Related papers: Axiomatizing Rumsfeld Ignorance
Explaining autonomous and intelligent systems is critical in order to improve trust in their decisions. Counterfactuals have emerged as one of the most compelling forms of explanation. They address ``why not'' questions by revealing how…
This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit…
FAIR data presupposes their successful communication between machines and humans while preserving their meaning and reference, requiring all parties involved to share the same background knowledge. Inspired by English as a natural language,…
Much artificial intelligence research focuses on the problem of deducing the validity of unobservable propositions or hypotheses from observable evidence.! Many of the knowledge representation techniques designed for this problem encode the…
The undecidability of basic decision problems for general FIFO machines such as reachability and unboundedness is well-known. In this paper, we provide an underapproximation for the general model by considering only runs that are…
Artificial Intelligence (AI) has become an integral part of domains such as security, finance, healthcare, medicine, and criminal justice. Explaining the decisions of AI systems in human terms is a key challenge--due to the high complexity…
It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various…
Instruction fine-tuning (IFT) can increase the informativeness of large language models (LLMs), but may reduce their truthfulness. This trade-off arises because IFT steers LLMs to generate responses containing long-tail knowledge that was…
We study first-order logic (FO) over the structure consisting of finite words over some alphabet $A$, together with the (non-contiguous) subword ordering. In terms of decidability of quantifier alternation fragments, this logic is…
Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Everyday activities performed by artificial assistants can potentially be executed naively and dangerously given their lack of common sense knowledge. This paper presents conceptual work towards obtaining prior knowledge on the usual…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…
In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in (Kontinen and Vaananen 2013) and (Hannula 2015). We prove a characterization…
Traditional learning approaches for classification implicitly assume that each mistake has the same cost. In many real-world problems though, the utility of a decision depends on the underlying context $x$ and decision $y$. However,…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
Numerous approaches have been recently proposed for learning fair representations that mitigate unfair outcomes in prediction tasks. A key motivation for these methods is that the representations can be used by third parties with unknown…
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it…