Related papers: A Fixpoint Semantics of Event Systems with and wit…
The paper introduces a knowledge representation language that combines the event calculus with description logic in a logic programming framework. The purpose is to provide the user with an expressive language for modelling and analysing…
The ultimate goal of verification is to guarantee the safety of deployed neural networks. Here, we claim that all the state-of-the-art verifiers we are aware of fail to reach this goal. Our key insight is that theoretical soundness…
Language Models (LMs) have demonstrated exceptional performance across various Natural Language Processing (NLP) tasks. Despite these advancements, LMs can inherit and amplify societal biases related to sensitive attributes such as gender…
Employing Large Language Models (LLM) in various downstream applications such as classification is crucial, especially for smaller companies lacking the expertise and resources required for fine-tuning a model. Fairness in LLMs helps ensure…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…
We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default…
The recent development of fact verification systems with natural logic has enhanced their explainability by aligning claims with evidence through set-theoretic operators, providing faithful justifications. Despite these advancements, such…
It is often argued that one goal of explaining automated decision systems (ADS) is to facilitate positive perceptions (e.g., fairness or trustworthiness) of users towards such systems. This viewpoint, however, makes the implicit assumption…
Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…
We study operations on fixpoint equation systems (FES) over arbitrary complete lattices. We investigate under which conditions these operations, such as substituting variables by their definition, and swapping the ordering of equations,…
To prove liveness properties of concurrent systems, it is often necessary to postulate progress, fairness and justness properties. This paper investigates how the necessary progress, fairness and justness assumptions can be added to or…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An…
In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Fixpoint operators are tools to reason on recursive programs and data types obtained by induction (e.g. lists, trees) or coinduction (e.g. streams). They were given a categorical treatment with the notion of categories with fixpoints. A…
F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and Yablo's can be analyzed with that tool to find graph-theoretic patterns. In this paper we present the F-systems…
Automated Fact-Checking has largely focused on verifying general knowledge against static corpora, overlooking high-stakes domains like law where truth is evolving and technically complex. We introduce CaseFacts, a benchmark for verifying…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…