scholarly journals Multi-type display calculus for propositional dynamic logic

2014 ◽  
Vol 26 (6) ◽  
pp. 2067-2104 ◽  
Author(s):  
Sabine Frittella ◽  
Giuseppe Greco ◽  
Alexander Kurz ◽  
Alessandra Palmigiano
Keyword(s):  
Dynamic Logic ◽  
Propositional Dynamic Logic ◽  
Display Calculus

scholarly journals Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (8) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Dynamic Logic ◽  
Order Theory ◽  
Simple Extension ◽  
Propositional Dynamic Logic ◽  
First Order ◽  
Time Semantics ◽  
Linear Time Temporal Logic ◽  
Obvious Manner

A simple extension of the propositional temporal logic of linear<br />time is proposed. The extension consists of strengthening the until<br />operator by indexing it with the regular programs of propositional<br />dynamic logic (PDL). It is shown that DLTL, the resulting logic, is<br />expressively equivalent to S1S, the monadic second-order theory<br />of omega-sequences. In fact a sublogic of DLTL which corresponds<br />to propositional dynamic logic with a linear time semantics is<br />already as expressive as S1S. We pin down in an obvious manner<br />the sublogic of DLTL which correponds to the first order fragment<br />of S1S. We show that DLTL has an exponential time decision<br />procedure. We also obtain an axiomatization of DLTL. Finally,<br />we point to some natural extensions of the approach presented<br />here for bringing together propositional dynamic and temporal<br />logics in a linear time setting.

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