Proof and entailment

Hello,

I'm asked in an assignment to define in a few words
the relationship between "proof" and "entailment".

Here is the skeleton of my answer:

I think entailment is another name for implication.

In logic, a proof is obtained from axioms and rules
of inference.

These axioms can be combined using tools such as
disjunction and conjunction to IMPLY new proofs.

So, entailment is a central tool in producing proofs...

Can you tell me if I'm going the right way ?

Thanks !


.

Relevant Pages

  • Re: Proof and entailment
    ... I think entailment is another name for implication. ... a proof is obtained from axioms and rules ... I'd say that 'entailment' is the inverse of 'logical consequence'. ... Now, if A entails B, then there is in principle a possible proof of B ...
    (sci.logic)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... very very basic difference between consistency and entailment. ... What happens if I say that are the _only_ axioms, ... Then implementable set theory is the set of sentences, in the language ...
    (sci.math)
  • Re: Axioms & quantification
    ... we would expect and want it to be (infer AxP from gamma where gamma ... his logical axioms: the result of prefixing arbitrarily many universal ... formulas closed under entailment, right?). ... that the axioms are all closures of the schemata listed (where 'psi is ...
    (sci.logic)
  • Re: Am I a crank?
    ... is the absence of logical inconsistency between them and their axioms ... long as the axioms are consistent). ... difference between entailment and consistency indicates again your lack ... claims you make without however demonstrating their truth. ...
    (sci.math)
  • Re: Am I a crank?
    ... is the absence of logical inconsistency between them and their axioms ... and not truth. ... long as the axioms are consistent). ... difference between entailment and consistency indicates again your lack ...
    (sci.math)