相关论文: Identity of Proofs Based on Normalization and Gene…

We analyze the informal notion of truth and conclude that it can be formalized in essentially two distinct ways: constructively, in terms of provability, or classically, as a hierarchy of concepts which satisfy Tarski's biconditional in…

Proof scores can be regarded as outlines of the formal verification of system properties. They have been historically used by the OBJ family of specification languages. The main advantage of proof scores is that they follow the same syntax…

Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over $GF(2)$ in…

For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…

Statisticians are largely focused on developing methods that perform well in a frequentist sense -- even the Bayesians. But the widely-publicized replication crisis suggests that these performance guarantees alone are not enough to instill…

This paper presents experiments on common knowledge logic, conducted with the help of the proof assistant Coq. The main feature of common knowledge logic is the eponymous modality that says that a group of agents shares a knowledge about a…

In the modern Bayesian view classical probability theory is simply an extension of conventional logic, i.e., a quantitative tool that allows for consistent reasoning in the presence of uncertainty. Classical theory presupposes, however,…

In 2018, Stanton proved two types of generalisations of the celebrated Andrews--Gordon and Bressoud identities (in their $q$-series version): one with a similar shape to the original identities, and one involving binomial coefficients. In…

Often in language and other areas of cognition, whether two components of an object are identical or not determine whether it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…

It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…

Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and…

Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…

At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…

Mathematical proofs should be paired with formal proofs, whenever feasible.

We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these…

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…