相关论文: Graph-Based Logic and Sketches 1: The General Fram…

The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…

We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…

The theory of limits of discrete combinatorial objects has been thriving for the last decade or so. The syntactic, algebraic approach to the subject is popularly known as "flag algebras", while the semantic, geometric one is often…

Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…

Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…

There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…

A program is usually represented as a word chain. It is exactly a word chain that appears as the lexical analyzer output and is parsed. The work shows that a program can be syntactically represented as an oriented word tree, that is a…

We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…

What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman…

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…

Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…

Scene graph is a structured representation of a scene that can clearly express the objects, attributes, and relationships between objects in the scene. As computer vision technology continues to develop, people are no longer satisfied with…

Graph-matching metrics such as Smatch are the de facto standard for evaluating neural semantic parsers, yet they capture surface overlap rather than logical equivalence. We reassess evaluation by pairing graph-matching with automated…

Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…

The present article is the first of a series whose goal is to define a logical formalism in which it is possible to reason about genetics. In this paper, we introduce the main concepts of our language whose domain of discourse consists of a…

We present a formal semantics and proof of soundness for shapes schemas, an expressive schema language for RDF graphs that is the foundation of Shape Expressions Language 2.0. It can be used to describe the vocabulary and the structure of…

In software system design, one of the purposes of diagrammatic modeling is to explain something (e.g., data tables) to others. Very often, syntax of diagrams is specified while the intended meaning of diagrammatic constructs remains…

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…