Related papers: Universal properties of truth
We introduce a framework for reasoning about the security of computer systems using modal logic. This framework is sufficiently expressive to capture a variety of known security properties, while also being intuitive and independent of…
We extend to semi-abelian categories the notion of characteristic subobject, which is widely used in group theory and in the theory of Lie algebras. Moreover, we show that many of the classical properties of characteristic subgroups of a…
The theory of stratified institutions is a general axiomatic approach to model theories where the satisfaction is parameterised by states of the models. In this paper we further develop this theory by introducing a new technique for…
Concepts play a central role in many applications. This includes settings where concepts have to be modelled in the absence of sentence context. Previous work has therefore focused on distilling decontextualised concept embeddings from…
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
Conscious experience permeates our daily lives, yet general consensus on a theory of consciousness remains elusive. In the face of such difficulty, an alternative strategy is to address a more general (meta-level) version of the problem for…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
We present the notions of positively complete theory and general forms of amalgamation in the framework of positive logic. We explore the fundamental properties of positively complete theories and study the behaviour of companion theories…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
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…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
In order to ensure the reliability of the explanations of machine learning models, it is crucial to establish their advantages and limits and in which case each of these methods outperform. However, the current understanding of when and how…
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…
One takes advantage of some basic properties of every homotopic $\lambda$-model (e.g.\ extensional Kan complex) to explore the higher $\beta\eta$-conversions, which would correspond to proofs of equality between terms of a theory of…
The predictive performance of any inferential model is critical to its practical success, but quantifying predictive performance is a subtle statistical problem. In this paper I show how the natural structure of any inferential problem…
We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical…