Related papers: Proof identity for mere mortals
Protecting secrets is a key challenge in our contemporary information-based era. In common situations, however, revealing secrets appears unavoidable, for instance, when identifying oneself in a bank to retrieve money. In turn, this may…
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
In some theory development tasks, a problem is satisfactorily solved once it is shown that a theorem (conjecture) is derivable from the background theory (premises). Depending on one's motivations, the details of the derivation of the…
The surge in digitized text data requires reliable inferential methods on observed textual patterns. This article proposes a novel two-sample text test for comparing similarity between two groups of documents. The hypothesis is whether the…
Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…
Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controversy. The intuitionist advocates for a strict notion of…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
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…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and…
The asymptotically optimal hypothesis testing problem with the general sources as the null and alternative hypotheses is studied under exponential-type error constraints on the first kind of error probability. Our fundamental philosophy in…
Established frameworks to understand problems with reproducibility in science begin with the relationship between our understanding of the prior probability of a claim and the statistical certainty that should be demanded of it, and explore…
The quantum analogue of the equality function, known as the quantum state identity problem, is the task of deciding whether $n$ unknown quantum states are equal or unequal, given the promise that all states are either pairwise orthogonal or…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.
In logic there is a clear concept of what constitutes a proof and what not. A proof is essentially defined as a finite sequence of formulae which are either axioms or derived by proof rules from formulae earlier in the sequence.…
A proxy, in general, is an object mediating access to an arbitrary target object. The proxy is then intended to be used in place of the target object. Ideally, a proxy is not distinguishable from other objects. Running a program with a…
A type system combining type application, constants as types, union types (associative, commutative and idempotent) and recursive types has recently been proposed for statically typing path polymorphism, the ability to define functions that…
The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…