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We propose Universal Causality, an overarching framework based on category theory that defines the universal property that underlies causal inference independent of the underlying representational formalism used. More formally, universal…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
After building a classifier with modern tools of machine learning we typically have a black box at hand that is able to predict well for unseen data. Thus, we get an answer to the question what is the most likely label of a given unseen…
Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…
As multimodal systems increasingly process sensitive personal data, the ability to selectively revoke specific data modalities has become a critical requirement for privacy compliance and user autonomy. We present Missing-by-Design (MBD), a…
This paper explains why internal and external validity cannot be simultaneously maximised. It introduces "evidential states" to represent the information available for causal inference and shows that routine study operations (restriction,…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
Machine learning is permeating every conceivable domain to promote data-driven decision support. The focus is often on advanced black-box models due to their assumed performance advantages, whereas interpretable models are often associated…
Most modern libraries for regular expression matching allow back-references (i.e., repetition operators) that substantially increase expressive power, but also lead to intractability. In order to find a better balance between expressiveness…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is…
We define LE-ALC, a generalization of the description logic ALC based on the propositional logic of general (i.e. not necessarily distributive) lattices, and semantically interpreted on relational structures based on formal contexts from…
Recursive reasoning systems alternate between acquiring new evidence and refining an accumulated understanding. Two design choices are typically left implicit: how to represent the evolving reasoning state, and when to stop iterating. This…
Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of 'freshness assumptions'; it is not always possible to 'choose a fresh variable…
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos…
This paper introduces an explanation framework designed to enhance the quality of rules in knowledge-based reasoning systems based on dataset-driven insights. The traditional method for rule induction from data typically requires…
We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define…