AI Seminar, 2nd November 2006, 13.15

Mikael Asker, AI@CS, LU & Axis

IMPROVING ACTIVE CONSEQUENCE

Active consequence is a semantically defined consequence relation for
active logics.  It has recently been shown that active consequence is
not paraconsistent, contrary to the expectations. In this paper we
study a subset of the active consequence, local consequence, which
turns out to be paraconsistent.  The relation between local
consequence and classical logic is investigated by first observing
that the active modus ponens rule is locally unsound.  But the part of
the consequence relation generated by that rule which is outside local
consequence is exactly that part where the premises are inconsistent.
We propose the name semantic residual for this part, and interpret it
as a reflection of artefacts in the proof theory.  The residual must
be included in the semantic consequence relation to achieve soundness.