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A Study Of Topological Polymodal Logics

By Vaughan Coulthard, To All At Rsise, Principally Raj Gore, Di Kossatz and Michelle Moravec

Abstract

Contents 1 Introduction and Motivation 1 2 Preliminaries 9 2.1 Relations as set-valued maps . . . . . . . . . . . . . . . . . . 9 2.1.1 Relations and functions . . . . . . . . . . . . . . . . . 9 2.1.2 Relations as set-valued maps . . . . . . . . . . . . . . 11 2.2 Operators on sets induced by relations . . . . . . . . . . . . . 16 2.3 Interior and closure operators of a topology . . . . . . . . . . 20 2.4 General topology of set-valued maps . . . . . . . . . . . . . . 22 2.4.1 Continuity concepts for relations . . . . . . . . . . . . 22 2.4.2 Alexandroff topologies . . . . . . . . . . . . . . . . . . 26 3 Topological Polymodal Logics - TopPML 35 3.1 The logic S4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.1.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.1.2 Topological semantics . . . . . . . . . . . . . . . . . . 37 3.1.3 Kripke relational semantics . . . . . . . . . . . . . . . 38 3.1.4 Corresponde

Year: 2000
OAI identifier: oai:CiteSeerX.psu:10.1.1.32.5841
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