scholarly journals ExpTime Tableaux with Global Caching for Hybrid PDL

2019 ◽  
Vol 64 (1) ◽  
pp. 21-52
Author(s):  
Linh Anh Nguyen
Keyword(s):  
Global Caching

scholarly journals Adaptive web caching: towards a new global caching architecture

1998 ◽  
Vol 30 (22-23) ◽  
pp. 2169-2177 ◽  
Author(s):  
Scott Michel ◽  
Khoi Nguyen ◽  
Adam Rosenstein ◽  
Lixia Zhang ◽  
Sally Floyd ◽  
...  
Keyword(s):  
Web Caching ◽  
Global Caching

scholarly journals Coalgebraic Reasoning with Global Assumptions in Arithmetic Modal Logics

2022 ◽  
Vol 23 (2) ◽  
pp. 1-34
Author(s):  
Clemens Kupke ◽  
Dirk Pattinson ◽  
Lutz Schröder
Keyword(s):  
Modal Logic ◽  
Upper Bound ◽  
Practical Reasoning ◽  
Linear Time ◽  
Modal Logics ◽  
Hybrid Logic ◽  
Complexity Bound ◽  
Elimination Algorithm ◽  
Polynomial Inequalities ◽  
Global Caching

We establish a generic upper bound ExpTime for reasoning with global assumptions (also known as TBoxes) in coalgebraic modal logics. Unlike earlier results of this kind, our bound does not require a tractable set of tableau rules for the instance logics, so that the result applies to wider classes of logics. Examples are Presburger modal logic, which extends graded modal logic with linear inequalities over numbers of successors, and probabilistic modal logic with polynomial inequalities over probabilities. We establish the theoretical upper bound using a type elimination algorithm. We also provide a global caching algorithm that potentially avoids building the entire exponential-sized space of candidate states, and thus offers a basis for practical reasoning. This algorithm still involves frequent fixpoint computations; we show how these can be handled efficiently in a concrete algorithm modelled on Liu and Smolka’s linear-time fixpoint algorithm. Finally, we show that the upper complexity bound is preserved under adding nominals to the logic, i.e., in coalgebraic hybrid logic.

ExpTime Tableaux for Using Sound Global Caching

2011 ◽  
Vol 50 (4) ◽  
pp. 355-381 ◽  
Author(s):  
Rajeev Goré ◽  
Linh Anh Nguyen
Keyword(s):  
Global Caching
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