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Approximating the Expressive Power of Logics in Finite Models [chapter]

Argimiro Arratia, Carlos E. Ortiz
2004 Lecture Notes in Computer Science  
In order to give a precise measure of the proximity between satisfaction of a formula in an arithmetic model and satisfaction of the same formula in the "approximate" model, we define the approximate formulas  ...  With this work we take steps towards understanding how well can we approximate, without a true order, the expressive power of logics that capture complexity classes on ordered structures.  ...  Our purpose is to approximate the expressive power of arithmetic relations occurring naturally in finite model theory by arithmetic relations that are "weaker" yet perform better under definability tools  ... 
doi:10.1007/978-3-540-24698-5_57 fatcat:cpgtycksqzhutnyubrmc3gawly

Page 6798 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
Summary: “This paper concentrates on comparing the relative expressive power of five nonmonotonic logics that have appeared in the literature.  ...  The expressive power of the priority logic of X. Wang, J.-H. You and L. Y. Yuan is also analyzed and shown to coincide with that of default logic.  ... 

Special Issue: Fixpoints in Computer Science 2000

2002 Journal of Logic and Computation  
We show that there is no finite set of modalities such that the temporal logic over and monadic logic of order have the same expressive power over the natural numbers.  ...  As a consequence of our proof, we obtain that there is no finite base temporal logic which is expressively complete for the -calculus. -Calculus with Explicit Points and Approximations M. Dam and D.  ...  We show that there is no finite set of modalities such that the temporal logic over and monadic logic of order have the same expressive power over the natural numbers.  ... 
doi:10.1093/logcom/12.1.211 fatcat:yowegpu725gxpbpi7eabhc6caa

Page 5248 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
The author demonstrates that the rough concepts logic is weaker in terms of expressive power than the first-order logic for rough concepts.  ...  The resolution of the repre- sentation system is expressed in the rough set model in terms of an equivalence relation called an indiscernibility relation.  ... 

Macromodeling of Nonlinear Digital I/O Drivers

B. Mutnury, M. Swaminathan, J.P. Libous
2006 IEEE Transactions on Advanced Packaging  
In this paper, a modeling technique using spline functions with finite time difference approximation is discussed for modeling moderately nonlinear digital input/output (I/O) drivers.  ...  Spline function with finite time difference approximation includes the previous time instances of the driver output voltage/current to capture the output dynamic characteristics of digital drivers accurately  ...  Black-box modeling techniques are helpful in modeling digital driver circuits since they are independent of the knowledge of the internal logic of the driver.  ... 
doi:10.1109/tadvp.2005.848396 fatcat:nxaqhwrwwras3alzsketccvfra

Page 4935 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
In the present paper, they discuss deductive query languages with recursive types. The first focus of the paper is to study the expressive power of two extensions of the language COL [S.  ...  ., to model spatial database applications, which may involve— finitely representable—infinite sets of points, as a consequence of which the active domain will no longer be finite in general.  ... 

On the maximality of logics with approximations

José Iovino
2001 Journal of Symbolic Logic (JSL)  
Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem).  ...  Now, when the underlying metric topology is discrete, the resulting model theory coincides with first order model theory, so this logic extends first order in the sense described above.  ...  The aim of this paper is to show that if one is to develop a smooth model theory for analytic structures, then the expressive power of the logic H cannot be increased.  ... 
doi:10.2307/2694984 fatcat:4y4lbm2edvbudfebzymxtsh224

Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)

Anuj Dawar, Erich Grädel, Phokion G. Kolaitis, Thomas Schwentick, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17361 "Finite and Algorithmic Model Theory".  ...  We formalize agent-based models as stochastic processes whose states are metafinite models, and we define a notion of abstraction.  ...  Our main results are conditions that imply an abstraction is sound, and further conditions that imply it preserves the Markov property.  ... 
doi:10.4230/dagrep.7.9.1 dblp:journals/dagstuhl-reports/DawarGKS17 fatcat:teyilwvdgrd6tch2gdb4d4dd5m

A Journey into Ontology Approximation: From Non-Horn to Horn (Abstract)

Anneke Haga, Carsten Lutz, Johannes Marti, Frank Wolter
2020 International Workshop on Description Logics  
Supported by the DFG Collaborative Research Center 1320 EASE -Everyday Activity Science and Engineering.  ...  Horn DLs, in contrast, enjoy favourable properties such as the existence of universal models and of 'consequence-based' reasoning algorithms that avoid reasoning by cases [6] .  ...  incomplete finite approximations in practice.  ... 
dblp:conf/dlog/HagaLMW20 fatcat:unleafp5xndydgqi6nooyfyenm

On expressive power and class invariance [article]

Yanjing Wang, Francien Dechesne
2009 arXiv   pre-print
In particular, we introduce the notion of class bisimulation to capture the expressive power of modal logics.  ...  One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive power.  ...  From the above results we know that expressive power can be approximated by distinguishing power for increasing sizes of classes of models.  ... 
arXiv:0905.4332v1 fatcat:toqzs57w7zaotowr37ffkohdzm

Page 4185 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
Such results turn the notoriously difficult questions of com- plexity theory into questions about the expressive power of logical languages on finite structures.  ...  Thus, for instance, Fagin’s theorem (in Chapter 7) tells us that the expressive power of existential second-order logic on finite structures corresponds exactly to the complexity class NP.  ... 

A rough logic formalism for fuzzy controllers: A hard and soft computing view

T.Y. Lin
1996 International Journal of Approximate Reasoning  
It starts with a symbolic model that describes the control system in terms of predicates in rough logic.  ...  In formal logic, the symbolic model is called a theory and the transformation an interpretation of the theory. Of course, interpretations are usually not unique.  ...  ACKNOWLEDGMENTS The author would like to express his deepest thanks to Professor Zadeh for his kind guidance and warm invitation to join the Berkeley Initiative in soft Computing (BISC) group.  ... 
doi:10.1016/s0888-613x(96)00076-x fatcat:6roqxojnand6plzeciurvovgcq

Report on BCTCS 2012

Ian Pratt-Hartmann
2012 Bulletin of the European Association for Theoretical Computer Science  
am Main ("On the expressive power of logics with invariant uses of arithmetic predicates") and Daniel Kroening, of Oxford University ("SAT over an Abstract Domain").  ...  As in previous years, the London Mathematical Society sponsored a keynote talk in Discrete Mathematics: for this, Rod Downey, of the Victoria University of Wellington, gave two lectures on "Fundamentals  ...  expressible as formula of the logic in hand and vice versa.  ... 
dblp:journals/eatcs/Pratt-Hartmann12 fatcat:cgww3bkyazb6ncfzowolyhdkk4

Modal Mu-Calculus [chapter]

Colin Stirling
2001 Texts in Computer Science  
During the 1970s, the theory of program correctness was extended by investigating more powerful logics, and studying them in a manner more similar to the traditions of mathematical logic.  ...  Since → is often used to represent the transition relation in models (alias the accessibility relation from modal logic), we use ⇒ rather than → for boolean implication.  ...  The expressive power of HML in this form is quite weak: obviously a given HML formula can only make statements about a given finite number of steps into the future.  ... 
doi:10.1007/978-1-4757-3550-5_5 fatcat:mfjlygtmd5e6lbmjdhr73oaisa

Page 8174 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
“A logic L is termed finitely approximable with respect to com- pleteness if for every finite system & that is incomplete in L there exists an extension of the logic L in which & remains incomplete.  ...  The logic does not have the finite model property. The main result of the paper is the proof of decidability, which is obtained by the application of the mosaic method. G.  ... 
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