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The Tangled Derivative Logic of the Real Line and Zero-Dimensional Space
Advances in Modal Logic
In a topological setting in which the diamond modality is interpreted as the derivative (set of limit points) operator, we study a 'tangled derivative' connective that assigns to any finite set of propositions the largest set in which all those propositions are strictly dense. Building on earlier work of ourselves and others we axiomatise the resulting logic of the real line. We then show that the logic of any zero-dimensional dense-initself metric space is the 'tangled' extension of KD4,dblp:conf/aiml/GoldblattH16 fatcat:jtwv6oxwpberzdnfzpmguhfzme