Graham Priest

deductively valid inference is one for which there is no situation in which all the premisses are true, but the conclusion is not.

But there are good reasons to suppose that ‘or’ and ‘and’, as they occur in English, are not truth functions – at least, not always.

Again, it is not merely the truth values of the disjuncts that are important, but the existence of a connection of a certain kind between them.