Results 281 to 290 of about 2,494,307 (343)

Toward a General Theory of Evidence and Proof: Connecting Legal Skepticism and Reform

What if every rule of evidence is built on a shaky foundation?
Kevin M. Clermont
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A proof theory for generic judgments

ACM Transactions on Computational Logic, 2005
The operational semantics of a computation system is often presented as inference rules or, equivalently, as logical theories. Specifications can be made more declarative and high level if syntactic details concerning bound variables and substitutions are encoded directly into the logic using term-level abstractions (λ-abstraction) and ...
Dale Miller, Alwen Tiu
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A Pattern in Number Theory: Example→ Generalization→ Proof

The Mathematics Teacher, 1971
The study of patterns is an integral part of the study of mathematics. As we teach mathematics, we must point out how to search for patterns and how patterns may aid us in problem solving. The following problem is one that combines patterns, ideas from number theory, and mathematical induction: “Prove that it is possible to pay, without requiring ...
David R. Duncan, Bonnie H. Litwiller
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Computer-generated conjectures(!) and proofs(!!) in combinatorial game theory (abstract only)

ACM Communications in Computer Algebra, 2008
The rapidly growing activity of experimental mathematics is still, to a large extent, a straightforward (albeit far-reaching) extension of the usual mode of paper-and-pencil research, where the pencil just got so much quicker and sharper and the paper so much larger.
Doron Zeilberger, Thotsaporn \\"Aek\\" Thanatipanonda   +1 more
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Generic power of number theory proofs

2022
To design generic proving multiple proof tasks, we use an epistemological tool in which the idea of generic power plays a crucial role. Thanks to a number theory case, we show how it works and then we open the discussion in a didactical way focusing on the Secondary-Tertiary transition.
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Generalization in Type Theory Based Proof Assistants

2002
This paper describes a mechanism to generalize mathematical results in type theory based proof assistants. The proposed mechanism starts from a proved theorem or a proved set of theorems (a theory) and makes it possible to get less specific results that can be instantiated and reused in other contexts.
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On the generation of d-ordered sets: a proof based on determinant theory

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1992
Summary: A \(d\)-ordered set is equivalent to an oriented matroid and thus is important for mathematical applications and theory. A method has been given for generating \(d\)-ordered sets from sets of points in \(\mathbb{R}^{d+1}\). Let \(X\subseteq\mathbb{R}^{d+1}\) be such a set of points, the elements of \(X\) being considered as column vectors. For
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A generalization of the proof of the triviality of scalar field theories

Journal of Mathematical Physics, 1983
The proof of the triviality of φ4 theory in d>4 dimensions is generalized. We show that the triviality of scalar field theories holds for a wide class of potentials.
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Computer-generated conjectures(!) and proofs(!!) in combinatorial game theory (II) (abstract only)

ACM Communications in Computer Algebra, 2008
This will be a follow up talk to my wonderful advisor Doron Zeilberger. People like to make fun of me for playing games. But playing games is fun and helps me do math better. I will give more examples of games and show how computers can make conjectures and prove theorems about them. (Received September 19, 2007).
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A Proof of the Generalized Second-Limit Theorem in the Theory of Probability

Communications in Statistics - Theory and Methods, 2011
Some theorems of q-additive and q-multiplicative functions are presented, where the summation is taken over some arithmetically interesting subsets of the integers.
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