相关论文: Why prove things?

We introduce the concept of protometric and present some properties of protometrics.

The import of Bell's Theorem is elucidated. The theorem's proof is illustrated both heuristically and in mathematical detail in a pedagogical fashion. In the same fashion, it is shown that the proof is correct mathematically, but it doesn't…

A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the…

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…

Part of the theoretical motivation for improving the present level of testing of the equivalence principle is reviewed. The general rationale for optimizing the choice of pairs of materials to be tested is presented. One introduces a…

These notes pose a "proof challenge": a proof, or disproof, of the proposition that "For any given body of information, I, expressed as a one-dimensional sequence of atomic symbols, a multiple alignment concept, described in the document,…

The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

We study the proof scheme "proof by example" in which a general statement can be proved by verifying it for a single example. This strategy can indeed work if the statement in question is an algebraic identity and the example is "generic".…

This communication contributes to research on proof validation as a lens for uncovering didactical phenomena related to proof and proving. We revisit the puzzling case of lower secondary students in France who validate circular proofs. That…

This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…

The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…

Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.

We analyze the informal semantic conception of proof and axiomatize the proof relation and the provability operator. A self referential propositional calculus which admits provable liar type sentences is introduced and proven consistent. We…