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Relational Differential Dynamic Logic [article]

Juraj Kolčák, Ichiro Hasuo, Jérémy Dubut, Shin-ya Katsumata, David Sprunger, Akihisa Yamada
2020 arXiv   pre-print
In the field of quality assurance of hybrid systems (that combine continuous physical dynamics and discrete digital control), Platzer's differential dynamic logic (dL) is widely recognized as a deductive  ...  A main technical challenge here is to relate two states of two dynamics at different time points.  ...  Platzer's differential dynamic logic dL [21] is a remarkable success in this direction.  ... 
arXiv:1903.00153v2 fatcat:qgnadja5wvcyflcscryt4ahely

Relational differential dynamic logic

Juraj Kolčák, Ichiro Hasuo, Jérémy Dubut, Shin-ya Katsumata, David Sprunger, Akihisa Yamada
2019 Proceedings of the 22nd ACM International Conference on Hybrid Systems Computation and Control - HSCC '19  
In the field of quality assurance of hybrid systems, Platzer's differential dynamic logic (dL) is widely recognized as a deductive verification method with solid mathematical foundations and sophisticated  ...  A main technical challenge is to combine two dynamics, so that the powerful inference rules of dL (such as the differential invariant rules) can be applied to such relational reasoning, yet in such a way  ...  Platzer's differential dynamic logic dL [21] is a remarkable success in this direction.  ... 
doi:10.1145/3302504.3313362 dblp:conf/hybrid/KolcakHDKSY19 fatcat:hkxyv3cxhvhuvctuloyvhonzxm

Relational Differential Dynamic Logic [chapter]

Juraj Kolčák, Jérémy Dubut, Ichiro Hasuo, Shin-ya Katsumata, David Sprunger, Akihisa Yamada
2020 Lecture Notes in Computer Science  
In the field of quality assurance of hybrid systems, Platzer's differential dynamic logic (dL) is widely recognized as a deductive verification method with solid mathematical foundations and sophisticated  ...  A main technical challenge is to combine two dynamics, so that the powerful inference rules of dL (such as the differential invariant rules) can be applied to such relational reasoning, yet in such a way  ...  Platzer's differential dynamic logic dL [21] is a remarkable success in this direction.  ... 
doi:10.1007/978-3-030-45190-5_11 fatcat:y77k3agaerei7ituxh2ss77xu4

A Formal Framework for Hybrid Event B

Jie Liu, Jing Liu
2014 Electronical Notes in Theoretical Computer Science  
Specifically, Hybrid Event B is an extension of Event B associating with differential dynamic logic.  ...  The main contribution of this paper is that we give the definition of a differential event in Hybrid Event B, which makes it possible using differential dynamic logic in modeling continuous dynamical systems  ...  For modeling continue dynamic systems and refinement relations, we have proposed a differential dynamical logical based.  ... 
doi:10.1016/j.entcs.2014.12.002 fatcat:cxrph6vianhi5c6opuatvaarl4

Logics of Dynamical Systems

Andre Platzer
2012 2012 27th Annual IEEE Symposium on Logic in Computer Science  
Index Terms-logic of dynamical systems, dynamic logic, differential dynamic logic, hybrid systems, axiomatization, deduction  ...  We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems.  ...  B. dL Formulas Differential dynamic logic dL [45] , [47] , [50] , [54] is a dynamic logic [64] for hybrid systems.  ... 
doi:10.1109/lics.2012.13 dblp:conf/lics/Platzer12 fatcat:uyo3s7frizgt7d2haga3yylifa

Towards a Hybrid Dynamic Logic for Hybrid Dynamic Systems

André Platzer
2007 Electronical Notes in Theoretical Computer Science  
We introduce a hybrid variant of a dynamic logic with continuous state transitions along differential equations, and we present a sequent calculus for this extended hybrid dynamic logic.  ...  With these extensions, our hybrid dynamic logic advances the capabilities for compositional reasoning about (semialgebraic) hybrid dynamic systems.  ...  This differential dynamic logic, dL, is suitable for verifying hybrid dynamic systems.  ... 
doi:10.1016/j.entcs.2006.11.026 fatcat:6r6ztgkqqfchdm24rfxjuwkpze

Page 8369 of Mathematical Reviews Vol. , Issue 2000k [page]

2000 Mathematical Reviews  
. * 20001 Logic, language and reasoning * 03009 Logic programming ....... * 68010 Logic programming with non-monotonic semantics: representing knowledge and its computation Logics of uncertainty Low dimensional  ...  systems computational techniques and optimization ; * 74003 Structure and dynamics of quantum many-body systems * 81007 * 91002 * 65012 * 32002 Study Group Backward Stochastic Differential Equations Surveys  ... 

Neural Dynamic Logic of Consciousness: the Knowledge Instinct

L.I. Perlovsky
2006 The 2006 IEEE International Joint Conference on Neural Network Proceedings  
Dynamic Logic Mathematical formulation NMF solves the CC problem by using dynamic logic [ xxii,xxiii,xxiv,x ].  ...  This is the mechanism of dynamic logic defining the neural dynamics of NMF. The dynamic evolution of fuzziness from large to small is the reason for the name "dynamic logic."  ... 
doi:10.1109/ijcnn.2006.246706 dblp:conf/ijcnn/Perlovsky06 fatcat:2jqpxg457jfwthxg2bwffk2x5y

Page 3852 of Mathematical Reviews Vol. , Issue 2000e [page]

2000 Mathematical Reviews  
geometry and applications Dortmund, 1999 Dualities in gauge and string theories Dynamical systems, 7 Dynamical systems and differential equations, Vol. | * 76008 * 65011 * 55002 * 58001 * 93002 * 90005  ...  fluid dynamics, 1998 ..  ... 

Parametric macromodels of differential drivers and receivers

I.S. Stievano, I.A. Maio, F.G. Canavero, C. Siviero
2005 IEEE Transactions on Advanced Packaging  
This paper addresses the modeling of differential drivers and receivers for the analog simulation of high-speed interconnection systems.  ...  The proposed methodology is demonstrated on example devices and is applied to the prediction of transient waveforms and eye diagrams of a typical low-voltage differential signaling (LVDS) data link.  ...  In general, differential receivers have a nearly linear dynamic behavior; thus, linear parametric relations can be used for the dynamic parts of the model.  ... 
doi:10.1109/tadvp.2005.846931 fatcat:srlbslhzmnchthne5acv4qt5sq

Page 1201 of Mathematical Reviews Vol. , Issue 94b [page]

1994 Mathematical Reviews  
Prediction Patterns and dynamics in reactive media Perspectives on the history of mathematical logic Prague, 1992 Princeton, NJ, 1987 Probability in Banach spaces, 8 Problems: Differential equations Proceedings  ...  Rennes, 1991 Representation theory of finite groups and finite-dimensional algebras Research into zeta functions related to automorphic forms Research on bifurcation in low-dimensional dynamical Ring theory  ... 

Fuzzy Reasoning and Rough Sets [chapter]

T. Y. Lin
1994 Rough Sets, Fuzzy Sets and Knowledge Discovery  
As in [2] , [3] , [4] , rough set theory, fuzzy logic control, and modern differential geometric view of non-linear dynamic systems are integrated into one mathematical formalism, called rough logic  ...  Modeling of Dynamic Systems Given a set of differential equations, one can model either the solution directly --the theory of differentiable manifolds, or the set of differential equations as an embedded  ... 
doi:10.1007/978-1-4471-3238-7_40 fatcat:zycz6rutxzdutjsg6cgachevpq

Page 1829 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
problems Computer science logic Conference: Arithmetic, Proof Theory, and Computational Complexity Bootstrapping and Related Techniques, International Combinatorial, 14th British Differential Equations  ...  * 01016 - *01001 Differential equations and applied problems Differential equations in Banach spaces Differential equations (qualitative theory) Dubrovnik, 1991 Dundee, 1992 Dynamic economic models and  ... 

Logical Analysis of Hybrid Systems [chapter]

André Platzer
2012 Lecture Notes in Computer Science  
Rule schemata of the free-variable calculus for differential dynamic logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Correspondence of dynamic proof rules and transition semantics  ...  programs and correspondence to dynamical systems . . . . . . . . . . . . . . . . . . . . ..3.4 Operators and meaning in differential-algebraic dynamic logic (DAL) . . . . . . . . . . . . . . . . . . .  ... 
doi:10.1007/978-3-642-31623-4_3 fatcat:b7gnxodcqfgsfgj7an4aiptazm

Dynamic Logics of Dynamical Systems [article]

André Platzer
2012 arXiv   pre-print
properties, even about relations between multiple dynamical systems.  ...  In this survey, we focus on some of the representatives of the family of differential dynamic logics, which share the ability to express properties of dynamical systems having continuous dynamics described  ...  We have surveyed differential dynamic logic (dL) for hybrid systems, quantified differential dynamic logic (QdL) for distributed hybrid systems, and stochastic differential dynamic logic (SdL) for stochastic  ... 
arXiv:1205.4788v1 fatcat:2ahunsfdzfamdiwzd66m5e4wzq
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