Related papers: When Bi-interpretability implies Synonymy

In this paper, we investigate diagrams, namely functors from any small category to a fixed category, and more particularly, their bisimilarity. Initially defined using the theory of open maps of Joyal et al., we prove several equivalent…

We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in…

The consequences of the theorems about ontological models are studied. "Maximally $\psi$-epistemic" is shown to be equivalent to the conjunction of two other conditions, each of which can be realized in Hilbert spaces of arbitrary…

A large amount of research about multimodal inference across text and vision has been recently developed to obtain visually grounded word and sentence representations. In this paper, we use logic-based representations as unified meaning…

We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…

The Myhill isomorphism is a variant of the Cantor-Bernstein theorem. It states that, from two injections that reduces two subsets of $\mathbb{N}$ to each other, there exists a bijection $\mathbb{N} \to \mathbb{N}$ that preserves them. This…

2-Theories are a canonical way of describing categories with extra structure. 2-theory-morphisms are used when discussing how one structure can be replaced with another structure. This is central to categorical coherence theory. We place a…

This paper builds model-theoretic tools to detect changes in complexity among the simple theories. We develop a generalization of dividing, called shearing, which depends on a so-called context c. This leads to defining c-superstability, a…

Every countable language which conforms to classical logic is shown to have an extension which conforms to classical logic, and has a definitional theory of truth. That extension has a semantical theory of truth, if every sentence of the…

This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…

We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…

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…

Coherence phenomena appear in two different situations. In the context of category theory the term `coherence constraints' refers to a set of diagrams whose commutativity implies the commutativity of a larger class of diagrams. In the…

Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single…

The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional…

As machine learning algorithms getting adopted in an ever-increasing number of applications, interpretation has emerged as a crucial desideratum. In this paper, we propose a mathematical definition for the human-interpretable model. In…

Regular synchronization languages can be used to define rational relations of finite words, and to characterize subclasses of rational relations, like automatic or recognizable relations. We provide a systematic study of the decidability of…

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions…

Layered monoidal theories provide a categorical framework for studying scientific theories at different levels of abstraction, via string diagrammatic algebra. We introduce models for three closely related classes of layered monoidal…

Deep neural networks have been well-known for their superb handling of various machine learning and artificial intelligence tasks. However, due to their over-parameterized black-box nature, it is often difficult to understand the prediction…