Related papers: A proof-theoretic metatheorem for nonlinear semigr…
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
This paper is part of the general project of proof mining, developed by Kohlenbach. By "proof mining" we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs.…
We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research program that aims to obtain the…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
In this paper we apply methods of proof mining to obtain a highly uniform effective rate of asymptotic regularity for the Ishikawa iteration associated to nonexpansive self-mappings of convex subsets of a class of uniformly convex geodesic…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Over extended systems of finite type arithmetic, we utilize a formal representation of the outer measure to define a translation which allows for the systematic formalization of probabilistic statements. As a main result, this translation…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
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 a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…
Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…
Using the functional interpretation from proof theory, we analyze nonconstructive proofs of several central theorems about polynomial and differential polynomial rings. We extract effective bounds, some of which are new to the literature,…
Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate…