Modal Logics with Transitive Closure

2014 ◽  
pp. 157-189
Author(s):  
Olivier Gasquet ◽  
Andreas Herzig ◽  
Bilal Said ◽  
François Schwarzentruber
Keyword(s):  
Transitive Closure ◽  
Modal Logics

scholarly journals Bisimulations on Data Graphs

2018 ◽  
Vol 61 ◽  
pp. 171-213 ◽  
Author(s):  
Sergio Abriola ◽  
Pablo Barceló ◽  
Diego Figueira ◽  
Santiago Figueira
Keyword(s):  
Constraint Satisfaction ◽  
Transitive Closure ◽  
Modal Logics ◽  
Closure Operators ◽  
External Observer ◽  
Complexity Bounds ◽  
Fundamental Notion ◽  
Labeled Graphs ◽  
Non Locality

Bisimulation provides structural conditions to characterize indistinguishability from an external observer between nodes on labeled graphs. It is a fundamental notion used in many areas, such as verification, graph-structured databases, and constraint satisfaction. However, several current applications use graphs where nodes also contain data (the so called "data graphs"), and where observers can test for equality or inequality of data values (e.g., asking the attribute 'name' of a node to be different from that of all its neighbors). The present work constitutes a first investigation of "data aware" bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath ---a language that extends modal logics like PDL with tests for data equality--- with and without transitive closure operators. We show that in general the problem is PSpace-complete, but identify several restrictions that yield better complexity bounds (coNP, PTime) by controlling suitable parameters of the problem, namely the amount of non-locality allowed, and the class of models considered (graphs, DAGs, trees). In particular, this analysis yields a hierarchy of tractable fragments.

Modal logics with Belnapian truth values

2010 ◽  
Vol 20 (3) ◽  
pp. 279-304 ◽  
Author(s):  
Serge P Odintsov ◽  
Heinrich Wansing
Keyword(s):  
Modal Logics ◽  
Truth Values

Non-well-founded Proof Theory of Transitive Closure Logic

2020 ◽  
Vol 21 (4) ◽  
pp. 1-31
Author(s):  
Liron Cohen ◽  
Reuben N. S. Rowe
Keyword(s):  
Proof Theory ◽  
Transitive Closure

Comparing the expressiveness of downward fragments of the relation algebra with transitive closure on trees

2020 ◽  
Vol 89 ◽  
pp. 101467 ◽  
Author(s):  
Jelle Hellings ◽  
Marc Gyssens ◽  
Yuqing Wu ◽  
Dirk Van Gucht ◽  
Jan Van den Bussche ◽  
...  
Keyword(s):  
Transitive Closure ◽  
Relation Algebra

scholarly journals On modal logics arising from scattered locally compact Hausdorff spaces

2019 ◽  
Vol 170 (5) ◽  
pp. 558-577
Author(s):  
Guram Bezhanishvili ◽  
Nick Bezhanishvili ◽  
Joel Lucero-Bryan ◽  
Jan van Mill
Keyword(s):  
Modal Logics ◽  
Hausdorff Spaces ◽  
Locally Compact

scholarly journals Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O ( n 2 barrier

2005 ◽  
Vol 52 (2) ◽  
pp. 147-156 ◽  
Author(s):  
Camil Demetrescu ◽  
Giuseppe F. Italiano
Keyword(s):  
Transitive Closure ◽  
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