Related papers: Bounded arithmetic AID for Frege system
Recent developments in Artificial Intelligence (AI) and their applications in critical industries such as healthcare, fin-tech and cybersecurity have led to a surge in research in explainability in AI. Innovative research methods are being…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and…
We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the…
We study cyclic proof systems for $\mu\mathsf{PA}$, an extension of Peano arithmetic by positive inductive definitions that is arithmetically equivalent to the (impredicative) subsystem of second-order arithmetic $\Pi^1_2$-$\mathsf{CA}_0$…
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a…
We present Bournemouth Forced Aligner (BFA), a system that combines a Contextless Universal Phoneme Encoder (CUPE) with a connectionist temporal classification (CTC)based decoder. BFA introduces explicit modelling of inter-phoneme gaps and…
This paper introduces the SEQ BIN meta-constraint with a polytime algorithm achieving general- ized arc-consistency according to some properties. SEQ BIN can be used for encoding counting con- straints such as CHANGE, SMOOTH or INCREAS- ING…
We present a version of arithmetic in all finite types which allows for a definition of equality at higher types for which all congruence are derivable, for which the soundness of the Dialectica interpretation is provable inside the system…
Automatic theorem proving with deep learning methods has attracted attentions recently. In this paper, we construct an automatic proof system for trigonometric identities. We define the normalized form of trigonometric identities, design a…
Confidence sequences based on test martingales provide time-uniform uncertainty quantification for the mean of bounded IID observations without parametric distributional assumptions. Their practical efficiency, however, depends strongly on…
This thesis develops a framework for formalizing reasoning about specifications of systems written in LF. This formalization centers around the development of a reasoning logic that can express the sorts of properties which arise in…
Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods either focus on theorem-only NL-to-FL…
Large Audio Language Models (LALMs) have garnered significant research interest. Despite being built upon text-based large language models (LLMs), LALMs frequently exhibit a degradation in knowledge and reasoning capabilities. We…
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
These notes present a compact and self-contained approach to iterated forcing with a particular emphasis on semiproper forcing. We tried to make our presentation accessible to any scholar who has some familiarity with forcing and boolean…
Large language models (LLMs) have emerged as a powerful foundation for intelligent reasoning and decision-making, demonstrating substantial impact across a wide range of domains and applications. However, their massive parameter scales and…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…