Introduction to non-classical logics, 2nd edition (Review)
Since this forum regularly becomes embroiled in discussions about logic, I offer this interesting text, written by philosopher Graham Priest. Since it is around 600 pp, I do not pretend to have waded through the whole, but what I have read so far has often been worth my time
Priest addresses both propositional logic (the simplest form of which is typically presented using the familiar truth tables) and quantifiers, usually relying on Smullyan's tableau method. The many topics include modal logic and intuitionistic logic.
Modal logic is handled using Kripke semantics. Here I might have preferred a syntactic approach (due to Boolos?) which makes the Godelian distinction between what is "true" and what is "provable," with "S is necessary" rendered as "S is provable" and "S is possible" rendered as "not-S is not provable," but so far as I can tell this view is not represented in the book: one reason for interest in such a perspective is that Godel produced an arithmetic sentence G satisfying " (G is not necessary) implies G" -- so (in some sense) we believe G because we have no proof of it
In the discussion of intuitionism, the absurdist interpretation of negation (parsing "not-S" as "S implies an absurdity" ) is relegated to a footnote, rather contrary (I think) to Brouwer's original intent; and the suspicion that the law of double-negation is not generally valid seems to me to flow naturally from that interpretation of negation
The book will not be digested in one sitting; but it is fun to read. Various philosophers, at least since the time of Socrates, have made a living by pointing out that our daily language is more muddled than we might like to think; and Priest does not disappoint in this respect: one of my favorite examples so far is the observation that
((A implies B) and (C implies D)) implies ((A implies D) or (C implies B))
is true when "implies" is read as material implication (think of truth tables here!) -- but although
" (If John is in Paris then John is in France) and (If John is in London then John is in England)" sees true enough
it nevertheless seems inappropriate to deduce from this
"Either (If John is in Paris then John is in England) or (If John is in London then John is in France)"
= new reply since forum marked as read
But I finally convinced myself that your deduction (the last proposition) is correct. 
