Theories of space and time: algebraic, topological and logical approaches
Contract №: DID02/32/2009
Tinko Tinchev, Sofia University "St. Kliment Ohridski"
Dimiter Vakarelov, Sofia University "St. Kliment Ohridski"
Georgi Dimov, Sofia University "St. Kliment Ohridski"
Dimitar Guelev, Bulgarian Academy of Sciences
Georgi Georgiev, Folio 3 Bulgaria
Vladislav Nenchev, PhD Student, Sofia University "St. Kliment Ohridski"
Nikolay Ivanov, PhD Student, Sofia University "St. Kliment Ohridski"
Yavor Nenov, PhD Student, University of Manchester
Philippe Balbiani, Institut de Recherche en Informatique de Toulouse
Ivo Düntsch, Brock University
Ian Pratt-Hartmann, University of Manchester
Michael Zakharyaschev, Birkbeck College, London
Our main objectives at the project are to obtain new theoretical results in the research fields described below, and to consider possible applications. More specifically we will consider the following sub-objectives related to themes of the project.
Theme 1: Region-based theory of space.
We will investigate region-based theory of space with its vocabulary extended by new connectives and predicates that denote connectedness, convexity, boundedness and other properties of regions and to characterize the new operations axiomatically and to obtain point-free representation theorems in the respective classes of point-based models.
Another direction is to study region-based theories based on weak assumptions of the underlying algebra of regions obtained by either eliminating all operations on regions and considering only spatial relations, or assuming algebras based on weak laws such as weak or no distributivity. In this setting our goal will be to identify an intuitively satisfactory class of point-based models.
Another goal is to investigate the corresponding logical systems that are sound and complete for the intended semantics, and will try to prove decidability and complexity results for them.
Theme 2: Time and change in region-based theory of space.
The main goal in this theme is to investigate dynamic versions of region-based theory of space that incorporate time and change of regions. This means identifying models which capture the dynamic features of regions in a satisfactory abstract point-free manner. Such features include stability and unstability of some relations between regions. Following Whitehead's idea to build space without points as one of the basic notions, our goal it to obtain a point-free characterization of dynamic theories without time instants. This will shed some new light on the intimate relation between space and time and will be a formal analog of Whitehead's epochal theory of time which is described shortly and informally in his famous book Process and reality (MacMillan, New York, 1929). For all such systems of dynamic region-based theory of space the study of the corresponding logical systems with respect to completeness, decidability and complexity is addressed.
Theme 3: Logics of time, knowledge and agency.
The objective is to contribute to the investigation of the model-checking problem and the validity problem for logics which combine epistemic, game-theoretic, and past temporal modalities and to study their formal properties with respect to completeness and complexity.
|10:00–11:00||Philippe Balbiani, Modal logics based on the derivative operation in topological spaces||view|
|11:30–12:30||Ivo Düntsch, Remarks on contact relations on Boolean algebras|
|12:40–13:20||Dimiter Vakarelov, Dynamic mereotopology||view|
|15:30–16:10||Georgi Dimov, A Whiteheadian-type description of Euclidean spaces, spheres and Tychonoff cubes||view|
|16:20–16:40||Georgi Dimov and Elza Ivanova, Yet another generalization of De Vries' Duality Theorem|
|17:10–17:50||Çiğdem Gencer, Universal models for extensions of K4 by closed formulas and finite model property|
|18:00–18:20||Mitko Yanchev, PSPACE completeness of Generalized Graded Modal Logic||view|
|18:30–18:50||Tatyana Ivanova, Logics for lines in Euclidean plane with predicates convergence, parallelism and perpendicularity|
|10:00–11:00||Roman Kontchakov, Topological Logics and Aleksandrov Spaces||view|
|11:30–12:30||Ian Pratt-Hartmann, Undecidability in Logics of Euclidean Spaces|
|12:40–13:00||Yavor Nenov, Expressiveness of Euclidean Spatial Logics||view|
|13:10–13:30||Vladislav Nenchev, Logics for Stable and Unstable Mereological Relations||view|
|15:30–16:10||Cătălin Dima, Automata for temporal epistemic logics||view|
|16:20–17:00||Dimitar P. Guelev, Model-checking predicate epistemic temporal properties of finite control pi-processes||view|
|17:30–17:50||Nikolay Ivanov, Relational Syllogistics|
|18:00–18:40||Tinko Tinchev, Complexity and completeness of some dynamic mereotopological logics||view|
|18:50–20:00||DISCUSSION: Logics of Space and Time|
I. In journals with impact factor
1. Georgi Dimov, Some generalizations of the Stone Duality Theorem. Publicationes Mathathematicæ Debrecen. In Print: Ref. no.: 4814 (2012), 1--39.
2. Dimiter Vakarelov, Dynamic Mereotopology: A Point-Free Theory of Changing Regions. I. Stable and unstable mereotopological
relations. Fundamenta Informaticæ 100 (2010) 1-22.
DOI: 10.3233/FI-2010-264, IOS Press
3. Sabine Koppelberg, Ivo Düntsch, Michael Winter, Remarks on contact relations on Boolean algebras. To appear in: Algebra Universalis.
II. In journals without impact factor
1. Dimiter Vakarelov, Dynamic Modalities. Studia Logica (2012) 100: 385--397.
2. Ivo Düntsch, Ewa Orlowska, Discrete Dualities for Double Stone Algebras. Studia Logica (2011) 99: 127-142.
3. Dimitar P. Guelev, Cătălin Dima, Constantin Enea, An alternating-time temporal logic with knowledge, perfect recall and past:
axiomatization and model-checking. Journal of Applied Non-Classical Logics, 21, No. 1/2011, pp. 93-131.
DOI: 10.3166/JANCL.21.93--131, Lavoisier, Paris.
III. In proceedings of conferences
1. Tinko Tinchev and Dimiter Vakarelov, Logics of Space with Connectedness Predicates: Complete axiomatizations. In:
Proceedings of the conference 8th Advances in Modal Logic. L. Beklemishev, V. Goranko, V. Shehtman (eds.), Advances in Modal Logic,
8, College Publications, London, 2010, pp. 409-427.
2.Vladislav Nenchev, Undecidability of Logics for Mereotopological Relations. In: Proceedings of the 8th Panhellenic Logic Symposium, July 4--8, 2011 Ioannina, Greece.
3. Dimitar Guelev and Mads Dam, An Epistemic Predicate CTL* for Finite Control π-Processes. In: Proceedings of the 7th Workshop on Methods for Modalities (M4M 2011) and the 4th Workshop on Logical Aspects of Multi-Agent Systems (LAMAS 2011), Osuna, Spain, November 2011, Electronic Notes in Theoretical Computer Science, 278, pp. 229-243, 2011.
4. Cătălin Dima, Constantin Enea and Dimitar Guelev, Model-Checking an Alternating-time Temporal Logic with Knowledge, Imperfect
Information, Perfect Recall and Communicating Coalitions. In: Proceedings of the First Symposium on Games, Automata, Logic, and
Formal Verification (GandALF 2010). Electronic Proceedings in Theoretical Computer Science (EPTCS), 25, pp. 103-117, 2010.
ISSN: 2075-2180, DOI: 10.4204/EPTCS
1. Georgi D. Dimov, A Whiteadean-type description of Euclidean spaces, spheres, tori and Tychonoff cubes. arXiv: 1203.4279v1 [math.GN] 19 March 2012.