scholarly journals Complexity Optimal Decision Procedure for a Propositional Dynamic Logic with Parallel Composition

2016 ◽  
pp. 373-388 ◽  
Author(s):  
Joseph Boudou
Keyword(s):  
Decision Procedure ◽  
Dynamic Logic ◽  
Optimal Decision ◽  
Parallel Composition ◽  
Propositional Dynamic Logic

scholarly journals A Product Version of Dynamic Linear Time Temporal Logic

1997 ◽  
Vol 4 (9) ◽  
Author(s):  
Jesper G. Henriksen ◽  
P. S. Thiagarajan
Keyword(s):  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Time ◽  
Dynamic Logic ◽  
Two Dimensions ◽  
Sequential Programs ◽  
Propositional Dynamic Logic ◽  
The Core ◽  
Finite Set ◽  
Linear Time Temporal Logic

We present here a linear time temporal logic which simultaneously extends LTL, the propositional temporal logic of linear time, along two dimensions. Firstly, the until operator is strengthened by indexing it with the regular programs of propositional dynamic logic (PDL). Secondly, the core formulas of the logic are decorated with names of sequential agents drawn from fixed finite set. The resulting logic has a natural semantics in terms of the runs of a distributed program consisting of a finite set of sequential programs that communicate by performing common actions together. We show that our logic, denoted DLTL, admits an exponential time decision procedure. We also show that DLTL is expressively equivalent to the so called regular product languages.

scholarly journals A Dynamic Epistemic Logic with Finite Iteration and Parallel Composition

2021 ◽  
Author(s):  
Andreas Herzig ◽  
Frédéric Maris ◽  
Elise Perrotin
Keyword(s):  
Epistemic Logic ◽  
Dynamic Logic ◽  
Dynamic Epistemic Logic ◽  
Finite Horizon ◽  
Parallel Composition ◽  
Propositional Dynamic Logic ◽  
Restricted Version ◽  
Standard Program

Existing dynamic epistemic logics combine standard epistemic logic with a restricted version of dynamic logic. Instead, we here combine a restricted epistemic logic with a rich version of dynamic logic. The epistemic logic is based on `knowing-whether' operators and basically disallows disjunctions and conjunctions in their scope; it moreover captures `knowing-what'. The dynamic logic has not only all the standard program operators of Propositional Dynamic Logic, but also parallel composition as well as an operator of inclusive nondeterministic composition; its atomic programs are assignments of propositional variables. We show that the resulting dynamic epistemic logic is powerful enough to capture several kinds of sequential and parallel planning, and so both in the unbounded and in the finite horizon version.

scholarly journals Propositional Dynamic Logic with Storing, Recovering and Parallel Composition

2011 ◽  
Vol 269 ◽  
pp. 95-107 ◽  
Author(s):  
Mario R.F. Benevides ◽  
Renata de Freitas ◽  
Petrucio Viana
Keyword(s):  
Dynamic Logic ◽  
Parallel Composition ◽  
Propositional Dynamic Logic

scholarly journals An Optimal Decision Procedure for MPNL over the Integers

2011 ◽  
Vol 54 ◽  
pp. 192-206
Author(s):  
Davide Bresolin ◽  
Angelo Montanari ◽  
Pietro Sala ◽  
Guido Sciavicco
Keyword(s):  
Decision Procedure ◽  
Optimal Decision

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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