"Soundness" Unsound

Unsound Inferences Make Proofs Shorter

We give examples of calculi that extend Gentzen’s sequent calculus LK by unsound quantifier inferences in such a way that (i) derivations lead only to true sequents, and (ii) proofs therein are non-elementarily shorter than LK-proofs.

Self-Correcting Unsound Reasoning Agents

This paper introduces a formal framework for relating learning and deduction in reasoning agents. Our goal is to capture imperfect reasoning as well as the progress, through introspection, towards a better reasoning ability. We capture the interleaving between these by a reasoning/deduction connection and we show how this—and related—definition apply to a setting in which agents are modeled by ...

Chelation Therapy: Unproven Claims and Unsound Theories

Chelation therapy, as discussed in this article, is a series of intravenous infusions containing disodium EDTA and various other substances. It is sometimes done by swallowing EDTA or other agents in pill form. Proponents claim that EDTA chelation therapy is effective against atherosclerosis and many other serious health problems. Its use is widespread because patients have been led to believe ...

Drawing Sound Conclusions from Unsound Premises

Given sets Φ1 = {φ11, . . . , φ1u(1)}, . . . ,Φz = {φz1, . . . , φzu(z)} of boolean formulas, a formula ω follows from the conjunction ∧ Φi = ∧ φij iff ¬ω ∧ ∧z i=1 Φi is unsatisfiable. Now assume that, given integers 0 ≤ ei < u(i), we must check if ¬ω ∧ ∧z i=1 Φ ′ i remains unsatisfiable, where Φ ′ i ⊆ Φi is obtained by deleting ei arbitrarily chosen formulas of Φi, for each i = 1, . . . , z. I...

Coinductive Intersection Types are Completely Unsound