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 Reasoning About the Transfer of Control

2010 ◽  
Vol 37 ◽  
pp. 437-477 ◽  
Author(s):  
W. Van der Hoek ◽  
D. Walther ◽  
M. Wooldridge
Keyword(s):  
Computational Complexity ◽  
Model Checking ◽  
Dynamic Logic ◽  
Second Order ◽  
Kripke Semantics ◽  
Alternative Semantics ◽  
Form Complex ◽  
Transfer Programs ◽  
First Order ◽  
State Of Affairs

We present DCL-PC: a logic for reasoning about how the abilities of agents and coalitions of agents are altered by transferring control from one agent to another. The logical foundation of DCL-PC is CL-PC, a logic for reasoning about cooperation in which the abilities of agents and coalitions of agents stem from a distribution of atomic Boolean variables to individual agents -- the choices available to a coalition correspond to assignments to the variables the coalition controls. The basic modal constructs of DCL-PC are of the form `coalition C can cooperate to bring about phi'. DCL-PC extends CL-PC with dynamic logic modalities in which atomic programs are of the form `agent i gives control of variable p to agent j'; as usual in dynamic logic, these atomic programs may be combined using sequence, iteration, choice, and test operators to form complex programs. By combining such dynamic transfer programs with cooperation modalities, it becomes possible to reason about how the power of agents and coalitions is affected by the transfer of control. We give two alternative semantics for the logic: a `direct' semantics, in which we capture the distributions of Boolean variables to agents; and a more conventional Kripke semantics. We prove that these semantics are equivalent, and then present an axiomatization for the logic. We investigate the computational complexity of model checking and satisfiability for DCL-PC, and show that both problems are PSPACE-complete (and hence no worse than the underlying logic CL-PC). Finally, we investigate the characterisation of control in DCL-PC. We distinguish between first-order control -- the ability of an agent or coalition to control some state of affairs through the assignment of values to the variables under the control of the agent or coalition -- and second-order control -- the ability of an agent to exert control over the control that other agents have by transferring variables to other agents. We give a logical characterisation of second-order control.

scholarly journals Constructing weak simulations from linear implications for processes with private names

2019 ◽  
Vol 29 (8) ◽  
pp. 1275-1308 ◽  
Author(s):  
Ross Horne ◽  
Alwen Tiu
Keyword(s):  
Expressive Power ◽  
Dual Pair ◽  
Proof System ◽  
Branching Time ◽  
First Order ◽  
Order Extension

AbstractThis paper clarifies that linear implication defines a branching-time preorder, preserved in all contexts, when used to compare embeddings of process in non-commutative logic. The logic considered is a first-order extension of the proof system BV featuring a de Morgan dual pair of nominal quantifiers, called BV1. An embedding of π-calculus processes as formulae in BV1 is defined, and the soundness of linear implication in BV1 with respect to a notion of weak simulation in the π -calculus is established. A novel contribution of this work is that we generalise the notion of a ‘left proof’ to a class of formulae sufficiently large to compare embeddings of processes, from which simulating execution steps are extracted. We illustrate the expressive power of BV1 by demonstrating that results extend to the internal π -calculus, where privacy of inputs is guaranteed. We also remark that linear implication is strictly finer than any interleaving preorder.

scholarly journals Twin-width I: Tractable FO Model Checking

2022 ◽  
Vol 69 (1) ◽  
pp. 1-46
Author(s):  
Édouard Bonnet ◽  
Eun Jung Kim ◽  
Stéphan Thomassé ◽  
Rémi Watrigant
Keyword(s):  
Model Checking ◽  
Elementary Function ◽  
First Order ◽  
Fpt Algorithm ◽  
Fixed Parameter ◽  
Dimension 2 ◽  
Bounded Size ◽  
Map Graphs ◽  
Dimensional Ball ◽  
Bounded Width

Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes (except map graphs without geometric embedding) we show how to compute in polynomial time a sequence of d -contractions , witness that the twin-width is at most d . We show that FO model checking, that is deciding if a given first-order formula ϕ evaluates to true for a given binary structure G on a domain D , is FPT in |ϕ| on classes of bounded twin-width, provided the witness is given. More precisely, being given a d -contraction sequence for G , our algorithm runs in time f ( d ,|ϕ |) · |D| where f is a computable but non-elementary function. We also prove that bounded twin-width is preserved under FO interpretations and transductions (allowing operations such as squaring or complementing a graph). This unifies and significantly extends the knowledge on fixed-parameter tractability of FO model checking on non-monotone classes, such as the FPT algorithm on bounded-width posets by Gajarský et al. [FOCS’15].

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.

First-Order-CTL Model Checking

1998 ◽  
pp. 283-294 ◽  
Author(s):  
Jürgen Bohn ◽  
Werner Damm ◽  
Orna Grumberg ◽  
Hardi Hungar ◽  
Karen Laster
Keyword(s):  
Model Checking ◽  
First Order
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