Tootfinder

This https://arxiv.org/abs/2305.07614 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIR_…

NevIR: Negation in Neural Information Retrieval
Negation is a common everyday phenomena and has been a consistent area of weakness for language models (LMs). Although the Information Retrieval (IR) community has adopted LMs as the backbone of modern IR architectures, there has been little to no research in understanding how negation impacts neural IR. We therefore construct a straightforward benchmark on this theme: asking IR models to rank two documents that differ only by negation. We show that the results vary widely according to the type…

This https://arxiv.org/abs/2312.17387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property
We construct an explicit algebraic example of a subshift of finite type over a group $Γ$ with an invariant Markov measure which has completely positive sofic entropy (with respect to `most' sofic approximations) and yet does not have a direct Bernoulli factor, because its model spaces shatter into exponentially many clusters of sub-exponential size. The example and its analysis are related to random low-density parity-check (LDPC) codes.

This https://arxiv.org/abs/2401.10056 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into Hilbert-style ca…

This https://arxiv.org/abs/2309.06764 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Adding an Implication to Logics of Perfect Paradefinite Algebras
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras. Their associated multiple-conclusion (Set-Set) and single-conclusion (Set-Fmla) order-preserving logics are non-algebraizable self-extensional logics of formal inconsistency and undeterminedness determined by a six-valued matrix, studied in depth by Gomes et…

This https://arxiv.org/abs/2401.10056 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Axiomatization of Boolean Connexive Logics with syncategorematic negation and modalities
In the article we investigate three classes of extended Boolean Connexive Logics. Two of them are extensions of Modal and non-Modal Boolean Connexive Logics with a property of closure under an arbitrary number of negations. The remaining one is an extension of Modal Boolean Connexive Logic with a property of closure under the function of demodalization. In our work we provide a formal presentation of mentioned properties and axiom schemata that allow us to incorporate them into Hilbert-style ca…

Perplexed: Understanding When Large Language Models are Confused
Nathan Cooper, Torsten Scholak
https://arxiv.org/abs/2404.06634 https://

Perplexed: Understanding When Large Language Models are Confused
Large Language Models (LLMs) have become dominant in the Natural Language Processing (NLP) field causing a huge surge in progress in a short amount of time. However, their limitations are still a mystery and have primarily been explored through tailored datasets to analyze a specific human-level skill such as negation, name resolution, etc. In this paper, we introduce perplexed, a library for exploring where a particular language model is perplexed. To show the flexibility and types of insights…

This https://arxiv.org/abs/2401.13145 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Epic math battle of history: Grothendieck vs Nikodym
We define a $σ$-centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular the existence of such an algebra is consistent with the negation of the continuum hypothesis. The algebra we construct consists of Borel subsets of the Cantor set and has cardinality $ω_1$. We also show how to apply our method to streamline Talagrand's construction of such an algebra under the continuum hypothesis.

Interplay between Negation of a Probability Distribution and Jensen Inequality
Amit Srivastava
https://arxiv.org/abs/2403.20027 https://

Interplay between Negation of a Probability Distribution and Jensen Inequality
Yager[5] proposed a transformation for opposing(negating) the occurence of an event that is not certain using the idea that one can oppose the occurence of any uncertain event by allocating its probability among the other outcomes in the sample space without preference to any particular outcome \textit{i.e.} the probability of every event in the sample space is redistributed equally among the other outcomes in the sample space. However this redistribution increases the uncertainty associated wi…

This https://arxiv.org/abs/2401.13145 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Epic math battle of history: Grothendieck vs Nikodym
We define a $σ$-centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular the existence of such an algebra is consistent with the negation of the continuum hypothesis. The algebra we construct consists of Borel subsets of the Cantor set and has cardinality $ω_1$. We also show how to apply our method to streamline Talagrand's construction of such an algebra under the continuum hypothesis.

Nonclassical logics and multivariate truth values
Volodymyr M. Zhuravlov
https://arXiv.org/abs/2401.15117 https://arXiv.org/pdf/2401.…

Nonclassical logics and multivariate truth values
The article demonstrates that logic is not necessarily singleton and does not always have the standard interpretation of negation. Appropriate generalizations of logic are suggested. Positive logic and multivalued negation operations are examined. An attempt is made to abstract from the fixed and absolute values of truth and falsehood; the ambiguity of logical values is interpreted as their relativity, projective logic.

This https://arxiv.org/abs/2401.02014 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSD_…

Enhancing Zero-Shot Multi-Speaker TTS with Negated Speaker Representations
Zero-shot multi-speaker TTS aims to synthesize speech with the voice of a chosen target speaker without any fine-tuning. Prevailing methods, however, encounter limitations at adapting to new speakers of out-of-domain settings, primarily due to inadequate speaker disentanglement and content leakage. To overcome these constraints, we propose an innovative negation feature learning paradigm that models decoupled speaker attributes as deviations from the complete audio representation by utilizing t…

Simple tableaux for two expansions of G\"odel modal logic
Marta Bilkova, Thomas Ferguson, Daniil Kozhemiachenko
https://arXiv.org/abs/2401.15395 https…

Simple tableaux for two expansions of Gödel modal logic
This paper considers two logics. The first one, $\mathbf{K}\mathsf{G}_\mathsf{inv}$, is an expansion of the Gödel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim_\mathsf{i}$ defined as $v({\sim_\mathsf{i}}ϕ,w)=1-v(ϕ,w)$. The second one, $\mathbf{K}\mathsf{G}_\mathsf{bl}$, is the expansion of $\mathbf{K}\mathsf{G}_\mathsf{inv}$ with the bi-lattice connectives and modalities. We explore their semantical properties w.r.t. the standard semantics on $[0,1]$-valued Kripke fra…