Related papers: Building on the Diamonds between Theories: Theory …
A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…
Combinatorial design theory studies set systems with certain balance and symmetry properties and has applications to computer science and elsewhere. This paper presents a modular approach to formalising designs for the first time using…
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds of applicative system. Each faithful cartesian club…
Advancements in the digital technologies have enabled researchers to develop a variety of Computational Music applications. Such applications are required to capture, process, and generate data related to music. Therefore, it is important…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
The ability to model search in a constraint solver can be an essential asset for solving combinatorial problems. However, existing infrastructure for defining search heuristics is often inadequate. Either modeling capabilities are extremely…
A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for…
Recent progress in time-series forecasting has led to rapidly increasing architectural complexity, yet many reported State-of-the-Art gains are statistically fragile or misattributed. We argue that progress requires a shift from model…
The knowledge of the world is passed on through libraries. Accordingly, domain expertise and experiences should also be transferred within an enterprise by a knowledge base. Therefore, models are an established medium to describe good…
Structuring theories is one of the main approaches to reduce the combinatorial explosion associated with reasoning and exploring large theories. In the past we developed the notion of development graphs as a means to represent and maintain…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a…
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contains unmodified combinatorial solvers. Using the presence of…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
We consider the problem of developing suitable learning representations (embeddings) for library packages that capture semantic similarity among libraries. Such representations are known to improve the performance of downstream learning…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…