Drawing Sound Conclusions from Unsound Premises

Details Drawing Sound Conclusions from Unsound Premises Drawing Sound Conclusions from Unsound Premises

2011-09-05

arxiv.org/abs/1109.0915v1

Computer Science

Logic in Computer Science

Scientific paper

Given sets $\Phi_1=\{\phi_{11},...,\phi_{1u(1)}\}, ...,\Phi_{z}=\{\phi_{z1},...,\phi_{zu(z)}\}$ of boolean formulas, a formula $\omega$ follows from the conjunction $\bigwedge\Phi_i= \bigwedge \phi_{ij}$ iff $\neg \omega\wedge \bigwedge_{i=1}^z \Phi_i$ is unsatisfiable. Now assume that, given integers $0\leq e_i < u(i)$, we must check if $\neg \omega\wedge \bigwedge_{i=1}^z \Phi'_i$ remains unsatisfiable, where $\Phi'_i\subseteq \Phi_i$ is obtained by deleting $\,\,e_{i}$ arbitrarily chosen formulas of $\Phi_i$, for each $i=1,...,z.$ Intuitively, does $\omega$ {\it stably} follow, after removing $e_i$ random formulas from each $\Phi_i$? We construct a quadratic reduction of this problem to the consequence problem in infinite-valued \luk\ logic \L$_\infty$. In this way we obtain a self-contained proof that the \L$_\infty$-consequence problem is coNP-complete.

Affiliated with

Also associated with

No associations

Rating

Drawing Sound Conclusions from Unsound Premises does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Drawing Sound Conclusions from Unsound Premises, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Drawing Sound Conclusions from Unsound Premises will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-450172