Related papers: The Modal Logic of Abstraction Refinement
The Abstraction Refinement Model has been widely adopted since it was firstly proposed many decades ago. This powerful model of software evolution process brings important properties into the system under development, properties such as the…
Large Language Models (LLMs) have demonstrated remarkable progress in reasoning across diverse domains. However, effective reasoning in real-world tasks requires adapting the reasoning strategy to the demands of the problem, ranging from…
The Abstraction and Reasoning Corpus (ARC) provides a compact laboratory for studying abstract reasoning, an ability central to human intelligence. Modern AI systems, including LLMs and ViTs, largely operate as sequence-of-behavior…
The notion of abstract Boehm tree has arisen as an operationally-oriented distillation of works on game semantics, and has been investigated in two papers. This paper revisits the notion, providing more syntactic support and more examples…
Abstraction is a desirable capability for deep learning models, which means to induce abstract concepts from concrete instances and flexibly apply them beyond the learning context. At the same time, there is a lack of clear understanding…
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…
We give thread-modular non-relational value analyses as abstractions of a local trace semantics. The semantics as well as the analyses are formulated by means of global invariants and side-effecting constraint systems. We show that a…
Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
Designing controllers to satisfy temporal requirements has proven to be challenging for dynamical systems that are affected by uncertainty. This is mainly due to the states evolving in a continuous uncountable space, the stochastic…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as…
This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…
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…
Saliency post-hoc explainability methods are important tools for understanding increasingly complex NLP models. While these methods can reflect the model's reasoning, they may not align with human intuition, making the explanations not…
In this paper we consider the problem of configuring partial predicate abstraction that combines two techniques that have been effective in analyzing infinite-state systems: predicate abstraction and fixpoint approximations. A fundamental…
Abstraction is one of the most important strategies for dealing with the state space explosion problem in model checking. In the abstract model, although the state space is largely reduced, however, a counterexample found in such a model…
Reasoning about functions that operate over algebraic data types is an important problem for a large variety of applications. One application of particular interest is network applications that manipulate or reason about complex message…