Related papers: Symbolic Languages and Ars Combinatoria
We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions.…
Defining the biperiodic Fibonacci words as a class of words over the alphabet $\{0,1\}$, and two specializations the $k-$Fibonacci and classical Fibonacci words, we provide a self-similar decomposition of these words into overlapping words…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
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…
This paper proposes a novel framework for understanding large language models (LLMs) by reconceptualizing them as semiotic machines rather than as imitations of human cognition. Drawing from structuralist and post-structuralist theories of…
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…
Recent breakthroughs in large language models (LLM) have stirred up global attention, and the research has been accelerating non-stop since then. Philosophers and psychologists have also been researching the structure of language for…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical…
Art, as a universal language, can be interpreted in diverse ways, with artworks embodying profound meanings and nuances. The advent of Large Language Models (LLMs) and the availability of Multimodal Large Language Models (MLLMs) raise the…
In this paper, we further develop the framework of Modular Systems that lays model-theoretic foundations for combining different declarative languages, agents and solvers. We introduce a multi-language logic of modular systems. We define…
Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Latent Semantic Analysis (LSA) was initially conceived by the cognitive psychology at the 90s decade. Since its emergence, the LSA has been used to model cognitive processes, pointing out academic texts, compare literature works and analyse…
Operational semantics have been enormously successful, in large part due to its flexibility and simplicity, but they are not compositional. Denotational semantics, on the other hand, are compositional but the lattice-theoretic models are…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
We outline a class of term-languages for epistemic grounding inspired by Prawitz's theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions.…