A Logical Account of Causal and Topological Maps

Abstract

Dissertation Overview 2 SSH Overview 6 The Spatial Semantic Hierarchy ....................... 6 Creating Schemas ............................... 8 The SSH topological level: regions ...................... 9 Physical Implementation of the SSH ..................... 10 3 Control Level 12 SSH control assumptions ............................ 13 3.1.1 The SSH control closure property .................. 13 3.1.2 Well separated dstate ......................... 13 3.1.3 From control laws to actions ..................... 14 Voronoi robots ................................ 14 4 Causal Level 16 Causal level Ontology ............................. 17 4.1.1 Views ................................. 17 4.1.2 Actions ................................ 17 4.1.3 Distinctive States ........................... 19 4.1.4 Schemas ............................... 19 4.1.5 Schema notation ........................... 20 4.1.6 Routines ............................... 20 SSH Causal theory .............................. 21 4.2.1 The E formulae ............................ 21 4.2.2 The SSH view graph ......................... 24 iv 4.2.3 CT(E) ................................. 26 4.3 The SSH causal graph ............................. 31 4.4 Calculating the models of CT(E) ....................... 32 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6.1 6.2 6.3 7.1 7.2 5 Topological Level 36 The SSH Topological Theory ......................... 37 teq versus ceq ................................. 58 The SSH topological map ........................... 59 What if Views uniquely identify distinctive states .............. 60 Coping with self intersecting paths ...................... 63 5.5.1 Converging paths ........................... 64 5.5.2 Self-intersecting paths ...............