New preference violation indices for the condition of order preservation

<p>Consistency of pairwise comparisons is one particular aspect that is studied thoroughly in the recent decades. However, since the introduction of the concept of the condition of the order preservation in 2008, there is no inconsistency measure based on the aforementioned condition. Therefore, the aim of this paper is to fill this gap and propose new preference violation indices for measuring violation of the condition of the order preservation. Further, an axiomatic system for the proposed measures is discussed, and it is shown that the proposed indices satisfy uniqueness, invariance under permutation, invariance under inversion of preferences and continuity axioms.</p> <p>&nbsp;</p>

Uncertainty-aware prediction of chemical reaction yields with graph neural networks

In this paper, we present a data-driven method for the uncertainty-aware prediction of chemical reaction yields. The reactants and products in a chemical reaction are represented as a set of molecular graphs. The predictive distribution of the yield is modeled as a graph neural network that directly processes a set of graphs with permutation invariance. Uncertainty-aware learning and inference are applied to the model to make accurate predictions and to evaluate their uncertainty. We demonstrate the effectiveness of the proposed method on benchmark datasets with various settings. Compared to the existing methods, the proposed method improves the prediction and uncertainty quantification performance in most settings.

Extracting Entity Synonymous Relations via Context-Aware Permutation Invariance

Discovering entity synonymous relations is an important work for many entity-based applications. Existing entity synonymous relation extraction approaches are mainly based on lexical patterns or distributional corpus-level statistics, ignoring the context semantics between entities. For example, the contexts around ''apple'' determine whether ''apple'' is a kind of fruit or Apple Inc. In this paper, an entity synonymous relation extraction approach is proposed using context-aware permutation invariance. Specifically, a triplet network is used to obtain the permutation invariance between the entities to learn whether two given entities possess synonymous relation. To track more synonymous features, the relational context semantics and entity representations are integrated into the triplet network, which can improve the performance of extracting entity synonymous relations. The proposed approach is implemented on three real-world datasets. Experimental results demonstrate that the approach performs better than the other compared approaches on entity synonymous relation extraction task.

Categoricity by convention

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic.