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Logics of Infinite Depth

2016
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Advances in Modal Logic
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Consider a definition of depth of a logic as the supremum of ordinal types of wellordered descending chains. This extends the usual definition of codimension to infinite depths. Logics may either have no depth, or have countable depth in case a maximal well-ordered chain exists, or be of depth !1. We shall exhibit logics of all three types. We show in particular that many well-known systems, among them K, K4, G, Grz and S4, have depth !1. Basically, if a logic is the intersection of its

dblp:conf/aiml/Kracht16
fatcat:u4dgqrd6svh6thwalpjju5yyca