Related papers: Datatype defining rewrite systems for naturals and…
The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to…
In this paper we study two operations, Pasting and Reversing, defined from a natural way to be applied over some rings such as the ring of polynomials and the ring of linear differential operators, which is a differential ring. We obtain…
Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence…
This paper describes the Direct Fourier Permuation Algorithm, an efficient method of computing Bit Reversal of natural indices [1, 2, 3, ..., 2^k] in a vectorial manner (k iterations) and also proposes the Vectorial Digit Reversal…
Data trees serve as an abstraction of structured data, such as XML documents. A number of specification formalisms for languages of data trees have been developed, many of them adhering to the paradigm of register automata, which is based…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
In the theory of species, differential as well as integral operators are known to arise in a natural way. In this paper, we shall prove that they precisely fit together in the algebraic framework of integro-differential rings, which are…
A derivative structure is a nonequivalent substitutional atomic configuration derived from a given primitive cell. The enumeration of derivative structures plays an essential role in searching for the ground states in multicomponent…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Reaction Systems (RSs) are a successful computational framework inspired by biological systems. A RS pairs a set of entities with a set of reactions over them. Entities can be used to enable or inhibit each reaction, and are produced by…
String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout…
The sequential recommender (SR) system is a crucial component of modern recommender systems, as it aims to capture the evolving preferences of users. Significant efforts have been made to enhance the capabilities of SR systems. These…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Session types statically prescribe bidirectional communication protocols for message-passing processes and are in a Curry-Howard correspondence with linear logic propositions. However, simple session types cannot specify properties beyond…
With the rise of AI-enabled cyber-physical systems, data annotation has become a critical yet often overlooked process in the development of these intelligent information systems. Existing work in requirements engineering (RE) has explored…
A lens is a single program that specifies two data transformations at once: one transformation converts data from source format to target format and a second transformation inverts the process. Over the past decade, researchers have…
We present two ways in which an infinite universal alphabet may be generated using a novel rewrite system that conserves zero (a special character of the alphabet and the symbol for that character) at every step. The recursive method…
Declarative Distributed Systems (DDSs) are distributed systems grounded in logic programming. Although DDS model-checking is undecidable in general, we detect decidable cases by tweaking the data-source bounds, the message expressiveness,…
In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…
Since Val Tannen's pioneer work on the combination of simply-typed lambda-calculus and first-order rewriting (LICS'88), many authors have contributed to this subject by extending it to richer typed lambda-calculi and rewriting paradigms,…