Gently Paraconsistent Calculi

Limits for Paraconsistent Calculi

This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa’s hierarchy of increasingly weaker paraconsistent calculi, known as Cn, 1≤ n≤ ω, is carefully studied. The calculus Cω, in particular, constitutes no more than a lower deductive bound to this hierarchy, and differs considerably from its companions. A long standing problem in the lite...

Gently adjusting open doors.

Gently Killing S–spaces

We produce a model of ZFC in which there are no locally compact first countable S–spaces, and in which 2א0 < 2א1 . A consequence of this is that in this model there are no locally compact, separable, hereditarily normal spaces of size א1, answering a question of the second author [9].

Shortest Gently Descending Paths

A path from s to t on a polyhedral terrain is descending if the height of a point p never increases while we move p along the path from s to t. We introduce a generalization of the shortest descending path problem, called the shortest gently descending path (SGDP) problem, where a path descends, but not too steeply. The additional constraint to disallow a very steep descent makes the paths more...

Paraconsistent Assertions

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where inconsistency does not lead to such an explosion. We argue that paraconsistent logics are especially advantageous in order to deal with assertions made by intelligent agents. Other propositional attitudes like knowledge and beliefs can in principle be treated...