Related papers: Instantiation Schemes for Nested Theories
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied…
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…
Motivated by gene set enrichment analysis, we investigate the problem of combined hypothesis testing on a graph. We introduce a general framework to effectively use the structural information of the underlying graph when testing…
Within the area of computational models of argumentation, the instantiation-based approach is gaining more and more attention, not at least because meaningful input for Dung's abstract frameworks is provided in that way. In a nutshell, the…
The growing AI field faces trust, transparency, fairness, and discrimination challenges. Despite the need for new regulations, there is a mismatch between regulatory science and AI, preventing a consistent framework. A five-layer nested…
The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to inductive proofs as commonly done by mathematicians. For this purpose, we provide a reasonably direct justification for coinductive proofs…
In this paper, we introduce the concept of a nested family of torsion pairs and will prove that this concept is strongly related to the existence of stratifying systems. Specifically, every stratifying system induces a nested family of…
In this paper, we have established a general framework of multistage hypothesis tests which applies to arbitrarily many mutually exclusive and exhaustive composite hypotheses. Within the new framework, we have constructed specific…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
Nested sampling is a promising tool for Bayesian statistical analysis because it simultaneously performs parameter estimation and facilitates model comparison. MultiNest is one of the most popular nested sampling implementations, and has…
This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…
Over the past several years Bayesian networks have been applied to a wide variety of problems. A central problem in applying Bayesian networks is that of finding one or more of the most probable instantiations of a network. In this paper we…
We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as…
Computer experiments can emulate the physical systems, help computational investigations, and yield analytic solutions. They have been widely employed with many engineering applications (e.g., aerospace, automotive, energy systems.…
Quantified formulas pose a significant challenge for Satisfiability Modulo Theories (SMT) solvers due to their inherent undecidability. Existing instantiation techniques, such as e-matching, syntax-guided, model-based, conflict-based, and…
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience developing the theorem prover Vampire. We describe the techniques we currently employ to…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…