Related papers: A Structural and Nominal Syntax for Diagrams
Multilinear Grammar provides a framework for integrating the many different syntagmatic structures of language into a coherent semiotically based Rank Interpretation Architecture, with default linear grammars at each rank. The architecture…
In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
We describe a generic construction of non-wellfounded syntax involving variable binding and its monadic substitution operation. Our construction of the syntax and its substitution takes place in category theory, notably by using monoidal…
We show that contrary to common belief in the DisCoCat community, a monoidal category is all that is needed to define a categorical compositional model of natural language. This relies on a construction which freely adds adjoints to a…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
Properties of morphisms represented by so-called 'string diagrams' of monoidal categories (and their braided and symmetric derivatives), mainly their resistance in value to isotopic deformation, have made the usage of graphical calculi…
In work of Fokkinga and Meertens a calculational approach to category theory is developed. The scheme has many merits, but sacrifices useful type information in the move to an equational style of reasoning. By contrast, traditional proofs…
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
The emergence of a variety of graph-based meaning representations (MRs) has sparked an important conversation about how to adequately represent semantic structure. These MRs exhibit structural differences that reflect different theoretical…
Minimizing finite automata, proving trace equivalence of labelled transition systems or representing sofic subshifts involve very similar arguments, which suggests the possibility of a unified formalism. We propose finite states…
In recent work we have presented a formal framework for linguistic annotation based on labeled acyclic digraphs. These `annotation graphs' offer a simple yet powerful method for representing complex annotation structures incorporating…
Graphs provide a unified representation of semantic content and relational structure, making them a natural fit for domains such as molecular modeling, citation networks, and social graphs. Meanwhile, large language models (LLMs) have…
This paper defines a language L for specifying LFG grammars. This enables constraints on LFG's composite ontology (c-structures synchronised with f-structures) to be stated directly; no appeal to the LFG construction algorithm is needed. We…
In this paper, we study a functional programming approach to natural language semantics, allowing us to increase the expressiveness of a more traditional denotation style. We will formalize a category based type and effect system to…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
Diagrams are common tools for representing complex concepts, relationships and events, often when it would be difficult to portray the same information with natural images. Understanding natural images has been extensively studied in…