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axiom.scroll
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import ../code/conceptPage.scroll
id axiom
name AXIOM
appeared 1992
tags pl
documentation https://axm.dev/language.html
rosettaCode http://www.rosettacode.org/wiki/Category:Axiom
centralPackageRepositoryCount 0
country United States
originCommunity IBM
reference https://semanticscholar.org/paper/5aa0cc98cc623c61d77cd900dbacc21d921152a3
wikipedia https://en.wikipedia.org/wiki/Axiom
summary An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning.As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), often shown in symbolic form, while non-logical axioms (e.g., a + b = b + a) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain. Any axiom is a statement that serves as a starting point from which other statements are logically derived. Whether it is meaningful (and, if so, what it means) for an axiom to be "true" is a subject of debate in the philosophy of mathematics.
backlinksCount 1197
pageId 928
dailyPageViews 994
created 2001
appeared 1964
hopl https://hopl.info/showlanguage.prx?exp=1673
isbndb 0
semanticScholar 6
year|title|doi|citations|influentialCitations|authors|paperId
1979|Programming Language Constructs for Which It Is Impossible To Obtain Good Hoare Axiom Systems|10.1145/322108.322121|163|7|E. Clarke|ab700e484d9874228ae428fc2edaf89b6ca278f4
1977|Programming language constructs for which it is impossible to obtain good hoare-like axiom systems|10.1145/512950.512952|52|1|E. Clarke|697fdb7fa9bed25e8fcb498b501697597f409cc7
1984|A good Hoare axiom system for an ALGOL-like language|10.1145/800017.800538|20|0|Joseph Y. Halpern|3c678b7e2829a743f28feb356f21f6415716d006
1992|Computation of the Jordan canonical form of a square matrix (using the Axiom programming language)|10.1145/143242.143295|10|1|I. Gil|7a72bdb20f9ea1e1ade90be6668d5abe067a70e0
2016|Verifying safety critical task scheduling systems in PPTL axiom system|10.1007/s10878-014-9776-3|6|0|N. Zhang and Mengfei Yang and B. Gu and Zhenhua Duan and Cong Tian|f4e6fb0d23cdab55e02ce3cf7d310ad073850cd4
1994|How to make AXIOM into a scratchpad|10.1145/190347.190357|5|0|R. Jenks and B. Trager|5aa0cc98cc623c61d77cd900dbacc21d921152a3