Zobrazeno 1 - 10
of 77
pro vyhledávání: '"03A99"'
Autor:
Inoué, Takao, Miwa, Tadayoshi
On March 8, 1995, was found the following nontrivial single axiom-schema characteristic of Le\'{s}niewski-Ishimoto's propositional ontology $\bf L_1$ (refer to Takao Inou\'{e}, A single axiom-schema of March 8th, Bulletin of the Section of Logic (L\'
Externí odkaz:
http://arxiv.org/abs/2402.07030
Autor:
Patrakeev, Mikhail
We construct a formal theory, which we call reflectica, whose language possesses the following properties of natural language: it is a self-reflecting language and an intensional language. By a self-reflecting language we understand an interpreted la
Externí odkaz:
http://arxiv.org/abs/2302.09077
Autor:
Ruelle, David
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyze. In particular the functioning of the hu
Externí odkaz:
http://arxiv.org/abs/2207.00859
Autor:
Bazhenov, Nikolay, Kalociński, Dariusz
Shapiro's notations for natural numbers, and the associated desideratum of acceptability - the property of a notation that all recursive functions are computable in it - is well-known in philosophy of computing. Computable structure theory, however,
Externí odkaz:
http://arxiv.org/abs/2205.00791
Autor:
Barendregt, Henk, Raffone, Antonino
Consciousness will be introduced axiomatically, inspired by Buddhist insight meditation and psychology, logic in computer science, and cognitive neuroscience, as consisting of a stream of $configurations$ that is $compound$, $discrete$, and (non-dete
Externí odkaz:
http://arxiv.org/abs/2202.05700
Autor:
Benci, Vieri
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
Comment: 28 pages
Comment: 28 pages
Externí odkaz:
http://arxiv.org/abs/2111.14162
Autor:
Rabern, Brian, Rabern, Landon
The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what rel
Externí odkaz:
http://arxiv.org/abs/2104.04626
Autor:
Beeson, Michael
Publikováno v:
The American Mathematical Monthly 129 (7), 2022, pp. 623-646
Euclid pioneered the concept of a mathematical theory developed from axioms by a series of justified proof steps. From the outset there were critics and improvers. In this century the use of computers to check proofs for correctness sets a new standa
Externí odkaz:
http://arxiv.org/abs/2103.09623
Autor:
Burke, John R.
In this paper we will develop an axiomatic foundation for the geometric study of straight edge, protractor, and compass constructions, which while being related to previous foundations, will be the first to have all axioms written and all proofs cond
Externí odkaz:
http://arxiv.org/abs/2009.06786
Autor:
Beeson, Michael
Publikováno v:
{B}eitr\"age zur {A}lgebra und {G}eometrie, July 2022
Euclid uses an undefined notion of "equal figures", to which he applies the common notions about equals added to equals or subtracted from equals. When (in previous work) we formalized Euclid Book~I for computer proof-checking, we had to add fifteen
Externí odkaz:
http://arxiv.org/abs/2008.12643