@article {Verdee01022013,
	title = {Strong, universal and provably non-trivial set theory by means of adaptive logic},
	journal = {Logic Journal of the IGPL},
	volume = {21},
	number = {1},
	year = {2013},
	pages = {108-125},
	abstract = {<p>In this article, I present a non-trivial but inconsistent set theory based on unrestricted comprehension. The theory is provably non-trivial and strong enough for most of the applications of regular mathematics. This is realized by distinguishing between strong and weak set membership and allowing for the derivation of strong membership from weak membership whenever this is not problematic (it does not lead to paradoxes). This idea of applying rules whenever unproblematic is formalized by means of an adaptive logic.</p>},
	doi = {10.1093/jigpal/jzs025},
	author = {Verd{\'e}e, Peter}
}
@conference {1859548,
	title = {Strong paraconsistency by separating composition and decomposition in classical logic},
	booktitle = {WoLLIC 2011 Proceedings LNAI Series},
	year = {2011},
	publisher = {Springer},
	organization = {Springer},
	abstract = {<p>In this paper I elaborate a proof system that is able to prove all classical first order logic consequences of consistent premise sets, without proving trivial consequences of inconsistent premises (as in A, {\textlnot}A\,\unmatched{22a2}\,B). Essentially this result is obtained by formally distinguishing consequences that are the result of merely decomposing the premises into their subformulas from consequences that may be the result of also composing {\textquoteleft}new{\textquoteright}, more complex formulas. I require that, whenever {\textquoteleft}new{\textquoteright} formulas are derived, they are to be preceded by a special +-symbol and these +-preceded formulas are not to be decomposed. By doing this, the proofs are separated into a decomposition phase followed by a composition phase. The proofs are recursive, axiomatizable and, as they do not trivialize inconsistent premise sets, they define a very strong non-transitive paraconsistent logic, for which I also provide an adequate semantics.</p>},
	isbn = {364220919X},
	url = {http://dx.doi.org/10.1007/978-3-642-20920-8\_26},
	author = {Verd{\'e}e, Peter},
	editor = {Goebel, R}
}
