Does anyone know/understand the different definitions for Inconsistency(adsbygoogle = window.adsbygoogle || []).push({});

in Sentence Logic and in Predicate Logic?

I know in Sentence Logic, that a sentence ( a Wff, actually) S is

contradictory, if from S we can derive (using theorems of

truth-functional logic ) a sentence of the type A&~A , where '&'

is 'and' and '~' stands for negation, i.e., we assume S, and, using

theorems, we can conclude, using MP, that S->(A&~A).

How do we define contradiction in Predicate Logic, tho? Is it

defined both syntactically and semantically, i.e., do we say

S|- (B&~B) and S|=(B&~B), i.e., we can both derive syntactically

(i.e., have a proof of) B&~B from S, and have a model for S in which

B&~B is true?

Thanks.

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# Inconsistency In Sentence Logic and in Predicate Logic

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