请输入您要查询的字词:

 

单词 PropositionalLogic
释义

propositional logic


A propositional logicPlanetmathPlanetmath is a logic in which the only objects are propositions, that is, objects which themselves have truth values. Variables represent propositions, and there are no relationsMathworldPlanetmath, functions, or quantifiersMathworldPlanetmath except for the constants T and (representing true and false respectively). The connectivesMathworldPlanetmath are typically ¬, , , and (representing negationMathworldPlanetmath, conjunctionMathworldPlanetmath, disjunctionMathworldPlanetmath, and implicationMathworldPlanetmath), however this set is redundant, and other choices can be used (T and can also be considered 0-ary connectives).

A model for propositional logic is just a truth function ν on a set of variables. Such a truth function can be easily extended to a truth function ν¯ on all formulasMathworldPlanetmath which contain only the variables ν is defined on by adding recursive clauses for the usual definitions of connectives. For instance ν¯(αβ)=T iff ν¯(α)=ν¯(β)=T.

Then we say νϕ if ν¯(ϕ)=T, and we say ϕ if for every ν such that ν¯(ϕ) is defined, νϕ (and say that ϕ is a tautologyMathworldPlanetmath).

Propositional logic is decidable: there is an easy way to determine whether a sentenceMathworldPlanetmath is a tautology. It can be done using truth tablesMathworldPlanetmath, since a truth table for a particular formula can be easily produced, and the formula is a tautology if every assignment of truth values makes it true. It is not known whether this method is efficient: the equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath problem of whether a formula is satisfiableMathworldPlanetmath (that is, whether its negation is a tautology) is a canonical example of an 𝒩𝒫-completePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath problem.

Titlepropositional logic
Canonical namePropositionalLogic
Date of creation2013-03-22 13:04:01
Last modified on2013-03-22 13:04:01
OwnerHenry (455)
Last modified byHenry (455)
Numerical id6
AuthorHenry (455)
Entry typeDefinition
Classificationmsc 03B05
Related topicImplication
Related topicBiconditionalMathworldPlanetmathPlanetmath
Related topicConjunction
Related topicDisjunction
Related topicPropositionalCalculus
Related topicExclusiveOr
Related topicInterpretationOfPropositions
Definesproposition
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/5 2:05:53