Related papers: Propagators and Solvers for the Algebra of Modular…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
The work we describe here is a part of a research program of developing foundations of declarative solving of search problems. We consider the model expansion task as the task representing the essence of search problems where we are given…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.
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…
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…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
This paper offers an approach to extensible knowledge representation and reasoning for a family of formalisms known as Description Logics. The approach is based on the notion of adding new concept constructors, and includes a heuristic…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Modern neural network architectures still struggle to learn algorithmic procedures that require to systematically apply compositional rules to solve out-of-distribution problem instances. In this work, we focus on formula simplification…
Transformers are effective and efficient at modeling complex relationships and learning patterns from structured data in many applications. The main aim of this paper is to propose and design NLAFormer, which is a transformer-based…
Constraint programming is a family of techniques for solving combinatorial problems, where the problem is modelled as a set of decision variables (typically with finite domains) and a set of constraints that express relations among the…
Despite demonstrating emergent reasoning abilities, Large Language Models (LLMS) often lose track of complex, multi-step reasoning. Existing studies show that providing guidance via decomposing the original question into multiple…
Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to…
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is required to create a user extension for an existing computer…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
In this paper, we show how solutions to explicit algebraic systems lead to solutions to infinite families of modular differential equations.
A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…
Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers.…