Related papers: A Structural and Nominal Syntax for Diagrams
In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and…
This paper shows how DATR, a widely used formal language for lexical knowledge representation, can be used to define an LTAG lexicon as an inheritance hierarchy with internal lexical rules. A bottom-up featural encoding is used for LTAG…
A functional hardware description language enables students to gain a working understanding of computer systems, and to see how the levels of abstraction fit together. By simulating circuits, digital design becomes a living topic, like…
In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial…
Many real-world domains can be expressed as graphs and, more generally, as multi-relational knowledge graphs. Though reasoning and learning with knowledge graphs has traditionally been addressed by symbolic approaches, recent methods in…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
We report on the idea to use colours to distinguish syntax and semantics as an educational tool in logic classes. This distinction gives also reason to reflect on some philosophical issues concerning semantics.
This work establishes a robust mathematical foundation for compositional System Dynamics modeling, leveraging category theory to formalize and enhance the representation, analysis, and composition of system models. Here, System Dynamics…
Despite several (accepted) standards, core notions typically employed in information technology or system engineering architectures lack the precise and exact foundations encountered in logic, algebra, and other branches of mathematics. In…
The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via…
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
Formally verifying the properties of formal systems using a proof assistant requires justifying numerous minor lemmas about capture-avoiding substitution. Despite work on category-theoretic accounts of syntax and variable binding, raw,…
The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
The data for many useful bidirectional constructions in applied category theory (optics, learners, games, quantum combs) can be expressed in terms of diagrams containing "holes" or "incomplete parts", sometimes known as comb diagrams. We…
We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are…
A symmetric monoidal category is a category equipped with an associative and commutative (binary) product and an object which is the unit for the product. In fact, those properties only hold up to natural isomorphisms which satisfy some…
We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…
Syntax connects words to each other in very specific ways. Two words are syntactically connected if they depend directly on each other. Syntactic connections usually happen within a sentence. Gathering all those connection across several…