Does anyone know/understand the different definitions for Inconsistency 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.