Related papers: Definability and Interpolation in Philosophy
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
In a recent paper, Amini et al. introduce a general framework to prove duality theorems between special decompositions and their dual combinatorial object. They thus unify all known ad-hoc proofs in one single theorem. While this…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
Even though Plato's philosophy in ancient times was always closely associated with mathematics, modern Platonic scholarship, during the last five centuries, has moved steadily toward de-mathematization. The present work aims to outline a…
We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.
We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
A logic has uniform interpolation if its formulas can be projected down to given subsignatures, preserving all logical consequences that do not mention the removed symbols; the weaker property of (Craig) interpolation allows the projected…
Concept-based explainability methods provide insight into deep learning systems by constructing explanations using human-understandable concepts. While the literature on human reasoning demonstrates that we exploit relationships between…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
Can humans and artificial intelligences share concepts and communicate? 'Making AI Intelligible' shows that philosophical work on the metaphysics of meaning can help answer these questions. Herman Cappelen and Josh Dever use the externalist…
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
Since the diagonal lemma plays a key role in the proof of the main limitative theorems of logic, its proof could shed light on the very essence of these fundamental theorems. Yet the lemma is often characterized as one of those important…
This paper argues that explainability is only one facet of a broader ideal that shapes our expectations towards artificial intelligence (AI). Fundamentally, the issue is to what extent AI exhibits systematicity--not merely in being…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…