Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics

Vakarelov, Dimiter

doi:10.1007/978-0-387-69245-6_6

Cited by 43 publications

(66 citation statements)

References 38 publications

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“…This definition relates Galton's adjacency spaces to the relational semantics of modal logic which makes it possible to use methods from modal logic for studying region-based theories of space. The truth is that the above-mentioned topological semantics and the relational perspective suggested by Galton are equivalent [23].…”

Section: Semanticsmentioning

confidence: 99%

“…This relational semantics is considered in [3][4][5]23]. Obviously, these binary relations are jointly exhaustive and pairwise disjoint on 2 W \{∅}, i.e.…”

Section: Semanticsmentioning

confidence: 99%

“…Its theorems are all formulas which can be derived from the axioms by means of the rules. See [5,23] for systems of axioms and rules characterizing validity with respect to different classes of frames. In order to make stronger an axiomatic system for C, we can add new axioms and new rules to it.…”

Section: Unifiabilitymentioning

confidence: 99%

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Finitariness of Elementary Unification in Boolean Region Connection Calculus

Balbiani

Gencer

2017

Frontiers of Combining Systems

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Section: Semanticsmentioning

confidence: 99%

“…This relational semantics is considered in [3][4][5]23]. Obviously, these binary relations are jointly exhaustive and pairwise disjoint on 2 W \{∅}, i.e.…”

Section: Semanticsmentioning

confidence: 99%

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Finitariness of Elementary Unification in Boolean Region Connection Calculus

Balbiani

Gencer

2017

Frontiers of Combining Systems

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“…Moreover, the axioms are either postulates or theorems of theories which are known as some standard approaches to the problem in the literature (see e.g. [1,2,7,20,24]). …”

Section: Separation Structuresmentioning

confidence: 99%

A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures

Gruszczyński

Pietruszczak

2018

Stud Logica

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Abstract.This is the first, out of two papers, devoted to Andrzej Grzegorczyk's pointfree system of topology from Grzegorczyk (Synthese 12(2-3): [228][229][230][231][232][233][234][235] 1960. https://doi. org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation (the dual notion of connection). Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze (quasi-)separation structures and Grzegorczyk structures, and establish their properties which will be useful in the sequel. We prove that in the class of Urysohn spaces with countable chain condition, to every topologically interpreted representative of a point in the sense of Grzegorczyk's corresponds exactly one point of a space. We also demonstrate that Tychonoff first-countable spaces give rise to complete Grzegorczyk structures. The results established below will be used in the second part devoted to points and topological spaces.

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“…[39] and [40], who both provide surveys of the classical approaches to this topic by Whitehead [29]- [31], De Laguna [35], Menger [41], Grzegorczyk [24], and Clarke [25]. More recent contributions include [42], [43], [27], [44], and [45]. and gestalt-theoretic approaches to psychology.…”

Section: B Atomistic Mereologymentioning

confidence: 99%

Proceedings of the LQMR 2015 Workshop

2015

Annals of Computer Science and Information Systems

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WThe idea of organizing this workshop originated from the project Logics for Qualitative Reasoning funded by the National Science Centre (DEC-2011/02/A/HS1/00395). The project is concerned with the logical foundations of qualitative representation and reasoning applied in artificial intelligence. Qualitative Reasoning (QR) has emerged as a subfield of Artificial Intelligence to deal with representation and reasoning about continuous aspects of entities and systems in a symbolic, but human-like manner. The main issue in the QR approach is to develop an adequate tool for modeling situations in which information is not sufficiently precise or cannot be described by numerical values.The project aims to develop logical theories and tools for qualitative representation and reasoning, with applications to many domains for which qualitative inference methods are significant.The project is also aimed at analysis of model-theoretic properties of qualitative logics, such as definability and expressive power, finite model property, and decidability, among others. The third research objective is the construction and implementation of deduction systems for the logics developed in the project. We focus on decidable logics and their automated decision procedures in the style of relational dual tableaux.The LQMR workshop categorically addresses the theory and application of logical formalisations of qualitative reasoning within engineering, technical, and computational cognitive systems. The workshops will build bridges between different research groups interested in qualitative modelling and reasoning. In particular, perspectives from logic and computer science employing formal methods for QR, formal methods for spatial reasoning, and researchers dealing with fundamental philosophical aspects of QR are of focus. Additionally, problems of more applied nature in the filed of engineering and artificial intelligence are also emphasised.The contributed papers focus on three main areas: qualitative spatial reasoning, its possible applications, and applications of qualitative methods to philosophical problems.In addition to the contributed papers, four invited keynote talks were delivered: by prof. Thomas Bittner from State University of New York at Buffalo, who spoke on vague region-based geometry, by dr Ian Pratt-Hartmann from The University of Manchester, who devoted his presentation to topological logics of Euclidean spaces, by prof. Kenneth Forbus, who spoke on three frontiers for qualitative reasoning, and by prof. Ivan Bratko, whose lecture was concerned with the problem of learning qualitative models.These Proceedings will augment state of the art in Qualitative Reasoning with several excellent references.We thank all authors and participants for their contributions. v HE AAIA'15 will bring researchers, developers, practitioners, and users to present their latest research, results, and ideas in all areas of artificial intelligence. We hope that theory and successful applications presented at the AAIA'15 will be of interest to ...

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Region-Based Theory of Space: Algebras of Regions, Representation Theory, and Logics

Cited by 43 publications

References 38 publications

Finitariness of Elementary Unification in Boolean Region Connection Calculus

Finitariness of Elementary Unification in Boolean Region Connection Calculus

A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures

Proceedings of the LQMR 2015 Workshop

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