Related papers: Hallucination, abstention, and computable insepara…
We study the problem of deciding whether a point escapes a closed subset of $\mathbb{R}^d$ under the iteration of a continuous map $f \colon \mathbb{R}^d \to \mathbb{R}^d$ in the bit-model of real computation. We give a sound partial…
Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with…
Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…
Large language models (LLMs) often generate reasoning traces that appear coherent but rest on unsupported assumptions, leading to hallucinated conclusions. Prior work mainly addresses factual hallucinations or relies on post-hoc…
Plausible, but inaccurate, tokens in model-generated text are widely believed to be pervasive and problematic for the responsible adoption of language models. Despite this concern, there is little scientific work that attempts to measure…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
Contemporary Language Models (LMs), while impressively fluent, often generate content that is factually incorrect or unfaithful to the input context - a critical issue commonly referred to as 'hallucination'. This tendency of LMs to…
Large language models (LLMs) are increasingly being adopted as the cognitive core of embodied agents. However, inherited hallucinations, which stem from failures to ground user instructions in the observed physical environment, can lead to…
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
We introduce a set of eight universal Rules of Inference by which computer programs with known properties (axioms) are transformed into new programs with known properties (theorems). Axioms are presented to formalize a segment of Number…
Despite their remarkable progress in multimodal understanding tasks, large vision language models (LVLMs) often suffer from "hallucinations", generating texts misaligned with the visual context. Existing methods aimed at reducing…
Large Reasoning Models (LRMs) have shown impressive capabilities in multi-step reasoning tasks. However, alongside these successes, a more deceptive form of model error has emerged--Reasoning Hallucination--where logically coherent but…
The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard…
The way a rational agent changes her belief in certain propositions/hypotheses in the light of new evidence lies at the heart of Bayesian inference. The basic natural assumption, as summarized in van Fraassen's Reflection Principle…
Abductive reasoning generates explanatory hypotheses for new observations using prior knowledge. This paper investigates the use of forgetting, also known as uniform interpolation, to perform ABox abduction in description logic (ALC)…
The widespread adoption of large language models (LLMs) across diverse AI applications is proof of the outstanding achievements obtained in several tasks, such as text mining, text generation, and question answering. However, LLMs are not…
Large language models (LLMs) frequently generate hallucinations-content that deviates from factual accuracy or provided context-posing challenges for diagnosis due to the complex interplay of underlying causes. This paper introduces a…