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gold_30_ver2_gpt-4_6shots_reasonTrue_wrongs.txt
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gold_30_ver2_gpt-4_6shots_reasonTrue_wrongs.txt
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1.Premise: This paper introduces the notions of vector field and flow on a general differentiable stack.
Hypothesis: The field of vectors contains a different stack of papers, but this one is the first to introduce the notion of a general differentiable stack.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The reasoning in this pair: The premise states that this paper introduces specific notions (vector field and flow) on a general differentiable stack, suggesting that the concept of a differentiable stack is already understood or established within the context. The hypothesis implies that this paper is the first to "introduce the notion of a general differentiable stack," which contradicts the implication in the premise that the concept is already known. Furthermore, the hypothesis introduces a confusing and potentially unrelated concept ("the field of vectors contains a different stack of papers"), which does not logically derive from the premise. Therefore, the relationship between the premise and the hypothesis is one of contradiction.
<End of Reasoning>
vcvp: don't like this example! The hypothesis doesn't make sense: "this one" might refer to a paper and it might not. there is no reason for it to be a contradiction. in particular
SUGGESTED NEW HYPOTHESIS:
This paper generalizes the notions of vector field and flow on a stack.
this is still neutral, as "introduce" does not entail "generalize" and one might need a differentiable stack for the definition
2.
Premise: We define eventually cyclic Boolean flows and the eventually cyclic spectrum of a Boolean flow.
Hypothesis: The definition of the eventually cyclic spectrum of a Boolean flow uses the definition of eventually cyclic Boolean flows.
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: entailment
The reasoning in this pair: If the premise introduces the definition of "eventually cyclic Boolean flows" alongside the "eventually cyclic spectrum of a Boolean flow," it is reasonable to infer that the concept of "eventually cyclic Boolean flows" would be used or referenced in the definition of the "eventually cyclic spectrum of a Boolean flow." Thus, the hypothesis is entailed by the premise.
<End of Reasoning>
vcvp: why is it reasonable to infer that "the concept of "eventually cyclic Boolean flows" would be used or referenced in the definition of the "eventually cyclic spectrum of a Boolean flow."? cyclicity of the spectrum is NOT necessarily connected to cyclicity of the Boolean flow itself.
3. Premise: The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor.
Hypothesis: The axioms bear a very strong resemblance to those for monoidal Abelian categories, even with the addition of an involutive functor.
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: entailment
vcvp: This is a bad example because the premise is of the form "X resembles Y plus Z", where there is ambiguity between "X resembles (Y plus Z}" or "(X resembles Y) plus Z." and the hypothesis is bad because "even" is playing a huge part. "even" has a contrastive meaning: we say "X even when Y" to mean "you would've thought X only if not Y".
the machine does not understand the meaning of "even".
SUGGESTED NEW HYPOTHESIS:
The axioms are the ones of monoidal Abelian categories.
Reasoning: The premise states that the axioms are similar to those for monoidal Abelian categories, with the specific inclusion of an "involutive functor." The hypothesis simply strengthens this statement by saying there's a "very strong resemblance" to those axioms for monoidal Abelian categories, while acknowledging the addition of an "involutive functor" as well. The core message—that the axioms for the two categories are closely related and include an involutive functor—is shared by both the premise and the hypothesis.
<End of Reasoning>
4. Premise: p: Neither enrichment nor a complex base field is presupposed.
Hypothesis: Field in this paper are not complex. (ungrammatical!) concordance
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: Entailment
The reasoning in this pair: The premise states that neither enrichment nor a complex base field is presupposed. This directly entails that fields in the paper are not assumed to be complex, as stated in the hypothesis. Hence, the relationship between the premise and the hypothesis is one of entailment.
<End of Reasoning>
vcvp: if we correct thegrammar of the sentence "Fields in this paper are not complex", I think the machine is correct, it's entailment, not neutral.
SUGGESTED NEW HYPOTHESIS:
The base field assumed is the real numbers.
5.Premise: A comparison to other approaches will be made in the introduction.
Hypothesis: Other approaches will be made in the introduction.
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: neutral
The reasoning in this pair: The premise suggests a comparison between different approaches will be mentioned in the introduction, while the hypothesis drops the comparison aspect and misrepresents the premise as saying other approaches themselves will be created or introduced in the introduction. This change of meaning makes the correct label neutral, as the relationship between the premise and the hypothesis is neither a direct contradiction nor an entailment.
<End of Reasoning>
vcvp: the premise means that the approach in this paper will be compared to other approaches in the literature.
the hypothesis asserts that the introduction of this paper will contain other approaches: to what? it might be to the subject of this paper, but it might be to something else.
6. Premise: For such a class of spaces homotopy orthogonality implies enriched orthogonality.
Hypothesis: For such a class of spaces enriched orthogonality implies homotopy orthogonality.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The premise states that "homotopy orthogonality implies enriched orthogonality," which suggests a specific direction of implication: A leads to B. However, the hypothesis reverses the implication, stating that "enriched orthogonality implies homotopy orthogonality," suggesting B leads to A. Since the direction of the implication is reversed, the premise and the hypothesis are in direct contradiction with each other.
<End of Reasoning>
vcvp: A-->B and B-->A are not necessarily contradictory. the machine is wrong, this is not a contradiction.
7. Premise: The state space of a machine admits the structure of time.
Hypothesis: Like time itself, the state space of a machine has loops.
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: neutral
The premise says the state space of a machine has a structure that admits time, which might imply order or progress through states that could be thought of as akin to the flow of time. However, the hypothesis introduces the concept of loops, which can be interpreted as repetitions or cyclical behavior in the state space. Loops could be a part of the structure that admits time, but they are not necessarily implied by the premise. Therefore, the hypothesis neither necessarily follows from the premise (entailment) nor directly disagrees with it (contradiction). Thus, the correct label is neutral.
<End of Reasoning>
vcvp: the reasoning of the machine is right, but its label is wrong. the premise has nothing about loops. moreover, time as usually construed has no loops.
8. Premise: We describe a simplified categorical approach to Galois descent theory.
Hypothesis: Up to this point, nobody has studied categorical approaches to Galois descent theory.
Label: neutral
Machine_label: contradiction
Machine_reasoning: contradiction
The reasoning in this pair: Since the premise states that a simplified categorical approach to Galois descent theory is being described, it contradicts the hypothesis that up to this point, nobody has studied categorical approaches to Galois descent theory. If the paper in the premise is describing such an approach, then the hypothesis that no one has studied it yet is false.
<End of Reasoning>
vcvp: I believe the machine is right and the reasoning is correct. to obtain a neutral example we could use
NEW HYPOTHESIS:
The previous categorical approach to Galois descent theory was correct, but convoluted.
9. Premise: Then we present three applications of groupoidification.
Hypothesis: Earlier we presented four applications of groupoidification.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
Reasoning for this pair: If the premise talks about presenting three applications of groupoidification in a sequential sense (indicated by "Then"), it implies that these are the applications that are currently being addressed or were just addressed. Given that the hypothesis suggests that four applications were presented earlier, this would imply a discrepancy in the number of applications presented, thus leading to a contradiction between the premise and the hypothesis. If in earlier parts of the text (not provided here) they discussed presenting four applications, then the current premise stating three would contradict that earlier statement.
<End of Reasoning>
vcvp: temporal reasoning is complicated. I'd prefer to have a different example.
SUGGESTED NEW HYPOTHESIS:
Two of these applications are well-known.
10. Premise: The second application is to Hecke algebras.
Hypothesis: The second application is to Hall algebras.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The premise specifically mentions "Hecke algebras" as the subject of the second application, while the hypothesis claims that "Hall algebras" are the subject of the second application. Since "Hecke algebras" and "Hall algebras" are distinct algebraic structures, the premise and hypothesis are directly in conflict with one another, hence the label is "contradiction."
<End of Reasoning>
vcvp: the machine is correct, human error,my own I believe.
SUGGESTED NEW HYPOTHESIS:
Hall algebras can also be an application.
11. Premise: We compute some simple examples and explore the elementary properties of these invariants.
Hypothesis: We explore the elementary properties of these invariants and prove that no other invariants exist.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The reasoning in this pair: The premise indicates that simple examples are computed and elementary properties are explored, but it does not make any statement about the exclusivity or completion of these invariants, as in proving no other invariants exist. The hypothesis, by claiming no other invariants exist, introduces information that directly contradicts the premise, which does not mention any such completeness or exclusivity. Therefore, the relationship between the premise and the hypothesis is one of contradiction.
<End of Reasoning>
vcvp: the machine is wrong, it is correct until the "Therefore, the relationship between the premise and the hypothesis is one of contradiction." which does not follow from what it was said before. The truth of the premise only implies half of the hypothesis.
12. Premise: We combine two recent ideas: cartesian differential categories, and restriction categories.
Hypothesis: We combine three ideas
Label: neutral
Machine_label: contradiction
Machine_reasoning: contradiction
The reasoning in this pair: The premise explicitly states that two ideas are combined, whereas the hypothesis inaccurately increases this number to three. As such, the hypothesis contradicts the information provided in the premise.
<End of Reasoning>
vcvp: machine seems right.
NEW HYPOTHESIS: Cartesian differential categories and restriction categories re concepts in categorical logic.
13. Premise: Vertical arrows give rise to modules between representables.
Hypothesis: Horizontal arrows give rise to modules between representables.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The reasoning in this pair: If the premise specifically states that "vertical arrows" give rise to modules between representables, the hypothesis stating "horizontal arrows" give rise to such modules directly conflicts with the premise unless there's a context where both can be true. Without additional context, stating the opposite (horizontal vs. vertical) introduces a contradiction.
<End of Reasoning>
vcvp: there is no reason why both horizontal and vertical arrows couldn't both give rise to modules.
14. Premise: Various concerns suggest looking for internal co-categories in categories with strong logical structure.
Hypothesis: We suggest looking for internal co-categories.
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: entailment
The reasoning in this pair: The premise describes a context ("various concerns" and "categories with strong logical structure") suggesting a search for "internal co-categories." The hypothesis simplifies this by stating that there is a suggestion to look for "internal co-categories," which is still true without mentioning the specific context. Hence, the hypothesis is entailed by the premise.
<End of Reasoning>
vcvp: agency? the machine reasoning seems correct for "There is a suggestion of looking for internal co-categories", but can we conclude that "we" suggest?
15. Premise: We give a new proof of the fact that every topos is adhesive.
Hypothesis: We conjecture that every topos is also non-adhesive.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The reasoning in this pair: If a new proof is given to show that every topos is adhesive, it directly contradicts the hypothesis that posits every topos could also be non-adhesive, as being adhesive and non-adhesive are mutually exclusive properties in this context.
<End of Reasoning>
vcvp: machine reasoning is correct, human error.
NEW HYPOTHESIS: The old proof of this fact had gaps.
16. Premise: We compare various different definitions of "the category of smooth objects".
Hypothesis: No one has given a definition of "the bicategory of smooth objects".
Label: neutral
Machine_label: entailment
Machine_reasoning: Label: neutral
The premise talks about comparing different definitions of "the category of smooth objects," which implies there are multiple definitions of a category that are being considered. The hypothesis, however, makes a claim about the bicategory of smooth objects and the lack of its definition. Since bicategories are a generalization of categories and the premise does not address the absence of a definition for a bicategory, the relationship cannot be determined as entailment or contradiction based on the given information. Hence, the label should be "neutral".
<End of Reasoning>
vcvp: the reasoning of the machine is correct, the label should be neutral
17. Premise: We clarify details of that work.
Hypothesis: We give details of a special case of that work.
Label: neutral
Machine_label: entailment
Machine_reasoning: neutral
The reasoning in this pair: The premise discusses clarification of details generally. The hypothesis narrows the focus to providing details of a special case. The premise neither confirms nor denies that details of a special case are given; thus, the relationship cannot be determined as entailment or contradiction, making it neutral.
<End of Reasoning>
vcvp: The reasoning of the machine is correct, but the label provided is wrong. not entailment, but neutral.
18. Premise: Our main conceptual tool is a monad on the category of grouped toposes.
Hypothesis: Our main conceptual tool is a comonad on the category of grouped toposes.
Label: neutral
Machine_label: contradiction
Machine_reasoning: Label: contradiction
The reasoning in this pair: If the premise states that the main conceptual tool is a "monad", then asserting that the tool is a "comonad" in the hypothesis directly contradicts the nature of the tool mentioned in the premise. A monad and a comonad are different structures in category theory.
<End of Reasoning>
vcvp: human error, machine is right.
NEW HYPOTHESIS: This paper presents a topos-theoretic investigation of isotropy and the Clifford sequence.