Datasets:
original_prompt stringlengths 233 468 | original_completion stringlengths 153 320 | enhanced_prompt float64 | enhanced_completion float64 |
|---|---|---|---|
Premises:
1. If a cello is tuned to concert pitch, then it is audited annually.
2. If a cello is audited annually, then it is logged in the registry.
Claimed step: Therefore, if a cello is tuned to concert pitch, then it is logged in the registry.
Does this step follow from the premises by deductive logic alone? Expl... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. Either Ada's cello is audited annually or it is fired above 1200 degrees.
2. Ada's cello is audited annually.
Claimed step: Therefore, Ada's cello is not fired above 1200 degrees.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict ... | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other.
Verdict: the step is invalid. | null | null |
Premises:
1. All whales are insured against flood.
2. All violins are insured against flood.
Claimed step: Therefore, every violin is a whale.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property insured against flood, but sharing a property does not put one class inside the other, so nothing follows about violins being whales.
Verdict: the step is invalid. | null | null |
Premises:
1. All ferns are sealed against salt water.
2. No cello is grown in shade.
Claimed step: Therefore, at least one fern is sealed against salt water.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is the existential fallacy. A universal claim about ferns says what holds of any fern there is, but it does not assert that a fern exists, so existence cannot be inferred. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a whale is audited annually, then it is checked for hairline cracks.
2. Priya's whale is audited annually.
Claimed step: Therefore, Priya's whale is checked for hairline cracks.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict... | This is modus ponens. The conditional says being audited annually is enough to be checked for hairline cracks, and the second premise asserts the antecedent for this whale, so the consequent follows.
Verdict: the step is valid. | null | null |
Premises:
1. All orchids are fired above 1200 degrees.
2. All ferns are fired above 1200 degrees.
Claimed step: Therefore, every fern is a orchid.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property fired above 1200 degrees, but sharing a property does not put one class inside the other, so nothing follows about ferns being orchids.
Verdict: the step is invalid. | null | null |
Premises:
1. Every fern is a sparrow.
2. All sparrows are tuned to concert pitch.
Claimed step: Therefore, every fern is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every fern falls inside the class of sparrows, and the second premise applies tuned to concert pitch to all of that class, so it applies to every fern as well.
Verdict: the step is valid. | null | null |
Premises:
1. All kilns are tuned to concert pitch.
2. No beetle is audited annually.
Claimed step: Therefore, everything that is tuned to concert pitch is a kiln.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All kilns are tuned to concert pitch' leaves room for things that are tuned to concert pitch without being kilns, so the reverse does not hold. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a orchid is warm-blooded, then it is checked for hairline cracks.
2. Baruch's orchid is not warm-blooded.
3. No ledger is fed by meltwater.
Claimed step: Therefore, Baruch's orchid is not checked for hairline cracks.
Does this step follow from the premises by deductive logic alone? Explain in two or t... | This denies the antecedent. Being warm-blooded is sufficient for being checked for hairline cracks, not necessary, so a orchid that is not warm-blooded may still be checked for hairline cracks. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. No nebula is repainted each spring.
2. Nadia's alloy is audited annually.
3. If a alloy is grown in shade, then it is audited annually.
Claimed step: Therefore, Nadia's alloy is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end w... | This affirms the consequent. The conditional only rules out being grown in shade without being audited annually; something can be audited annually for another reason entirely, so the antecedent does not follow. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a violin is audited annually, then it is load-bearing.
2. If a violin is load-bearing, then it is grown in shade.
Claimed step: Therefore, if a violin is audited annually, then it is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, th... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. Every sparrow is a orchid.
2. All orchids are insured against flood.
Claimed step: Therefore, every sparrow is insured against flood.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every sparrow falls inside the class of orchids, and the second premise applies insured against flood to all of that class, so it applies to every sparrow as well.
Verdict: the step is valid. | null | null |
Premises:
1. If a kiln is stored below freezing, then it is logged in the registry.
2. If a kiln is logged in the registry, then it is audited annually.
Claimed step: Therefore, if a kiln is stored below freezing, then it is audited annually.
Does this step follow from the premises by deductive logic alone? Explain i... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a glacier is stored below freezing, then it is insured against flood.
2. Mateo's glacier is not stored below freezing.
Claimed step: Therefore, Mateo's glacier is not insured against flood.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end wi... | This denies the antecedent. Being stored below freezing is sufficient for being insured against flood, not necessary, so a glacier that is not stored below freezing may still be insured against flood.
Verdict: the step is invalid. | null | null |
Premises:
1. All kilns are insured against flood.
Claimed step: Therefore, everything that is insured against flood is a kiln.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All kilns are insured against flood' leaves room for things that are insured against flood without being kilns, so the reverse does not hold.
Verdict: the step is invalid. | null | null |
Premises:
1. If a glacier is fired above 1200 degrees, then it is insured against flood.
2. If a glacier is insured against flood, then it is grown in shade.
Claimed step: Therefore, if a glacier is fired above 1200 degrees, then it is grown in shade.
Does this step follow from the premises by deductive logic alone? ... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. No ledger is audited annually.
2. All aqueducts are tuned to concert pitch.
Claimed step: Therefore, anything that is not tuned to concert pitch is not a aqueduct.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All aqueducts are tuned to concert pitch' and 'whatever is not tuned to concert pitch is not a aqueduct' are logically equivalent, so the step preserves the premise exactly. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. No comet is stored below freezing.
2. If a violin is sealed against salt water, then it is repainted each spring.
3. Lucia's violin is not repainted each spring.
Claimed step: Therefore, Lucia's violin is not sealed against salt water.
Does this step follow from the premises by deductive logic alone? Exp... | This is modus tollens. Denying the consequent denies the antecedent: if being sealed against salt water guaranteed being repainted each spring, then something that is not repainted each spring cannot be sealed against salt water. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All beetles are magnetically shielded.
2. No comet is checked for hairline cracks.
Claimed step: Therefore, everything that is magnetically shielded is a beetle.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All beetles are magnetically shielded' leaves room for things that are magnetically shielded without being beetles, so the reverse does not hold. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a lighthouse is fed by meltwater, then it is stored below freezing.
2. If a lighthouse is stored below freezing, then it is audited annually.
Claimed step: Therefore, if a lighthouse is fed by meltwater, then it is audited annually.
Does this step follow from the premises by deductive logic alone? Exp... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a cello is insured against flood, then it is repainted each spring.
2. Lucia's cello is not insured against flood.
Claimed step: Therefore, Lucia's cello is not repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a v... | This denies the antecedent. Being insured against flood is sufficient for being repainted each spring, not necessary, so a cello that is not insured against flood may still be repainted each spring.
Verdict: the step is invalid. | null | null |
Premises:
1. If a granite is repainted each spring, then it is mapped by survey.
2. Ines's granite is not repainted each spring.
Claimed step: Therefore, Ines's granite is not mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict... | This denies the antecedent. Being repainted each spring is sufficient for being mapped by survey, not necessary, so a granite that is not repainted each spring may still be mapped by survey.
Verdict: the step is invalid. | null | null |
Premises:
1. No violin is grown in shade.
2. All ferns are warm-blooded.
Claimed step: Therefore, at least one fern is warm-blooded.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is the existential fallacy. A universal claim about ferns says what holds of any fern there is, but it does not assert that a fern exists, so existence cannot be inferred. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a lighthouse is logged in the registry, then it is stored below freezing.
2. Celia's lighthouse is stored below freezing.
Claimed step: Therefore, Celia's lighthouse is logged in the registry.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end... | This affirms the consequent. The conditional only rules out being logged in the registry without being stored below freezing; something can be stored below freezing for another reason entirely, so the antecedent does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Ada's orchid is stored below freezing or it is repainted each spring.
2. No fern is magnetically shielded.
3. Ada's orchid is not stored below freezing.
Claimed step: Therefore, Ada's orchid is repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain in two ... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All violins are tuned to concert pitch.
2. All alloys are tuned to concert pitch.
Claimed step: Therefore, every alloy is a violin.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property tuned to concert pitch, but sharing a property does not put one class inside the other, so nothing follows about alloys being violins.
Verdict: the step is invalid. | null | null |
Premises:
1. All kilns are fed by meltwater.
2. No turbine is load-bearing.
Claimed step: Therefore, anything that is not fed by meltwater is not a kiln.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All kilns are fed by meltwater' and 'whatever is not fed by meltwater is not a kiln' are logically equivalent, so the step preserves the premise exactly. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All ferns are warm-blooded.
Claimed step: Therefore, anything that is not warm-blooded is not a fern.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All ferns are warm-blooded' and 'whatever is not warm-blooded is not a fern' are logically equivalent, so the step preserves the premise exactly.
Verdict: the step is valid. | null | null |
Premises:
1. If a orchid is fired above 1200 degrees, then it is audited annually.
2. Jonas's orchid is not audited annually.
Claimed step: Therefore, Jonas's orchid is not fired above 1200 degrees.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a ve... | This is modus tollens. Denying the consequent denies the antecedent: if being fired above 1200 degrees guaranteed being audited annually, then something that is not audited annually cannot be fired above 1200 degrees.
Verdict: the step is valid. | null | null |
Premises:
1. If a comet is load-bearing, then it is sealed against salt water.
2. Mateo's comet is not sealed against salt water.
Claimed step: Therefore, Mateo's comet is not load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict lin... | This is modus tollens. Denying the consequent denies the antecedent: if being load-bearing guaranteed being sealed against salt water, then something that is not sealed against salt water cannot be load-bearing.
Verdict: the step is valid. | null | null |
Premises:
1. All ferns are fired above 1200 degrees.
Claimed step: Therefore, anything that is not fired above 1200 degrees is not a fern.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All ferns are fired above 1200 degrees' and 'whatever is not fired above 1200 degrees is not a fern' are logically equivalent, so the step preserves the premise exactly.
Verdict: the step is valid. | null | null |
Premises:
1. All turbines are logged in the registry.
2. No kiln is tuned to concert pitch.
Claimed step: Therefore, anything that is not logged in the registry is not a turbine.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All turbines are logged in the registry' and 'whatever is not logged in the registry is not a turbine' are logically equivalent, so the step preserves the premise exactly. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Tomas's granite is audited annually or it is tuned to concert pitch.
2. Tomas's granite is audited annually.
3. No whale is load-bearing.
Claimed step: Therefore, Tomas's granite is not tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or thre... | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. Keiko's sparrow is not grown in shade.
2. No aqueduct is insured against flood.
3. Either Keiko's sparrow is grown in shade or it is stored below freezing.
Claimed step: Therefore, Keiko's sparrow is stored below freezing.
Does this step follow from the premises by deductive logic alone? Explain in two o... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Hoang's cello is load-bearing or it is audited annually.
2. Hoang's cello is not load-bearing.
Claimed step: Therefore, Hoang's cello is audited annually.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands.
Verdict: the step is valid. | null | null |
Premises:
1. All mammals are load-bearing.
2. All ferns are load-bearing.
3. No aqueduct is repainted each spring.
Claimed step: Therefore, every mammal is a fern.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property load-bearing, but sharing a property does not put one class inside the other, so nothing follows about mammals being ferns. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a turbine is logged in the registry, then it is insured against flood.
2. No beetle is load-bearing.
3. If a turbine is load-bearing, then it is logged in the registry.
Claimed step: Therefore, if a turbine is load-bearing, then it is insured against flood.
Does this step follow from the premises by d... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Omar's nebula is warm-blooded or it is magnetically shielded.
2. Omar's nebula is warm-blooded.
Claimed step: Therefore, Omar's nebula is not magnetically shielded.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other.
Verdict: the step is invalid. | null | null |
Premises:
1. All ledgers are warm-blooded.
Claimed step: Therefore, everything that is warm-blooded is a ledger.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All ledgers are warm-blooded' leaves room for things that are warm-blooded without being ledgers, so the reverse does not hold.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Lucia's violin is sealed against salt water or it is audited annually.
2. Lucia's violin is not sealed against salt water.
Claimed step: Therefore, Lucia's violin is audited annually.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands.
Verdict: the step is valid. | null | null |
Premises:
1. Either Hoang's kiln is stored below freezing or it is repainted each spring.
2. No nebula is sealed against salt water.
3. Hoang's kiln is not stored below freezing.
Claimed step: Therefore, Hoang's kiln is repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain i... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. No nebula is warm-blooded.
2. If a turbine is insured against flood, then it is load-bearing.
3. Sofia's turbine is insured against flood.
Claimed step: Therefore, Sofia's turbine is load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then en... | This is modus ponens. The conditional says being insured against flood is enough to be load-bearing, and the second premise asserts the antecedent for this turbine, so the consequent follows. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. No orchid is insured against flood.
2. Lucia's turbine is stored below freezing.
3. Either Lucia's turbine is stored below freezing or it is fed by meltwater.
Claimed step: Therefore, Lucia's turbine is not fed by meltwater.
Does this step follow from the premises by deductive logic alone? Explain in two... | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a cello is mapped by survey, then it is insured against flood.
2. If a cello is insured against flood, then it is sealed against salt water.
Claimed step: Therefore, if a cello is mapped by survey, then it is sealed against salt water.
Does this step follow from the premises by deductive logic alone? ... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a mammal is load-bearing, then it is stored below freezing.
2. Celia's mammal is not load-bearing.
Claimed step: Therefore, Celia's mammal is not stored below freezing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This denies the antecedent. Being load-bearing is sufficient for being stored below freezing, not necessary, so a mammal that is not load-bearing may still be stored below freezing.
Verdict: the step is invalid. | null | null |
Premises:
1. No kiln is repainted each spring.
2. Omar's orchid is audited annually.
3. If a orchid is audited annually, then it is mapped by survey.
Claimed step: Therefore, Omar's orchid is mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then en... | This is modus ponens. The conditional says being audited annually is enough to be mapped by survey, and the second premise asserts the antecedent for this orchid, so the consequent follows. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Ines's submarine is mapped by survey.
2. If a submarine is mapped by survey, then it is insured against flood.
3. No granite is magnetically shielded.
Claimed step: Therefore, Ines's submarine is insured against flood.
Does this step follow from the premises by deductive logic alone? Explain in two or th... | This is modus ponens. The conditional says being mapped by survey is enough to be insured against flood, and the second premise asserts the antecedent for this submarine, so the consequent follows. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a beetle is magnetically shielded, then it is audited annually.
2. No monsoon is mapped by survey.
3. Keiko's beetle is magnetically shielded.
Claimed step: Therefore, Keiko's beetle is audited annually.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentence... | This is modus ponens. The conditional says being magnetically shielded is enough to be audited annually, and the second premise asserts the antecedent for this beetle, so the consequent follows. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a alloy is magnetically shielded, then it is tuned to concert pitch.
2. If a alloy is tuned to concert pitch, then it is stored below freezing.
3. No mammal is grown in shade.
Claimed step: Therefore, if a alloy is magnetically shielded, then it is stored below freezing.
Does this step follow from the... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a comet is load-bearing, then it is logged in the registry.
2. Farid's comet is not logged in the registry.
Claimed step: Therefore, Farid's comet is not load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is modus tollens. Denying the consequent denies the antecedent: if being load-bearing guaranteed being logged in the registry, then something that is not logged in the registry cannot be load-bearing.
Verdict: the step is valid. | null | null |
Premises:
1. If a aqueduct is grown in shade, then it is fired above 1200 degrees.
2. If a aqueduct is fired above 1200 degrees, then it is sealed against salt water.
Claimed step: Therefore, if a aqueduct is grown in shade, then it is sealed against salt water.
Does this step follow from the premises by deductive lo... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a comet is insured against flood, then it is grown in shade.
2. No orchid is logged in the registry.
3. Celia's comet is insured against flood.
Claimed step: Therefore, Celia's comet is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences,... | This is modus ponens. The conditional says being insured against flood is enough to be grown in shade, and the second premise asserts the antecedent for this comet, so the consequent follows. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Ada's lighthouse is fed by meltwater or it is magnetically shielded.
2. Ada's lighthouse is fed by meltwater.
3. No whale is tuned to concert pitch.
Claimed step: Therefore, Ada's lighthouse is not magnetically shielded.
Does this step follow from the premises by deductive logic alone? Explain in ... | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. All kilns are tuned to concert pitch.
2. No kiln is load-bearing.
Claimed step: Therefore, at least one kiln is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is the existential fallacy. A universal claim about kilns says what holds of any kiln there is, but it does not assert that a kiln exists, so existence cannot be inferred. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a orchid is tuned to concert pitch, then it is fed by meltwater.
2. Mateo's orchid is fed by meltwater.
Claimed step: Therefore, Mateo's orchid is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This affirms the consequent. The conditional only rules out being tuned to concert pitch without being fed by meltwater; something can be fed by meltwater for another reason entirely, so the antecedent does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. If a nebula is mapped by survey, then it is warm-blooded.
2. If a nebula is warm-blooded, then it is insured against flood.
Claimed step: Therefore, if a nebula is mapped by survey, then it is insured against flood.
Does this step follow from the premises by deductive logic alone? Explain in two or three... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. Every fern is a beetle.
2. All beetles are logged in the registry.
Claimed step: Therefore, every fern is logged in the registry.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every fern falls inside the class of beetles, and the second premise applies logged in the registry to all of that class, so it applies to every fern as well.
Verdict: the step is valid. | null | null |
Premises:
1. Every violin is a alloy.
2. No submarine is warm-blooded.
3. All alloys are mapped by survey.
Claimed step: Therefore, every violin is mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every violin falls inside the class of alloys, and the second premise applies mapped by survey to all of that class, so it applies to every violin as well. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a cello is magnetically shielded, then it is tuned to concert pitch.
2. Rafa's cello is magnetically shielded.
Claimed step: Therefore, Rafa's cello is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict l... | This is modus ponens. The conditional says being magnetically shielded is enough to be tuned to concert pitch, and the second premise asserts the antecedent for this cello, so the consequent follows.
Verdict: the step is valid. | null | null |
Premises:
1. All sparrows are checked for hairline cracks.
2. All granites are checked for hairline cracks.
Claimed step: Therefore, every granite is a sparrow.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property checked for hairline cracks, but sharing a property does not put one class inside the other, so nothing follows about granites being sparrows.
Verdict: the step is invalid. | null | null |
Premises:
1. No aqueduct is logged in the registry.
2. Hoang's orchid is grown in shade.
3. If a orchid is mapped by survey, then it is grown in shade.
Claimed step: Therefore, Hoang's orchid is mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then... | This affirms the consequent. The conditional only rules out being mapped by survey without being grown in shade; something can be grown in shade for another reason entirely, so the antecedent does not follow. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Celia's kiln is sealed against salt water or it is fed by meltwater.
2. Celia's kiln is not sealed against salt water.
3. No lighthouse is tuned to concert pitch.
Claimed step: Therefore, Celia's kiln is fed by meltwater.
Does this step follow from the premises by deductive logic alone? Explain in... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All lighthouses are fed by meltwater.
2. All cellos are fed by meltwater.
3. No comet is fired above 1200 degrees.
Claimed step: Therefore, every lighthouse is a cello.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property fed by meltwater, but sharing a property does not put one class inside the other, so nothing follows about lighthouses being cellos. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a comet is tuned to concert pitch, then it is logged in the registry.
2. Nadia's comet is logged in the registry.
Claimed step: Therefore, Nadia's comet is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdi... | This affirms the consequent. The conditional only rules out being tuned to concert pitch without being logged in the registry; something can be logged in the registry for another reason entirely, so the antecedent does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. If a alloy is repainted each spring, then it is fired above 1200 degrees.
2. Greta's alloy is not fired above 1200 degrees.
Claimed step: Therefore, Greta's alloy is not repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end wi... | This is modus tollens. Denying the consequent denies the antecedent: if being repainted each spring guaranteed being fired above 1200 degrees, then something that is not fired above 1200 degrees cannot be repainted each spring.
Verdict: the step is valid. | null | null |
Premises:
1. Every sparrow is a lighthouse.
2. All lighthouses are stored below freezing.
3. No turbine is audited annually.
Claimed step: Therefore, every sparrow is stored below freezing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict lin... | This chains two universal claims. Every sparrow falls inside the class of lighthouses, and the second premise applies stored below freezing to all of that class, so it applies to every sparrow as well. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a granite is warm-blooded, then it is grown in shade.
2. Hoang's granite is grown in shade.
Claimed step: Therefore, Hoang's granite is warm-blooded.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This affirms the consequent. The conditional only rules out being warm-blooded without being grown in shade; something can be grown in shade for another reason entirely, so the antecedent does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. Every orchid is a monsoon.
2. All monsoons are repainted each spring.
Claimed step: Therefore, every orchid is repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every orchid falls inside the class of monsoons, and the second premise applies repainted each spring to all of that class, so it applies to every orchid as well.
Verdict: the step is valid. | null | null |
Premises:
1. Either Sofia's mammal is grown in shade or it is fired above 1200 degrees.
2. No lighthouse is fired above 1200 degrees.
3. Sofia's mammal is grown in shade.
Claimed step: Therefore, Sofia's mammal is not fired above 1200 degrees.
Does this step follow from the premises by deductive logic alone? Explain ... | This affirms a disjunct. An inclusive 'or' is satisfied when both disjuncts hold, so confirming one does not rule out the other. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. All ledgers are warm-blooded.
Claimed step: Therefore, anything that is not warm-blooded is not a ledger.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is contraposition. 'All ledgers are warm-blooded' and 'whatever is not warm-blooded is not a ledger' are logically equivalent, so the step preserves the premise exactly.
Verdict: the step is valid. | null | null |
Premises:
1. Every sparrow is a glacier.
2. All glaciers are checked for hairline cracks.
Claimed step: Therefore, every sparrow is checked for hairline cracks.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every sparrow falls inside the class of glaciers, and the second premise applies checked for hairline cracks to all of that class, so it applies to every sparrow as well.
Verdict: the step is valid. | null | null |
Premises:
1. All beetles are magnetically shielded.
Claimed step: Therefore, everything that is magnetically shielded is a beetle.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All beetles are magnetically shielded' leaves room for things that are magnetically shielded without being beetles, so the reverse does not hold.
Verdict: the step is invalid. | null | null |
Premises:
1. If a mammal is fed by meltwater, then it is logged in the registry.
2. If a mammal is logged in the registry, then it is mapped by survey.
Claimed step: Therefore, if a mammal is fed by meltwater, then it is mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in tw... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a nebula is checked for hairline cracks, then it is insured against flood.
2. Quinn's nebula is checked for hairline cracks.
Claimed step: Therefore, Quinn's nebula is insured against flood.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end w... | This is modus ponens. The conditional says being checked for hairline cracks is enough to be insured against flood, and the second premise asserts the antecedent for this nebula, so the consequent follows.
Verdict: the step is valid. | null | null |
Premises:
1. No aqueduct is stored below freezing.
2. All sparrows are grown in shade.
3. Every glacier is a sparrow.
Claimed step: Therefore, every glacier is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every glacier falls inside the class of sparrows, and the second premise applies grown in shade to all of that class, so it applies to every glacier as well. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a aqueduct is fed by meltwater, then it is load-bearing.
2. Quinn's aqueduct is load-bearing.
Claimed step: Therefore, Quinn's aqueduct is fed by meltwater.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This affirms the consequent. The conditional only rules out being fed by meltwater without being load-bearing; something can be load-bearing for another reason entirely, so the antecedent does not follow.
Verdict: the step is invalid. | null | null |
Premises:
1. If a submarine is fed by meltwater, then it is warm-blooded.
2. If a submarine is warm-blooded, then it is tuned to concert pitch.
Claimed step: Therefore, if a submarine is fed by meltwater, then it is tuned to concert pitch.
Does this step follow from the premises by deductive logic alone? Explain in t... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. If a beetle is load-bearing, then it is grown in shade.
2. Tomas's beetle is not grown in shade.
Claimed step: Therefore, Tomas's beetle is not load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is modus tollens. Denying the consequent denies the antecedent: if being load-bearing guaranteed being grown in shade, then something that is not grown in shade cannot be load-bearing.
Verdict: the step is valid. | null | null |
Premises:
1. If a submarine is load-bearing, then it is grown in shade.
2. Rafa's submarine is grown in shade.
3. No lighthouse is sealed against salt water.
Claimed step: Therefore, Rafa's submarine is load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, ... | This affirms the consequent. The conditional only rules out being load-bearing without being grown in shade; something can be grown in shade for another reason entirely, so the antecedent does not follow. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. If a violin is load-bearing, then it is sealed against salt water.
2. If a violin is sealed against salt water, then it is stored below freezing.
Claimed step: Therefore, if a violin is load-bearing, then it is stored below freezing.
Does this step follow from the premises by deductive logic alone? Expla... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent.
Verdict: the step is valid. | null | null |
Premises:
1. All granites are load-bearing.
Claimed step: Therefore, at least one granite is load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is the existential fallacy. A universal claim about granites says what holds of any granite there is, but it does not assert that a granite exists, so existence cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. If a violin is logged in the registry, then it is checked for hairline cracks.
2. No whale is sealed against salt water.
3. Omar's violin is not checked for hairline cracks.
Claimed step: Therefore, Omar's violin is not logged in the registry.
Does this step follow from the premises by deductive logic al... | This is modus tollens. Denying the consequent denies the antecedent: if being logged in the registry guaranteed being checked for hairline cracks, then something that is not checked for hairline cracks cannot be logged in the registry. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All submarines are checked for hairline cracks.
2. All ledgers are checked for hairline cracks.
Claimed step: Therefore, every ledger is a submarine.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property checked for hairline cracks, but sharing a property does not put one class inside the other, so nothing follows about ledgers being submarines.
Verdict: the step is invalid. | null | null |
Premises:
1. If a whale is checked for hairline cracks, then it is insured against flood.
2. Rafa's whale is not insured against flood.
Claimed step: Therefore, Rafa's whale is not checked for hairline cracks.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then en... | This is modus tollens. Denying the consequent denies the antecedent: if being checked for hairline cracks guaranteed being insured against flood, then something that is not insured against flood cannot be checked for hairline cracks.
Verdict: the step is valid. | null | null |
Premises:
1. If a comet is rated for deep pressure, then it is stored below freezing.
2. If a comet is stored below freezing, then it is magnetically shielded.
3. No glacier is tuned to concert pitch.
Claimed step: Therefore, if a comet is rated for deep pressure, then it is magnetically shielded.
Does this step foll... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. If a beetle is audited annually, then it is tuned to concert pitch.
2. Sofia's beetle is not tuned to concert pitch.
Claimed step: Therefore, Sofia's beetle is not audited annually.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdic... | This is modus tollens. Denying the consequent denies the antecedent: if being audited annually guaranteed being tuned to concert pitch, then something that is not tuned to concert pitch cannot be audited annually.
Verdict: the step is valid. | null | null |
Premises:
1. If a turbine is mapped by survey, then it is magnetically shielded.
2. Ada's turbine is not mapped by survey.
Claimed step: Therefore, Ada's turbine is not magnetically shielded.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict l... | This denies the antecedent. Being mapped by survey is sufficient for being magnetically shielded, not necessary, so a turbine that is not mapped by survey may still be magnetically shielded.
Verdict: the step is invalid. | null | null |
Premises:
1. All violins are insured against flood.
Claimed step: Therefore, everything that is insured against flood is a violin.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All violins are insured against flood' leaves room for things that are insured against flood without being violins, so the reverse does not hold.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Ada's nebula is checked for hairline cracks or it is magnetically shielded.
2. Ada's nebula is not checked for hairline cracks.
Claimed step: Therefore, Ada's nebula is magnetically shielded.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then ... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands.
Verdict: the step is valid. | null | null |
Premises:
1. No kiln is rated for deep pressure.
2. Nadia's turbine is not logged in the registry.
3. If a turbine is logged in the registry, then it is rated for deep pressure.
Claimed step: Therefore, Nadia's turbine is not rated for deep pressure.
Does this step follow from the premises by deductive logic alone? E... | This denies the antecedent. Being logged in the registry is sufficient for being rated for deep pressure, not necessary, so a turbine that is not logged in the registry may still be rated for deep pressure. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Nadia's lighthouse is rated for deep pressure or it is grown in shade.
2. Nadia's lighthouse is not rated for deep pressure.
3. No mammal is fed by meltwater.
Claimed step: Therefore, Nadia's lighthouse is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. All comets are repainted each spring.
Claimed step: Therefore, at least one comet is repainted each spring.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is the existential fallacy. A universal claim about comets says what holds of any comet there is, but it does not assert that a comet exists, so existence cannot be inferred.
Verdict: the step is invalid. | null | null |
Premises:
1. No kiln is audited annually.
2. If a violin is checked for hairline cracks, then it is fired above 1200 degrees.
3. If a violin is sealed against salt water, then it is checked for hairline cracks.
Claimed step: Therefore, if a violin is sealed against salt water, then it is fired above 1200 degrees.
Doe... | This is a hypothetical syllogism. The two conditionals share a middle term, so they compose into a single conditional from the first antecedent to the last consequent. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Dmitri's submarine is grown in shade or it is load-bearing.
2. Dmitri's submarine is not grown in shade.
Claimed step: Therefore, Dmitri's submarine is load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands.
Verdict: the step is valid. | null | null |
Premises:
1. All turbines are mapped by survey.
Claimed step: Therefore, everything that is mapped by survey is a turbine.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This converts a universal claim illicitly. 'All turbines are mapped by survey' leaves room for things that are mapped by survey without being turbines, so the reverse does not hold.
Verdict: the step is invalid. | null | null |
Premises:
1. All ledgers are magnetically shielded.
2. No sparrow is sealed against salt water.
3. All beetles are magnetically shielded.
Claimed step: Therefore, every ledger is a beetle.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line... | The middle term is undistributed. Both classes share the property magnetically shielded, but sharing a property does not put one class inside the other, so nothing follows about ledgers being beetles. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. Every mammal is a sparrow.
2. All sparrows are load-bearing.
Claimed step: Therefore, every mammal is load-bearing.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | This chains two universal claims. Every mammal falls inside the class of sparrows, and the second premise applies load-bearing to all of that class, so it applies to every mammal as well.
Verdict: the step is valid. | null | null |
Premises:
1. All kilns are checked for hairline cracks.
2. All cellos are checked for hairline cracks.
3. No alloy is mapped by survey.
Claimed step: Therefore, every kiln is a cello.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict line. | The middle term is undistributed. Both classes share the property checked for hairline cracks, but sharing a property does not put one class inside the other, so nothing follows about kilns being cellos. The extra premise plays no part in this step.
Verdict: the step is invalid. | null | null |
Premises:
1. Either Rafa's comet is fed by meltwater or it is mapped by survey.
2. Rafa's comet is not fed by meltwater.
3. No alloy is tuned to concert pitch.
Claimed step: Therefore, Rafa's comet is mapped by survey.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands. The extra premise plays no part in this step.
Verdict: the step is valid. | null | null |
Premises:
1. Either Celia's violin is magnetically shielded or it is grown in shade.
2. Celia's violin is not magnetically shielded.
Claimed step: Therefore, Celia's violin is grown in shade.
Does this step follow from the premises by deductive logic alone? Explain in two or three sentences, then end with a verdict l... | This is a disjunctive syllogism. One of the two disjuncts must hold, and the first has been ruled out, so the second stands.
Verdict: the step is valid. | null | null |
End of preview. Expand in Data Studio
Formal Logic Step Verification
Single-step deductive reasoning: given premises and a claimed step, explain whether it follows and end with a verdict. Covers six valid forms (modus ponens and tollens, hypothetical and disjunctive syllogism, contraposition, universal chaining) and six named fallacies.
| 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; labels are exact by construction, 50/50 valid and invalid, 35% of items carry an irrelevant distractor 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-step-verification-12k-c4", split="train")
import pandas as pd
df = pd.read_parquet("hf://datasets/rodriguescarson/adaption-logic-step-verification-12k-c4/data.parquet")
Published by Carson Rodrigues (Hugging Face, Kaggle).
- Downloads last month
- 62