Related papers: Reasoning with Intervals on Granules

Deconstructing a time index into time granularities can assist in exploration and automated analysis of large temporal data sets. This paper describes classes of time deconstructions using linear and cyclic time granularities. Linear…

Representing and reasoning about qualitative temporal information is an essential part of many artificial intelligence tasks. Lots of models have been proposed in the litterature for representing such temporal information. All derive from a…

We study sequential interval scheduling when task start and end times are random. The set of tasks and their weights are known in advance, while each task's start and end times are drawn from known discrete distributions and revealed only…

Time-series data is being increasingly collected and stud- ied in several areas such as neuroscience, climate science, transportation, and social media. Discovery of complex patterns of relationships between individual time-series, using…

A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…

The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…

This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

We propose to leverage news discourse profiling to model document-level temporal structures for building temporal dependency graphs. Our key observation is that the functional roles of sentences used for profiling news discourse signify…

The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.

System identification is an important area of science, which aims to describe the characteristics of the system, representing them by mathematical models. Since many of these models can be seen as recursive functions, it is extremely…

Time intervals between purchasing items are a crucial factor in sequential recommendation tasks, whereas existing approaches focus on item sequences and often overlook by assuming the intervals between items are static. However, dynamic…

Answering time-sensitive questions from long documents requires temporal reasoning over the times in questions and documents. An important open question is whether large language models can perform such reasoning solely using a provided…

We present an elementary introduction to a new logic for reasoning about behaviors that occur over time. This logic is based on temporal type theory. The syntax of the logic is similar to the usual first-order logic; what differs is the…

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…

The expressiveness of Metric Temporal Logic (MTL) has been extensively studied throughout the last two decades. In particular, it has been shown that the \emph{interval-based} semantics of MTL is strictly more expressive than the…