Related papers: Allen's Interval Algebra Makes the Difference
Join-preserving maps on the discrete time scale $\omega^+$, referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps…
We define interval spacing as the difference in the order statistics of data over a gap of some width. We derive its density, expected value, and variance for uniform, exponential, and logistic variates. We show that interval spacing is…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We introduce a new Hopf algebra that operates on pairs of finite interval partitions and permutations of equal length. This algebra captures vincular patterns, which involve specifying both the permutation patterns and the consecutive…
Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs. HEX-programs extend ASP with external atoms for accessing arbitrary external information, which can introduce values that do not…
Constructing datasets representative of the target domain is essential for training effective machine learning models. Active learning (AL) is a promising method that iteratively extends training data to enhance model performance while…
In this note we consider the problem of introducing variables in temporal logic programs under the formalism of "Temporal Equilibrium Logic" (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators.…
Active Learning (AL) aims to enhance the performance of deep models by selecting the most informative samples for annotation from a pool of unlabeled data. Despite impressive performance in closed-set settings, most AL methods fail in…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed.…
In this thesis, we introduce a novel formal framework to represent and reason about qualitative direction and distance relations between extended objects using Answer Set Programming (ASP). We take Cardinal Directional Calculus (CDC) as a…
In this paper we describe a framework for model-based diagnosis of dynamic systems, which extends previous work in this field by using and expressing temporal uncertainty in the form of qualitative interval relations a la Allen. Based on a…
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…
Deductive formalisms have been strongly developed in recent years; among them, Answer Set Programming (ASP) gained some momentum, and has been lately fruitfully employed in many real-world scenarios. Nonetheless, in spite of a large number…
By the example of the proof of Minkowski's conjecture on critical determinant we give a category theory framework for interval computation.
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces…
We present a hierarchical framework for analysing propositional linear-time temporal logic (PTL) to obtain standard results such as a small model property, decision procedures and axiomatic completeness. Both finite time and infinite time…
In the design of integrated circuits, one critical metric is the maximum delay introduced by combinational modules within the circuit. This delay is crucial because it represents the time required to perform a computation: in an…
The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor.…