilt after the flood.
4. If a aqueduct is not measured at dawn, then it is not signed off by two inspectors.
Does the claim... | The conditionals compose into a single chain from signed off by two inspectors through to traced to a single quarry, and the fact supplies signed off by two inspectors for this aqueduct, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it sti... | null | null |
Premises:
1. Either Sofia's fern is fired above 1200 degrees or it is stamped with a serial number.
2. Sofia's fern is not fired above 1200 degrees.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Sofia's fern is stamped with a serial nu... | One disjunct is ruled out, leaving the other. That is a disjunctive syllogism.
Rule: disjunctive syllogism (the step is valid). | null | null |
Premises:
1. Tomas's beetle is rebuilt after the flood.
2. If a beetle is repainted each spring, then it is rated for deep pressure.
3. If a beetle is rebuilt after the flood, then it is load-bearing.
4. If a beetle is load-bearing, then it is signed off by two inspectors.
Does the claimed step follow from the premise... | The chain is interrupted: no premise carries signed off by two inspectors to checked for hairline cracks, and the spare conditionals join properties that are not on the chain, so the derivation stops before checked for hairline cracks and the conclusion does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. If a aqueduct is not magnetically shielded, then it is not repainted each spring.
2. If a aqueduct is not kept under vacuum, then it is not warm-blooded.
3. If a aqueduct is measured at dawn, then it is mapped by survey.
4. Vera's aqueduct is fed by meltwater.
5. If a aqueduct is fed by meltwater, then it ... | The chain is interrupted: no premise carries kept under vacuum to insured against flood, and the spare conditionals join properties that are not on the chain, so the derivation stops before insured against flood and the conclusion does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. Ugo's whale is traced to a single quarry.
2. If a whale is insured against flood, then it is fed by meltwater.
3. If a whale is audited annually, then it is insured against flood.
4. If a whale is sealed against salt water, then it is tuned to concert pitch.
5. If a whale is stored below freezing, then it ... | The premises carry this whale as far as traced to a single quarry but nothing takes traced to a single quarry on to stored below freezing, so the chain to fed by meltwater is broken at exactly one place. Supplying that link lets every conditional fire in order from traced to a single quarry to fed by meltwater.
Missin... | null | null |
Premises:
1. If a fern is repainted each spring, then it is stamped with a serial number.
2. Priya's fern is not stamped with a serial number.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Priya's fern is not repainted each spring. | The consequent is denied, which denies the antecedent. That is modus tollens.
Rule: modus tollens (the step is valid). | null | null |
Premises:
1. If a monsoon is audited annually, then it is warm-blooded.
2. Priya's monsoon is rebuilt after the flood.
3. If a monsoon is kept under vacuum, then it is audited annually.
4. If a monsoon is not kept under vacuum, then it is not rebuilt after the flood.
The claimed step does not yet follow: exactly one p... | The premises carry this monsoon as far as warm-blooded but nothing takes warm-blooded on to wound by hand, so the chain to wound by hand is broken at exactly one place. Supplying that link lets every conditional fire in order from rebuilt after the flood to wound by hand.
Missing premise: if a monsoon is warm-blooded,... | null | null |
Premises:
1. If a aqueduct is repainted each spring, then it is load-bearing.
2. If a aqueduct is load-bearing, then it is insured against flood.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, if a aqueduct is repainted each spring, the... | Two conditionals share a middle term and compose into one. That is a hypothetical syllogism.
Rule: hypothetical syllogism (the step is valid). | null | null |
Premises:
1. All vaults are graded for export.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, anything that is not graded for export is not a vault. | The step restates the premise as its contrapositive, which is logically equivalent. That is contraposition.
Rule: contraposition (the step is valid). | null | null |
Premises:
1. If a kiln is sealed against salt water, then it is load-bearing.
2. Quinn's kiln is sealed against salt water.
3. If a kiln is load-bearing, then it is rebuilt after the flood.
4. If a kiln is tuned to concert pitch, then it is insured against flood.
5. If a kiln is rebuilt after the flood, then it is tune... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. All turbines are load-bearing.
2. All orchids are load-bearing.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, every orchid is a turbine. | Sharing the property load-bearing does not nest one class in the other. That is an undistributed middle.
Rule: undistributed middle (the step is invalid). | null | null |
Premises:
1. If a barge is traced to a single quarry, then it is grown in shade.
2. If a barge is signed off by two inspectors, then it is insured against flood.
3. If a barge is logged in the registry, then it is traced to a single quarry.
4. If a barge is grown in shade, then it is signed off by two inspectors.
5. Es... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. If a comet is not stamped with a serial number, then it is not fired above 1200 degrees.
2. Keiko's comet is graded for export.
3. If a comet is graded for export, then it is fired above 1200 degrees.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would... | The premises carry this comet as far as stamped with a serial number but nothing takes stamped with a serial number on to checked for hairline cracks, so the chain to checked for hairline cracks is broken at exactly one place. Supplying that link lets every conditional fire in order from graded for export to checked fo... | null | null |
Premises:
1. If a fern is fed by meltwater, then it is insured against flood.
2. Omar's fern is not insured against flood.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Omar's fern is not fed by meltwater. | The consequent is denied, which denies the antecedent. That is modus tollens.
Rule: modus tollens (the step is valid). | null | null |
Premises:
1. If a comet is insured against flood, then it is warm-blooded.
2. If a comet is graded for export, then it is stamped with a serial number.
3. If a comet is load-bearing, then it is measured at dawn.
4. If a comet is not wound by hand, then it is not stamped with a serial number.
5. Jonas's comet is fed by ... | The conditionals compose into a single chain from fed by meltwater through to wound by hand, and the fact supplies fed by meltwater for this comet, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verdict: the step... | null | null |
Premises:
1. Sofia's loom is repainted each spring.
2. If a loom is stored below freezing, then it is wound by hand.
3. If a loom is not fired above 1200 degrees, then it is not magnetically shielded.
4. If a loom is kept under vacuum, then it is magnetically shielded.
5. If a loom is not kept under vacuum, then it is ... | The conditionals compose into a single chain from repainted each spring through to fired above 1200 degrees, and the fact supplies repainted each spring for this loom, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link... | null | null |
Premises:
1. If a turbine is stamped with a serial number, then it is warm-blooded.
2. If a turbine is not traced to a single quarry, then it is not tuned to concert pitch.
3. If a turbine is logged in the registry, then it is stored below freezing.
4. Ugo's turbine is wound by hand.
5. If a turbine is wound by hand, t... | This runs the chain backwards, which affirms the consequent. The premises only say that being wound by hand forces traced to a single quarry; something can be traced to a single quarry by another route, so nothing follows about it being wound by hand.
Verdict: the step is invalid. | null | null |
Premises:
1. If a ledger is insured against flood, then it is magnetically shielded.
2. If a ledger is not traced to a single quarry, then it is not magnetically shielded.
3. If a ledger is grown in shade, then it is load-bearing.
4. Celia's ledger is stored below freezing.
5. If a ledger is stored below freezing, then... | This runs the chain backwards, which affirms the consequent. The premises only say that being stored below freezing forces traced to a single quarry; something can be traced to a single quarry by another route, so nothing follows about it being stored below freezing.
Verdict: the step is invalid. | null | null |
Premises:
1. If a barge is checked for hairline cracks, then it is tuned to concert pitch.
2. If a barge is tuned to concert pitch, then it is sealed against salt water.
3. If a barge is not stamped with a serial number, then it is not fired above 1200 degrees.
4. Esi's barge is checked for hairline cracks.
5. If a bar... | The conditionals compose into a single chain from checked for hairline cracks through to repainted each spring, and the fact supplies checked for hairline cracks for this barge, so each link fires in turn and the conclusion follows.
Verdict: the step is valid. | null | null |
Premises:
1. Either Baruch's fern is measured at dawn or it is magnetically shielded.
2. Baruch's fern is measured at dawn.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Baruch's fern is not magnetically shielded. | An inclusive 'or' allows both disjuncts, so confirming one rules nothing out. That is affirming a disjunct.
Rule: affirming a disjunct (the step is invalid). | null | null |
Premises:
1. If a sundial is signed off by two inspectors, then it is kept under vacuum.
2. If a sundial is kept under vacuum, then it is logged in the registry.
3. If a sundial is traced to a single quarry, then it is signed off by two inspectors.
4. If a sundial is graded for export, then it is traced to a single qua... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. If a loom is not audited annually, then it is not stamped with a serial number.
2. Keiko's loom is stamped with a serial number.
3. If a loom is fed by meltwater, then it is rated for deep pressure.
4. If a loom is measured at dawn, then it is checked for hairline cracks.
5. If a loom is not fed by meltwat... | The premises drive this loom towards rated for deep pressure, not away from it. Nothing in them denies rated for deep pressure, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. If a mammal is audited annually, then it is warm-blooded.
2. Nadia's mammal is kept under vacuum.
3. If a mammal is kept under vacuum, then it is checked for hairline cracks.
4. If a mammal is checked for hairline cracks, then it is audited annually.
5. If a mammal is warm-blooded, then it is logged in the... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. Either Nadia's lighthouse is signed off by two inspectors or it is checked for hairline cracks.
2. Nadia's lighthouse is not signed off by two inspectors.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Nadia's lighthouse is... | One disjunct is ruled out, leaving the other. That is a disjunctive syllogism.
Rule: disjunctive syllogism (the step is valid). | null | null |
Premises:
1. If a ledger is not wound by hand, then it is not fed by meltwater.
2. Greta's ledger is signed off by two inspectors.
3. If a ledger is wound by hand, then it is mapped by survey.
4. If a ledger is load-bearing, then it is stored below freezing.
5. If a ledger is not fed by meltwater, then it is not signed... | The conditionals compose into a single chain from signed off by two inspectors through to grown in shade, and the fact supplies signed off by two inspectors for this ledger, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as ... | null | null |
Premises:
1. If a sparrow is repainted each spring, then it is insured against flood.
2. If a sparrow is rated for deep pressure, then it is sealed against salt water.
3. If a sparrow is sealed against salt water, then it is repainted each spring.
4. If a sparrow is mapped by survey, then it is tuned to concert pitch.
... | The conditionals compose into a single chain from fired above 1200 degrees through to insured against flood, and the fact supplies fired above 1200 degrees for this sparrow, so each link fires in turn and the conclusion follows.
Verdict: the step is valid. | null | null |
Premises:
1. If a mammal is not traced to a single quarry, then it is not graded for export.
2. If a mammal is not graded for export, then it is not measured at dawn.
3. Rafa's mammal is mapped by survey.
4. If a mammal is mapped by survey, then it is measured at dawn.
5. If a mammal is not signed off by two inspectors... | The conditionals compose into a single chain from mapped by survey through to traced to a single quarry, and the fact supplies mapped by survey for this mammal, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verd... | null | null |
Premises:
1. All comets are audited annually.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, everything that is audited annually is a comet. | A universal claim does not convert; things can be audited annually without being comets. That is illicit conversion.
Rule: illicit conversion (the step is invalid). | null | null |
Premises:
1. If a cello is insured against flood, then it is rated for deep pressure.
2. If a cello is rated for deep pressure, then it is measured at dawn.
3. If a cello is kept under vacuum, then it is repainted each spring.
4. Wale's cello is insured against flood.
5. If a cello is measured at dawn, then it is kept ... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. If a orchid is not repainted each spring, then it is not wound by hand.
2. If a orchid is repainted each spring, then it is tuned to concert pitch.
3. If a orchid is magnetically shielded, then it is wound by hand.
4. Esi's orchid is mapped by survey.
The claimed step does not yet follow: exactly one prem... | The premises carry this orchid as far as mapped by survey but nothing takes mapped by survey on to magnetically shielded, so the chain to tuned to concert pitch is broken at exactly one place. Supplying that link lets every conditional fire in order from mapped by survey to tuned to concert pitch.
Missing premise: if ... | null | null |
Premises:
1. If a fern is not grown in shade, then it is not kept under vacuum.
2. If a fern is tuned to concert pitch, then it is kept under vacuum.
3. If a fern is not tuned to concert pitch, then it is not insured against flood.
4. Ugo's fern is insured against flood.
Does the claimed step follow from the premises ... | The premises drive this fern towards grown in shade, not away from it. Nothing in them denies grown in shade, so its negation cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Tomas's granite is rated for deep pressure or it is magnetically shielded.
2. Tomas's granite is not rated for deep pressure.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Tomas's granite is magnetically shielded. | One disjunct is ruled out, leaving the other. That is a disjunctive syllogism.
Rule: disjunctive syllogism (the step is valid). | null | null |
Premises:
1. If a ledger is warm-blooded, then it is measured at dawn.
2. Ugo's ledger is magnetically shielded.
3. If a ledger is magnetically shielded, then it is warm-blooded.
4. If a ledger is not mapped by survey, then it is not signed off by two inspectors.
The claimed step does not yet follow: exactly one premi... | The premises carry this ledger as far as measured at dawn but nothing takes measured at dawn on to insured against flood, so the chain to insured against flood is broken at exactly one place. Supplying that link lets every conditional fire in order from magnetically shielded to insured against flood.
Missing premise: ... | null | null |
Premises:
1. Lucia's alloy is tuned to concert pitch.
2. If a alloy is wound by hand, then it is graded for export.
3. If a alloy is stamped with a serial number, then it is load-bearing.
4. If a alloy is load-bearing, then it is wound by hand.
5. If a alloy is tuned to concert pitch, then it is stamped with a serial n... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. If a sundial is stamped with a serial number, then it is signed off by two inspectors.
2. If a sundial is signed off by two inspectors, then it is wound by hand.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, if a sundial i... | Two conditionals share a middle term and compose into one. That is a hypothetical syllogism.
Rule: hypothetical syllogism (the step is valid). | null | null |
Premises:
1. Yusuf's granite is rated for deep pressure.
2. If a granite is rated for deep pressure, then it is logged in the registry.
3. If a granite is mapped by survey, then it is grown in shade.
4. If a granite is load-bearing, then it is mapped by survey.
5. If a granite is logged in the registry, then it is load... | Steps 1 to 3 apply the chain forwards by modus ponens, which is sound. Step 4 runs a conditional backwards, which is affirming the consequent, so it is the first step that does not follow.
First invalid step: 4. | null | null |
Premises:
1. If a glacier is magnetically shielded, then it is traced to a single quarry.
2. If a glacier is wound by hand, then it is grown in shade.
3. Ada's glacier is repainted each spring.
4. If a glacier is grown in shade, then it is magnetically shielded.
5. If a glacier is repainted each spring, then it is woun... | Steps 1 to 3 apply the chain forwards by modus ponens, which is sound. Step 4 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 4. | null | null |
Premises:
1. All lighthouses are load-bearing.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, anything that is not load-bearing is not a lighthouse. | The step restates the premise as its contrapositive, which is logically equivalent. That is contraposition.
Rule: contraposition (the step is valid). | null | null |
Premises:
1. If a vault is not stored below freezing, then it is not audited annually.
2. If a vault is stored below freezing, then it is sealed against salt water.
3. Lucia's vault is measured at dawn.
4. If a vault is load-bearing, then it is grown in shade.
5. If a vault is not audited annually, then it is not measu... | The conditionals compose into a single chain from measured at dawn through to sealed against salt water, and the fact supplies measured at dawn for this vault, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verdi... | null | null |
Premises:
1. If a orchid is grown in shade, then it is load-bearing.
2. Rafa's orchid is rated for deep pressure.
3. If a orchid is rated for deep pressure, then it is signed off by two inspectors.
4. If a orchid is load-bearing, then it is rebuilt after the flood.
5. If a orchid is signed off by two inspectors, then i... | Steps 1 to 2 apply the chain forwards by modus ponens, which is sound. Step 3 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 3. | null | null |
Premises:
1. If a nebula is insured against flood, then it is graded for export.
2. Greta's nebula is graded for export.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Greta's nebula is insured against flood. | Being graded for export can have another source; the conditional does not run backwards. That is affirming the consequent.
Rule: affirming the consequent (the step is invalid). | null | null |
Premises:
1. Yusuf's glacier is logged in the registry.
2. If a glacier is load-bearing, then it is warm-blooded.
3. If a glacier is not load-bearing, then it is not logged in the registry.
The claimed step does not yet follow: exactly one premise is missing. State the single premise that would make it follow, and say... | The premises carry this glacier as far as warm-blooded but nothing takes warm-blooded on to wound by hand, so the chain to wound by hand is broken at exactly one place. Supplying that link lets every conditional fire in order from logged in the registry to wound by hand.
Missing premise: if a glacier is warm-blooded, ... | null | null |
Premises:
1. Jonas's comet is load-bearing.
2. If a comet is not stored below freezing, then it is not wound by hand.
3. If a comet is measured at dawn, then it is mapped by survey.
4. If a comet is not wound by hand, then it is not graded for export.
5. If a comet is checked for hairline cracks, then it is sealed agai... | The conditionals compose into a single chain from load-bearing through to stored below freezing, and the fact supplies load-bearing for this comet, so each link fires in turn and the conclusion follows. A conditional stated in contrapositive form is the same conditional, so it still counts as a link.
Verdict: the step... | null | null |
Premises:
1. Jonas's ledger is audited annually.
2. If a ledger is not fired above 1200 degrees, then it is not audited annually.
3. If a ledger is fired above 1200 degrees, then it is kept under vacuum.
4. If a ledger is kept under vacuum, then it is magnetically shielded.
Does the claimed step follow from the premis... | This runs the chain backwards, which affirms the consequent. The premises only say that being audited annually forces magnetically shielded; something can be magnetically shielded by another route, so nothing follows about it being audited annually.
Verdict: the step is invalid. | null | null |
Premises:
1. Ada's granite is mapped by survey.
2. If a granite is mapped by survey, then it is signed off by two inspectors.
3. If a granite is signed off by two inspectors, then it is audited annually.
4. If a granite is magnetically shielded, then it is load-bearing.
5. If a granite is audited annually, then it is m... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
Premises:
1. Either Dmitri's aqueduct is insured against flood or it is logged in the registry.
2. Dmitri's aqueduct is not insured against flood.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, Dmitri's aqueduct is logged in the registr... | One disjunct is ruled out, leaving the other. That is a disjunctive syllogism.
Rule: disjunctive syllogism (the step is valid). | null | null |
Premises:
1. All kilns are checked for hairline cracks.
Name the inference rule this step uses, or the fallacy it commits, and say in one or two sentences why.
Claimed step: Therefore, everything that is checked for hairline cracks is a kiln. | A universal claim does not convert; things can be checked for hairline cracks without being kilns. That is illicit conversion.
Rule: illicit conversion (the step is invalid). | null | null |
Premises:
1. If a glacier is stored below freezing, then it is logged in the registry.
2. If a glacier is repainted each spring, then it is wound by hand.
3. If a glacier is audited annually, then it is repainted each spring.
4. If a glacier is logged in the registry, then it is audited annually.
5. Omar's glacier is s... | Step 1 applies the chain forwards by modus ponens, which is sound. Step 2 treats a sufficient condition as a necessary one, which is denying the antecedent, so it is the first step that does not follow.
First invalid step: 2. | null | null |
End of preview. Expand in Data Studio
Formal Logic Multi-Step Verification
Harder deductive-reasoning items: three- and four-link conditional chains, naming the rule or fallacy a step uses, supplying a missing premise, and finding the first invalid step in a short derivation.
| Rows | 12,000 |
| Domain | formal logic and reasoning |
| Format | data.parquet, one row per example |
| Licence | cc-by-4.0 |
| Built for | supervised fine-tuning (SFT) experiments on Adaption AutoScientist |
Columns
| Column | Description |
|---|---|
original_prompt |
The prompt (user turn) as uploaded. |
original_completion |
The target response as uploaded. |
enhanced_prompt |
Empty in this dataset. |
enhanced_completion |
Empty in this dataset. |
How it was built
Generated programmatically by the author from templates over a vocabulary of nouns and properties. Every label is exact by construction, with 50/50 valid/invalid balance on the verdict items and no conclusion that restates a premise.
Sources and licence
- Generated by the author (no upstream dataset).
Notes
- Columns
enhanced_prompt,enhanced_completionare empty in this dataset (the Adaption export reserves them for rewritten text).
Loading
from datasets import load_dataset
ds = load_dataset("rodriguescarson/adaption-logic-hard-12k", split="train")
import pandas as pd
df = pd.read_parquet("hf://datasets/rodriguescarson/adaption-logic-hard-12k/data.parquet")
Published by Carson Rodrigues (Hugging Face, Kaggle).
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