“Conjunction introduction”的意思、由来-开放百科全书

词条

Conjunction introduction

释义

Formal notation
References

Conjunction introduction (often abbreviated simply as conjunction and also called and introduction)^[1]^[2]^[3] 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's true that it's raining, and it's true that I'm inside, then it's true that "it's raining and I'm inside". The rule can be stated:

where the rule is that wherever an instance of "" and "" appear on lines of a proof, a "" can be placed on a subsequent line.

Formal notation

The conjunction introduction rule may be written in sequent notation:

where is a metalogical symbol meaning that is a syntactic consequence if and are each on lines of a proof in some logical system;

where and are propositions expressed in some formal system.

References

1. ^{{cite book |title=A Concise Introduction to Logic 4th edition |last=Hurley |first=Patrick |authorlink= |coauthors= |year=1991 |publisher=Wadsworth Publishing |location= |isbn= |page= |pages=346–51 |url= |accessdate=}}
2. ^Copi and Cohen
3. ^Moore and Parker

2 : Rules of inference|Theorems in propositional logic

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