An Exposition and Development of Kanger’s Early Semantics for Modal Logic

Abstract

Stig Kanger — born of Swedish parents in China in 1924 — was professor of Theoretical Philosophy at Uppsala University from 1968 until his death in 1988. He received his Ph. D. from Stockholm University in 1957 under the supervision of Anders Wedberg. Kanger’s dissertation, Provability in Logic, was remarkably short, only 47 pages, but also very rich in new ideas and results. By combining Gentzen-style techniques with a model theory a la Tarski, Kanger obtained new and simplified proofs of central metalogical results of classical predicate logic: Godel’s completeness theorem, Lowenheim-Skolem’s theorem and Gentzen’s Hauptsatz. The part that had the greatest impact, however, was the 15 pages devoted to modal logic. There Kanger developed a new semantic interpretation for quantified modal logic which had a close family resemblance to semantic theories that were developed around the same time by Jaakko Hintikka, Richard Montague and Saul Kripke (independently of each other and independently of Kanger).