In categorical semantics, there have traditionally been two approaches to modelling environments, one by use of finite products in cartesian closed categories, the other by use of the base categories of indexed categories with structure. Each requires modifications in order to account for environments in call-by-value programming languages. There have been two more general definitions along bot...

The classical account for systematicity of human cognition supposes: (1) syntactically compositional representations; and (2) processes that are sensitive to their structure. The problem with this account is that there is no explanation as to why these two components must be compatible, other than by ad hoc assumption (convention) to exclude nonsystematic variants that, e.g., mix prefix and pos...

We give a FST description of nominal and finite verb morphology of Azarbaijani Turkish. We use a hybrid approach where nominal inflection is expressed as a slot-based paradigm and major parts of verb inflection are expressed as optional paths on the FST. We collapse adjective and noun categories in a single nominal category as they behave similarly as far as their paradigms are concerned. Thus,...

In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensions. Rogers’ definitions focussed on a specific representation of higher dimensional trees. This paper pres...

Sharing knowledge across projects is often considered impossible, especially if the systems involved present differences in underlying theory, representation, or even programming language. This paper, taking a collaboration between the CAT2 and PANGLOSS MT projects as an example, demonstrates that it is possible to combine resources developed separately to support the processing of different mo...

An important objective in materials design is to develop a systematic methodology for replacing unavailable or expensive material building blocks by simpler and abundant ones, while maintaining or improving the functionality of the material. The mathematical field of category theory provides a formal specification language which lies at the heart of such a methodology. In this paper, we apply m...

The categorical approach is well-suited for concise definitions of graph transformation concepts. At the same time, it allows for elegant proofs of their properties. We show that these categorical concepts also allow for a similarly simple and modular implementation of graphs and graph transformations by following Rydeheard and Burstall’s idea of Computational Category Theory. We first present ...

In his seminal paper on “Types, Abstraction and Parametric Polymorphism,” John Reynolds called for homomorphisms to be generalized from functions to relations. He reasoned that such a generalization would allow type-based “abstraction” (representation independence, information hiding, naturality or parametricity) to be captured in a mathematical theory, while accounting for higher-order types. ...

Partial information is common in real-world databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit support for nulls. The sketch data model is a recently developed approach to database specification bas...

Geometry of Interaction (GoI) reacts against the absence of any satisfactory explanation for logic. The usual one is that of a symbolic calculus of truth values, which supposes that truth values preexist and formulas as well. This was later improved into a symbolic calculus of category-theoretic diagrams, what is still unsatisfactory: since this calculus rests upon an oriented rewriting, one si...