Related papers: Intrinsic justifications for large-cardinal axioms
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
A new and rapidly growing econometric literature is making advances in the problem of using machine learning methods for causal inference questions. Yet, the empirical economics literature has not started to fully exploit the strengths of…
The aim of this chapter is to present an introduction and also an overview of some of the most relevant results concerning positivity energy theorems in General Relativity. These theorems provide the answer to a long standing problem that…
This paper is directed towards combining Pearl's structural-model approach to causal reasoning with high-level formalisms for reasoning about actions. More precisely, we present a combination of Pearl's structural-model approach with…
The societal and ethical implications of the use of opaque artificial intelligence systems for consequential decisions, such as welfare allocation and criminal justice, have generated a lively debate among multiple stakeholder groups,…
We argue that, although Wittgenstein's reservations on Goedel's interpretation of his own formal reasoning are, indeed, of historical importance, the uneasiness that academicians and philosophers continue to sense, and express, over…
Abstract argumentation provides us with methods such as gradual and Dung semantics with which to evaluate arguments after potential attacks by other arguments. Some of these methods can take intrinsic strengths of arguments as input, with…
We study self-rewarding reasoning large language models (LLMs), which can simultaneously generate step-by-step reasoning and evaluate the correctness of their outputs during the inference time-without external feedback. This integrated…
Inspired by Zermelo's quasi-categoricity result characterizing the models of second-order Zermelo-Fraenkel set theory $\text{ZFC}_2$, we investigate when those models are fully categorical, characterized by the addition to $\text{ZFC}_2$…
In this work we derive important properties regarding matrix invariants which occur in the theory of differential equations with reflection.
This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section 2 presents the traditional…
The purpose of this article is to provide an overall critical appraisal of Integrated Information Theory(IIT) of consciousness. We explore how it has evolved and what problems are involved in the theory. IIT is a hypothesis that…
This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from…
Pearl observes that causal knowledge enables predicting the effects of interventions, such as actions, whereas descriptive knowledge only permits drawing conclusions from observation. This paper extends Pearl's approach to causality and…
We introduce the notion of reflections for selfinjective algebras from the point of view of torsion theories induced by two-term tilting complexes. As an application, we determine the transformations of Brauer trees associated with…
Self-reflection -- the ability of a large language model (LLM) to revisit, evaluate, and revise its own reasoning -- has recently emerged as a powerful behavior enabled by reinforcement learning with verifiable rewards (RLVR). While…
n this paper, we review and connect the three essential conditions needed by the collapse model to achieve a complete and exact formulation, namely the theoretical, the experimental, and the ontological ones. These features correspond to…
Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A"$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement. In 2024, the…
This paper extends the foundational reflection theory of Nichols algebras to the setting of some certain coquasi-Hopf algebras. Our primary motivation arises from the classification of pointed finite-dimensional coquasi-Hopf algebras. We…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…