Related papers: Computational Paths -- An approach in the $LND_{EQ…
${\rm CTT}_{\rm qe}$ is a version of Church's type theory that includes quotation and evaluation operators that are similar to quote and eval in the Lisp programming language. With quotation and evaluation it is possible to reason in ${\rm…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
In order to create a corpus exploration method providing topics that are easier to interpret than standard LDA topic models, here we propose combining two techniques called Entity linking and Labeled LDA. Our method identifies in an…
Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in term…
In this paper, we provide the first practical algorithms with provable guarantees for the problem of inferring the topics assigned to each document in an LDA topic model. This is the primary inference problem for many applications of topic…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Typology is a subfield of linguistics that focuses on the study and classification of languages based on their structural features. Unlike genealogical classification, which examines the historical relationships between languages, typology…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
While large language models (LLMs) have demonstrated remarkable reasoning capabilities, they often struggle with complex tasks that require specific thinking paradigms, such as divide-and-conquer and procedural deduction, \etc Previous…
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Large language models (LLMs) have shown an impressive ability to perform tasks believed to require thought processes. When the model does not document an explicit thought process, it becomes difficult to understand the processes occurring…
We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos…
Optimizing compilers, as well as other translator systems, often work by rewriting expressions according to equivalence preserving rules. Given an input expression and its optimized form, finding the sequence of rules that were applied is a…
Higher-dimensional rewriting systems are tools to analyse the structure of formally reducing terms to normal forms, as well as comparing the different reduction paths that lead to those normal forms. This higher structure can be captured by…
Improving the accessibility of psychotherapy with the aid of Large Language Models (LLMs) is garnering a significant attention in recent years. Recognizing cognitive distortions from the interviewee's utterances can be an essential part of…
In type theory, coinductive types are used to represent processes, and are thus crucial for the formal verification of non-terminating reactive programs in proof assistants based on type theory, such as Coq and Agda. Currently, programming…
Regular Path Queries (RPQs) are a type of graph query where answers are pairs of nodes connected by a sequence of edges matching a regular expression. We study the techniques to process such queries on a distributed graph of data. While…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…