Related papers: Disjunctions with stopping condition
Counterfactual explanations offer an intuitive and straightforward way to explain black-box models and offer algorithmic recourse to individuals. To address the need for plausible explanations, existing work has primarily relied on…
This paper presents a formal theory of Krivine's classical realisability interpretation for first-order Peano arithmetic ($\mathsf{PA}$). To formulate the theory as an extension of $\mathsf{PA}$, we first modify Krivine's original…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
After highlighting the cases in which the semantics of a language cannot be mechanically reproduced (in which case it is called inherent), the main epistemological consequences of the first incompleteness Theorem for the two fundamental…
Let $(M,\scott X) \models \ACA$ be such that $P_\scott X$, the collection of all unbounded sets in $\scott X$, admits a definable complete ultrafilter and let $T$ be a theory extending first order arithmetic coded in $\scott X$ such that…
Humans can seamlessly reason with circumstantial preconditions of commonsense knowledge. We understand that a glass is used for drinking water, unless the glass is broken or the water is toxic. Despite state-of-the-art (SOTA) language…
This is an exposition of facts about Arithmetic with an approach via mathematical logic. In Section 1 we present Peano Arithmetic, PA, and the complete theory of $\mathbb{N}$, and we show that $\mathbb{N}$ is a prime model of the theory of…
We congratulate the authors on their exciting paper, which introduces a novel idea for assessing the estimation bias in causal estimates. Doubly robust estimators are now part of the standard set of tools in causal inference, but a typical…
The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
Counterfactuals are central in causal human reasoning and the scientific discovery process. The uplift, also called conditional average treatment effect, measures the causal effect of some action, or treatment, on the outcome of an…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…
The paper contains a combinatorial theorem (the sequence of Newton polygons of a reccurent sequence of polynomials is quasi-linear) and two applications of it in classical and quantum topology, namely in the behavior of the $A$-polynomial…
In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model $\mathcal{M}$ of PA (Peano arithmetic) is recursively saturated iff $\mathcal{M}$ has an expansion that satisfies the subsystem…
In the present paper we prove the compactness theorem with respect to partial structures and quasi-truth, using the technique of ultraproducts. Partial structures and quasi-truth are two notions developed within the partial structures…
A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms…
We show confluence of a conditional term rewriting system CL-pc${}^1$, which is an extension of Combinatory Logic by Boolean constants. This solves problem 15 from the RTA list of open problems. The proof has been fully formalised in the…
We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*(L). This paper is a contribution…