相关论文: Logical coherence in Bayesian simultaneous three-w…

In this paper, we present a generalized effective completeness theorem for continuous logic. The primary result is that any continuous theory is satisfied in a structure which admits a presentation of the same Turing degree. It then follows…

Language models (LMs) show state of the art performance for common sense (CS) question answering, but whether this ability implies a human-level mastery of CS remains an open question. Understanding the limitations and strengths of LMs can…

We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…

Although hypothesis tests play a prominent role in Science, their interpretation can be challenging. Three issues are (i) the difficulty in making an assertive decision based on the output of an hypothesis test, (ii) the logical…

To identify statistically significant conclusions, it is proposed to simultaneously test hypotheses and alternatives. It is shown that, under the condition of free combination of hypotheses and alternatives, the closure method leads to…

We present three syntactic forcing models for coherent logic. These are based on sites whose underlying category only depends on the signature of the coherent theory, and they do not presuppose that the logic has equality. As an application…

Three-way logical question answering (QA) assigns one of $\text{True}$, $\text{False}$, or $\text{Unknown}$ to a hypothesis $H$ given a premise set $S$. We study this task as a compact compositional inference problem: predictions for $H$…

We present three tiers of Bayesian consistency tests for the general case of $correlated$ datasets. Building on duplicates of the model parameters assigned to each dataset, these tests range from Bayesian evidence ratios as a global summary…

Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…

At the staggering pace with which the capabilities of large language models (LLMs) are increasing, creating future-proof evaluation sets to assess their understanding becomes more and more challenging. In this paper, we propose a novel…

The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…

ChatGPT has gained a huge popularity since its introduction. Its positive aspects have been reported through many media platforms, and some analyses even showed that ChatGPT achieved a decent grade in professional exams, adding extra…

Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the…

We present a comprehensive study of surrogate loss functions for learning to defer. We introduce a broad family of surrogate losses, parameterized by a non-increasing function $\Psi$, and establish their realizable $H$-consistency under…

As large language models (LLMs) often generate plausible but incorrect content, error detection has become increasingly critical to ensure truthfulness. However, existing detection methods often overlook a critical problem we term as…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

Imagine that you could calculate of posttest probabilities, i.e. Bayes theorem with simple addition. This is possible if we stop thinking of probabilities as ranging from 0 to 1.0. There is a naturally occurring linear probability space…

The recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic and learning are both practices of the human brain, it leads to another…

This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…

In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…