Related papers: Logic of fusion
To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
The theorem of factorisation forests shows the existence of nested factorisations -- a la Ramsey -- for finite words. This theorem has important applications in semigroup theory, and beyond. The purpose of this paper is to illustrate the…
This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an…
Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information which instances…
In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of resources---a form of state transition system---to describe the state-based program…
Parametricity states that polymorphic functions behave the same regardless of how they are instantiated. When developing polymorphic programs, Wadler's free theorems can serve as free specifications, which can turn otherwise partial…
Based on laboratory based growth of plant-like structures from inorganic materials, we present new theory for the emergence of plant structure at a range of scales dictated by levels of ionization (charge density), which can be traced…
Image fusion aims to combine complementary information from multiple source images to generate more comprehensive scene representations. Existing methods primarily rely on the stacking and design of network architectures to enhance the…
We present a generic way to hybridize physical and data-driven methods for predicting physicochemical properties. The approach `distills' the physical method's predictions into a prior model and combines it with sparse experimental data…
In the recent past, the reduction-based and the model-based methods to prove cut elimination have converged, so that they now appear just as two sides of the same coin. This paper details some of the steps of this transformation.
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
We give a definition of coisotropic morphisms of shifted Poisson (i.e. $P_n$) algebras which is a derived version of the classical notion of coisotropic submanifolds. Using this we prove that an intersection of coisotropic morphisms of…
Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On…
This paper presents a general method for combining uncertain and paradoxical source of evidences for a wide class of fusion problems. From the foundations of the Dezert-Smarandache Theory (DSmT) we show how the DSm rule of combination can…
The logic of bunched implications (BI) is a substructural logic that forms the backbone of separation logic, the much studied logic for reasoning about heap-manipulating programs. Although the proof theory and metatheory of BI are…