Paraconsistent Semantics for Natural Language?

Reader Antonio Marmo writes with a request:

bq. I do miss a paraconsistent approach of natural language semantics. This is a branch of logic that, more than 30 years after it started, has grown for the last 12 years. My question to you is whether you know some linguists working with these ideas in formal linguistics. I have browsed the web and could not find anyone yet.

I have to say that I have not really run across any work in linguistic semantics which employs “paraconsistent logic”:http://plato.stanford.edu/entries/logic-paraconsistent/. The only paper dealing with it that I myself ever read was David Lewis’ “Logic for Equivocators” (Noûs 16 (1982), pp 431–441), which is reprinted in his “Papers in Philosophical Logic”:http://tinyurl.com/2asxg. Other promising places to check out are Greg Restall’s list of publications and an interesting looking paper by Achille Varzi: “Inconsistency Without Contradiction”, Notre Dame Journal of Formal Logic, 38:4 (1997), 621–638 (”preprint pdf”:http://www.columbia.edu/~av72/papers/Ndjfl_1997.pdf).

But of course these are all references in the realm of philosophy. As I said, I don’t know of any specifically linguistic work in this area, although it would seem that especially in the area of propositional attitude semantics, we all have to deal with the fact that real people hold inconsistent beliefs without having their brains suffer the kind of melt-down supercomputing intelligences on Star Trek usually experience when Captain Kirk feeds them contradictory statements.

My suspicion is that most of us imagine that we can get away with having the semantics presuppose a consistent belief state and appealing to mechanisms like paraconsistent logic or supervaluation strategies to explain how attitude descriptions manage to be at least sort of true of actual people. At some point, I thought about using something like paraconsistent logic directly in the semantics for desire predicates, where it seems more of a stretch to presuppose consistency. But I never pursued this line in any detail.

Anyway, if anyone has a pointer to linguistic semantic work employing paraconsistent logics or relatives thereof, please let us know in the comments. Antonio (and I) would be grateful.