Related papers: The Mathematical Abstraction Theory, The Fundament…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…
Drori et al. (2022) report that "A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level ... [It] automatically answers 81\% of university-level mathematics…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
Whereas distributed computing research has been very successful in exploring the solvability/impossibility border of distributed computing problems like consensus in representative classes of computing models with respect to model…
Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of…
The field of artificial intelligence (AI) represents an enormous endeavour of humankind that is currently transforming our societies down to their very foundations. Its task, building truly intelligent systems, is underpinned by a vast…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
We present a methodology for formulating simplifying abstractions in machine learning systems by identifying and harnessing the utility structure of decisions. Machine learning tasks commonly involve high-dimensional output spaces (e.g.,…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
In this paper, we propose a generalizable knowledge framework for data abstraction, i.e. finding compact abstract model for input data using predefined abstract terms. Based on these abstract terms, intelligent autonomous systems, such as a…
Machine learning about language can be improved by supplying it with specific knowledge and sources of external information. We present here a new version of the linked open data resource ConceptNet that is particularly well suited to be…
While abstraction is a classic tool of verification to scale it up, it is not used very often for verifying neural networks. However, it can help with the still open task of scaling existing algorithms to state-of-the-art network…
The ability to think abstractly and reason by analogy is a prerequisite to rapidly adapt to new conditions, tackle newly encountered problems by decomposing them, and synthesize knowledge to solve problems comprehensively. We present…
For half a century, artificial intelligence research has attempted to reproduce the human qualities of abstraction and reasoning - creating computer systems that can learn new concepts from a minimal set of examples, in settings where…