Related papers: On formal concepts of random formal contexts
Machines that can replicate human intelligence with type 2 reasoning capabilities should be able to reason at multiple levels of spatio-temporal abstractions and scales using internal world models. Devising formalisms to develop such…
We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…
We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…
We introduce a new framework for creating point-wise confidence intervals for the distribution of event times for current status data. Existing methods are based on asymptotics. Our framework is based on binomial properties and motivates…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
Simple representations of documents based on the occurrences of terms are ubiquitous in areas like Information Retrieval, and also frequent in Natural Language Processing. In this work we propose a logical-probabilistic approach to the…
Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following…
This paper develops the model theory of normal modal logics based on partial "possibilities" instead of total "worlds," following Humberstone (1981) instead of Kripke (1963). Possibility semantics can be seen as extending to modal logic the…
Defeasible reasoning is a kind of reasoning where some generalisations may not be valid in all circumstances, that is general conclusions may fail in some cases. Various formalisms have been developed to model this kind of reasoning, which…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take…
With the widespread dissemination of user-generated content on different social networks, and online consumer systems such as Amazon, the quantity of opinionated information available on the Internet has been increased. One of the main…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
With the growing popularity of general-purpose Large Language Models (LLMs), comes a need for more global explanations of model behaviors. Concept-based explanations arise as a promising avenue for explaining high-level patterns learned by…
We study the maximum of the random assignment process on rectangular matrices. We derive first-order asymptotics for the expected maximum, prove a law of large numbers under mild tail assumptions, and obtain exponential upper bounds for the…
Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
This paper aims to expand and detail the notion of formal semantics of Conjectures by applying a theoretic-model approach. After a short introduction to the concepts and basics of Conjectures, we will start from the notion of Simple…