A Concise Introduction to Propositional Dynamic Logic by Krister Segerberg

By Krister Segerberg

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KRISTER. "A completeness theorem in the modalloQic of prog~m~". In T. Traczyk (ed), Universal algebra and ~ appizcatlOllS, pp. 31-46. Banach Cellter Publicatiolls vol 9 Warsaw: PWN,1982.

The idea of using Henkin's method in modal logic occurred, independently, to a number of other authors as well, for example, David Makinson, Max Cresswell and Kurt Schtltte, but those authors restricted themselves to case studies and did not see and did not seek the generality that Lemmon and Scott achieved. The concept of filtration, which they also employed, was modelled on an algebraic construction of J. C C. McKinsey. L 62 In the bibliography four textbooks have been listed. Lemmon's book, the published version of a draft completed three days before Lemmon's death, is of great historical interest.

In other woids. his proof contained a gap and therefore was no proof. The author's . lllg produced the first con'ect proof for dynamic logic belongs to Pankh. Later he and Dexter Kozen published a shorter proof, which is now regarded as the classic ref~rence for the completeness of PDL. The author's mended proof, essentially the proof given here, was presented in March 1978 at the Banach Center in Warsaw. The ~urvey alticle by David Harel,an informative if difficult paper, proVides an account of the intense period of work following the initial petiod described above.

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