Related papers: Valuations and Metrics on Partially Ordered Sets

In this paper we examine different meaning representations that are commonly used in different natural language applications today and discuss their limits, both in terms of the aspects of the natural language meaning they are modelling and…

This paper will focus on the semantic representation of verbs in computer systems and its impact on lexical selection problems in machine translation (MT). Two groups of English and Chinese verbs are examined to show that lexical selection…

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…

We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

We explore the structure of non-redundant and minimal sets consisting of graded if-then rules. The rules serve as graded attribute implications in object-attribute incidence data and as similarity-based functional dependencies in a…

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type…

An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…

In the past, several works have investigated ways for combining quantitative and qualitative methods in research assessment exercises. In this work, we aim at introducing a methodology to explore whether citation-based metrics, calculated…

In many domains it is desirable to assess the preferences of users in a qualitative rather than quantitative way. Such representations of qualitative preference orderings form an importnat component of automated decision tools. We propose a…

This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a…

Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of…

Randomized mechanisms, which map a set of bids to a probability distribution over outcomes rather than a single outcome, are an important but ill-understood area of computational mechanism design. We investigate the role of randomized…

Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.

While the embedding of words has revolutionized the field of Natural Language Processing, the embedding of concepts has received much less attention so far. A dense and meaningful representation of concepts, however, could prove useful for…

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…

Large Language Models (LLMs) are increasingly expected to handle complex decision-making tasks, yet their ability to perform structured resource allocation remains underexplored. Evaluating their reasoning is also difficult due to data…

Modeling the preferences of agents over a set of alternatives is a principal concern in many areas. The dominant approach has been to find a single reward/utility function with the property that alternatives yielding higher rewards are…

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…