标签：predicate logical logic conjunction true order
- junction [Origin: junctio, from jungere; JOIN] a place where one road, track etc joins another =intersection
- con- [Origin: com-] together; with
Conjunction may refer to:
- Conjunction (astronomy), in which two astronomical bodies appear close together in the sky
- Conjunction (astrology), astrological aspect in horoscopic [占星术的] astrology
- Conjunction (grammar), a part of speech [词性]
- Logical conjunction, a mathematical operator
- Conjunction introduction, a rule of inference of propositional logic
Conjunctions: Grammar Rules and Examples
Conjunctions are words that link other words, phrases, or clauses together. For example, in "I like cooking and eating, but I don’t like washing dishes afterward. Sophie is clearly exhausted, yet she insists on dancing till dawn," the words in bold type are conjuctions. Conjunctions allow you to form complex, elegant sentences and avoid the choppiness of multiple short sentences. Make sure that the phrases joined by conjunctions are parallel (share the same structure).
In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true. An operand of a conjunction is a conjunct.
3 + 5 是个表达式(expression)，3和5都是operand(操作数; 运算对象; 运算元; 运算数)，+是operator(运算符; 操作符).
Beyond logic, the term "conjunction" also refers to similar concepts in other fields:
- In programming languages, the short-circuit and control structure. 在C语言里，if (0 && (a < b))...，(a < b)不会被evaluate.
- In set theory, intersection.
- In lattice theory, logical conjunction (greatest lower bound).
- In predicate logic, universal quantification.
- 格论中的一个概念。偏序关系
A universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("∀x", "∀(x)", or sometimes by "(x)" alone). Universal quantification is distinct from existential quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. An existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)").
First-order logic - also known as predicate logic, quantificational logic, and first-order predicate calculus - is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
The adjective "first-order" distinguishes first-order logic from higher-order logic, in which there are predicates having predicates or functions as arguments, or in which one or both of predicate quantifiers or function quantifiers are permitted. In first-order theories, predicates are often associated with sets. In interpreted higher-order theories, predicates may be interpreted as sets of sets. Gérard Huet has shown that unifiability is undecidable in a type theoretic flavor of third-order logic, that is, there can be no algorithm to decide whether an arbitrary equation between third-order (let alone arbitrary higher-order) terms has a solution.
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition p is true, and proposition q is true, then the logical conjunction of the two propositions p and q is true. For example, if it is true that "it's raining", and it is true that "I'm inside", then it is true that "it's raining and I'm inside".
六级/考研单词: junction, conjunction, astronomy, logic, mathematics, infer, exhaust, dawn, bold, elegant, multiple, parallel, linguistic, evaluate, bind, quantify, interpret, domain, discourse, denote, invariable, assert, compute, adjective, seldom, flavor, arbitrary, equate, abbreviation, valid
标签：predicate,logical,logic,conjunction,true,order 来源： https://www.cnblogs.com/funwithwords/p/16587968.html
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