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.
There’s a fair bit of natural language work in paraconsistent logics, much along the lines Kai suggests (presupposition by e.g. Sch\”{o}ter and belief by e.g. Konolige). Some suggested refs follow.
Cheers,
David
Andreas Schoter (1995) The Computational Application of Bilattice Logic to Natural Reasoning, PhD Dissertation, University of Edinburgh
Andreas Schöter, Evidential Bilattice Logic and Lexical Inference (1994), Center for Cognitive Science Tech Report EUCCS RP-64, University of Edinbugh
Andreas Schoter and Carl Vogel, editors, Edinburgh Working Papers in Cognitive Science: Nonclassical Feature Systems (1995)
Vogel, C., & Cooper, R. (1995). Robust Chart Parsing with Mildly Inconsistent Feature Structures. In A. Schoter and C. Vogel (Eds.) RANLT 137 Edinburgh Working Papers in Cognitive Science: Nonclassical Feature Systems, Volume 10 (pp. 197-216).
(Don’t remember if the following actually uses paraconsistent logics in the technical sense, but I suspect so.)
Konolige, K., Belief and incompleteness. in: J. R. Hobbs and R. C. Moore (eds.) Formal Theories of the Commonsense World, Ablex Publishing Company, 1985.
I believe here’s also lots of AI work in default and nonmonotonic logic that references or builds on work in paraconsistent logic, and much of this has been applied to natural language. You should ask someone who really knows this stuff, like Rich Thomason, Michael Morreau or Nic Asher.
January 28th, 2004, at 12:01 am #Thank you very much, Mr. Beaver. Your post has been a great help. And I could find at least one
of the aforementioned paper.
However, now the question is locate the whereabouts of Andreas Schöter in the internet, to see if he has done more after the 90´s. If
February 26th, 2004, at 4:18 am #anyone knows his webpage, please let us know.