A Concise Introduction to Propositional Dynamic Logic by Krister Segerberg

By Krister Segerberg

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A. 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.

Mo~llogic: from a theoretical point of view, dym\l~llC logIC IS a genera~l~ation of modal logic. Consequently the tec~mques that mo~alloglclans have built up are almost immediately aVaIlable for studYlllg dYl1ronic logic. tv1ichael Fischer and Richard Ladner, who were able to prove in 1976 that PDLthe set of formulre valid in all standard frames-has the stron" fmp and so is decidable. '" In modal logic it is unsual for an fmp result to be proved before completeness has been settled, but in this case completeness turned out to be hard.

Therefore it is probably the best choice for those whose interest in modal logic is secondary to their interest in dynamic logic. { Lemmon's book contains a valuable historical introduction. Some historical remarks are also made in the survey article by Robert Bull and the author. 2 we touched on tense logic. For further discussion, see the survey paper by Burgess listed in the bibliography. The author's paper "On von Wright's tense-logic", also listed in the bibliography, was to ~ave b~en the ~rst publication of a completeness proof for the tenselogIC of dIscrete linear future time with operators for both 'next' and' at all times'.

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