相关论文: On the Herbrand Functional Interpretation
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
In the recent advances of natural language processing, the scale of the state-of-the-art models and datasets is usually extensive, which challenges the application of sample-based explanation methods in many aspects, such as explanation…
An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies…
In this paper, we propose a set theoretic approach for knowledge representation. While the syntax of an application domain is captured by set theoretic constructs including individuals, concepts and operators, knowledge is formalized by…
In this paper, it is demonstrated that there is a parallelism between the relational interpretation of Rovelli and the interpretation of soft matter based on intermediate asymptotics. The general interpretation of physics strongly assumes…
We consider the problem of formalizing the familiar notion of widening in abstract interpretation in higher-order logic. It turns out that many axioms of widening (e.g. widening sequences are ascending) are not useful for proving…
We develop our interpretation of the joint belief distribution and of evidential updating that matches the following basic requirements: * there must exist an efficient method for reasoning within this framework * there must exist a clear…
We explore denotational interpreters: denotational semantics that produce coinductive traces of a corresponding small-step operational semantics. By parameterising our denotational interpreter over the semantic domain and then varying it,…
We study the problem of estimating a functional or a parameter in the context where outcome is subject to nonignorable missingness. We completely avoid modeling the regression relation, while allowing the propensity to be modeled by a…
To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its…
Most research on the interpretability of machine learning systems focuses on the development of a more rigorous notion of interpretability. I suggest that a better understanding of the deficiencies of the intuitive notion of…
The functional ANOVA, or Hoeffding decomposition, provides a principled framework for interpretability by decomposing a model prediction into main effects and higher-order interactions. For independent inputs, this classical decomposition…
Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and…
Disentangling the encodings of neural models is a fundamental aspect for improving interpretability, semantic control and downstream task performance in Natural Language Processing. Currently, most disentanglement methods are unsupervised…
We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT…
The main objective of explanations is to transmit knowledge to humans. This work proposes to construct informative explanations for predictions made from machine learning models. Motivated by the observations from social sciences, our…
The different interpretations of quantum mechanics yield the same experimental results, which may give the impression that the question of what interpretation is the true one, is a philosophical question, not a scientific one. But in this…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Difficulties and discomfort with the interpretation of quantum mechanics are due to differences in language between it and classical physics. Analogies to The Special Theory of Relativity, which also required changes in the basic worldview…