Outline Logics of Space with Connectedness Predicates Tinko Tinchev and Dimiter Vakarelov Faculty of Mathematics and Computer Science Department of Mathematical logic Sofia University tu-logo Advances in Modal Logic 2010 (AiML-2010), 24-27 August, Moscow, Russia ur-logo Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Outline Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Hystorical introduction Whiteheadean approach Contact algebras with connectedness predicates RBTS and computer science Spatial RCC-like logics with connectedness predicates THE AIM OF THE PAPER Concluding remarks Outline Hystorical introduction 1 Whiteheadean approach RBTS and computer science THE AIM OF THE PAPER Contact algebras with connectedness predicates 2 Contact algebras Contact algebras with connectedness predicates Representation theory of contact algebras with connectedness predicates Spatial RCC-like logics with connectedness predicates 3 Syntax and semantics tu-logo Axiomatizations Completeness theorems ur-logo Concluding remarks 4 Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
Hystorical introduction Whiteheadean approach Contact algebras with connectedness predicates RBTS and computer science Spatial RCC-like logics with connectedness predicates THE AIM OF THE PAPER Concluding remarks Whiteheadean theory of space The paper is in the field of a new theory of space originated by Whitehead: A. N. Whitehead, The Organization of Though , London, William and Norgate, 1917, page 195 “...It follows from the relative theory that a point should be definable in terms of the relations between material things . So far as I am aware, this outcome of the theory has escaped the notice of mathematicians, who have invariably assumed the point as the ultimate starting ground of their reasoning.Many years ago I explained some types of ways in which we might tu-logo achieve such a definition, and more recently have added some others...” The main contribution of Whitehead is in the book ur-logo A. N. Whitehead, Process and Reality , New York, MacMillan, 1929. Tinko Tinchev and Dimiter Vakarelov Logics of Space with Connectedness Predicates
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