Information Change and First-Order Dynamic Logic

2013 ◽  
Author(s):  
Barteld Kooi
Keyword(s):  
Dynamic Logic ◽  
First Order ◽  
Information Change

scholarly journals Dynamic Logic for Data-aware Systems: Decidability Results

2017 ◽  
Author(s):  
Francesco Belardinelli ◽  
Andreas Herzig
Keyword(s):  
Model Checking ◽  
Dynamic Logic ◽  
English Auctions ◽  
First Order ◽  
Formal Framework ◽  
Data Content ◽  
Order Extension

We introduce a first-order extension of dynamic logic (FO-DL), suitable to represent and reason about the behaviour of Data-aware Systems (DaS), which are systems whose data content is explicitly exhibited in the system’s description. We illustrate the expressivity of the formal framework by modelling English auctions as DaS, and by specifying relevant properties in FO-DL. Most importantly, we develop an abstraction-based verification procedure, thus proving that the model checking problem for DaS against FO-DL is actually decidable, provided some mild assumptions on the interpretationdomain.

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.

scholarly journals A Programming Language for the Inductive Sets, and Applications

1982 ◽  
Vol 11 (143) ◽  
Author(s):  
David Harel ◽  
Dexter Kozen
Keyword(s):  
Programming Language ◽  
Relational Database ◽  
Query Language ◽  
Dynamic Logic ◽  
Computational Approach ◽  
Turing Machines ◽  
First Order ◽  
Separation Result ◽  
Alternating Turing Machines ◽  
Order Structures

We introduce a programming language IND that generalizes alternating Turing machines to arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting IND programs, loop-free IND programs) accept precisely the inductively definable (respectively, hyperelementary, elementary) relations. We give several examples showing how the language provides a robust and computational approach to the theory of first-order inductive definability. We then show: (1) on all acceptable structures (in the sense of Moschovakis), r.e. Dynamic Logic is more expressive than finite-test Dynamic Logic. This refines a separation result of Meyer and Parikh; (2) IND provides a natural query language for the set of fixpoint queries over a relational database, answering a question of Chandra and Harel.

ON THE COMPUTING POWER OF PROGRAMS WITH SETS

1992 ◽  
Vol 03 (02) ◽  
pp. 161-180
Author(s):  
ALEXEI P. STOLBOUSHKIN
Keyword(s):  
Complexity Theory ◽  
Dynamic Logic ◽  
Computable Function ◽  
Data Complexity ◽  
Computing Power ◽  
First Order ◽  
Finite Structures ◽  
Generalized Computability ◽  
Global Predicates ◽  
Order Structures

The class FDSet of while-programs equipped with finite sets as internal data type is considered in the context of generalized computability over abstract first order structures. This class is proved to be semi-universal, i.e. to be able to compute every computable function in every infinite finitely-generated structure. However, for this class the halting problem on finite structures is decidable within LinearSpace complexity (on the cardinality of structure), and it is proved that the dynamic logic of the class FDSet describes exactly the class LinearSpace computable global predicates on the class of all one-generated finite structures of a given signature. Some other classes of data complexity are also described in the paper in similar terms. Due to the semi-universality, this class FDSet is a good basis for developing generalized complexity theory.

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