Topology, connectedness, and modal logic

Roman Kontchakov; Ian Pratt-Hartmann; Frank Wolter; Michael Zakharyaschev

Topology, connectedness, and modal logic

Roman Kontchakov, Ian Pratt-Hartmann, Frank Wolter, Michael Zakharyaschev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces. © 2008, the author(s).

Original language	English
Title of host publication	Advances in Modal Logic 2006\|Adv. Modal Logic
Place of Publication	London
Publisher	College Publications
Pages	151-176
Number of pages	25
Volume	7
ISBN (Print)	1904987206, 9781904987680
Publication status	Published - 2008
Event	7th Conference on Advances in Modal Logic, AiML-2008 - Nancy Duration: 1 Jul 2008 → …

Conference

Conference	7th Conference on Advances in Modal Logic, AiML-2008
City	Nancy
Period	1/07/08 → …

Keywords

Connectedness
Modal logic
Spatial logic
Topology

Cite this

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title = "Topology, connectedness, and modal logic",

abstract = "This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces. {\textcopyright} 2008, the author(s).",

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note = "7th Conference on Advances in Modal Logic, AiML-2008 ; Conference date: 01-07-2008",

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TY - GEN

T1 - Topology, connectedness, and modal logic

AU - Kontchakov, Roman

AU - Pratt-Hartmann, Ian

AU - Wolter, Frank

AU - Zakharyaschev, Michael

PY - 2008

Y1 - 2008

N2 - This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces. © 2008, the author(s).

AB - This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (low-dimensional) Euclidean spaces. © 2008, the author(s).

KW - Connectedness

KW - Modal logic

KW - Spatial logic

KW - Topology

M3 - Conference contribution

SN - 1904987206

SN - 9781904987680

VL - 7

SP - 151

EP - 176

BT - Advances in Modal Logic 2006|Adv. Modal Logic

PB - College Publications

CY - London

T2 - 7th Conference on Advances in Modal Logic, AiML-2008

Y2 - 1 July 2008

ER -

Topology, connectedness, and modal logic

Abstract

Conference

Keywords

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Cite this