Related papers: When Bi-interpretability implies Synonymy

The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…

Without the assumption of complete, shared awareness, it is necessary to consider communication between agents who may entertain different representations of the world. A syntactic (language-based) approach provides powerful tools to…

Given two conformal field theories related to each other by a marginal perturbation, and string field theories constructed around such backgrounds, we show how to construct explicit redefinition of string fields which relate these two…

We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…

Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…

A first-order theory T has the Schr\"oder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and…

Interpretability research often adopts a neuron-centric lens, treating individual neurons as the fundamental units of explanation. However, neuron-level explanations can be undermined by superposition, where single units respond to mixtures…

Mechanistic Interpretability aims to understand neural networks through causal explanations. We argue for the Explanatory View Hypothesis: that Mechanistic Interpretability research is a principled approach to understanding models because…

Interpretable deep learning is a fundamental building block towards safer AI, especially when the deployment possibilities of deep learning-based computer-aided medical diagnostic systems are so eminent. However, without a computational…

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…

We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions…

Interpretability research takes counterfactual theories of causality for granted. Most causal methods rely on counterfactual interventions to inputs or the activations of particular model components, followed by observations of the change…

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

We study comparisons between interpretations in description logics with respect to "logical consequences" of the form of semi-positive concepts (like semi-positive concept assertions). Such comparisons are characterized by conditions…

We develop the theory of strong and commutative monads in the 2-dimensional setting of bicategories. This provides a framework for the analysis of effects in many recent models which form bicategories and not categories, such as those based…

The interpretation of anaphors depends on their antecedents as the semantic value that an anaphor eventually conveys is co-specified by the value of its antecedent. Interestingly, when occurring in a given syntactic position, different…