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

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 ...

##
###
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

doi:10.1093/logcom/12.1.211
fatcat:yowegpu725gxpbpi7eabhc6caa
*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. ...##
###
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

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. ...

##
###
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

2001
*
Journal of Symbolic Logic (JSL)
*

Lindström, one cannot extend

doi:10.2307/2694984
fatcat:4y4lbm2edvbudfebzymxtsh224
*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. ...##
###
Finite and Algorithmic Model Theory (Dagstuhl Seminar 17361)

2018
*
Dagstuhl Reports
*

This report documents

doi:10.4230/dagrep.7.9.1
dblp:journals/dagstuhl-reports/DawarGKS17
fatcat:teyilwvdgrd6tch2gdb4d4dd5m
*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. ...##
###
A Journey into Ontology Approximation: From Non-Horn to Horn (Abstract)

2020
*
International Workshop on Description Logics
*

Supported by

dblp:conf/dlog/HagaLMW20
fatcat:unleafp5xndydgqi6nooyfyenm
*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. ...##
###
On expressive power and class invariance
[article]

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*. ...

##
###
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

1996
*
International Journal of Approximate Reasoning
*

It starts with a symbolic

doi:10.1016/s0888-613x(96)00076-x
fatcat:6roqxojnand6plzeciurvovgcq
*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. ...##
###
Report on BCTCS 2012

2012
*
Bulletin of the European Association for Theoretical Computer Science
*

am Main ("On

dblp:journals/eatcs/Pratt-Hartmann12
fatcat:cgww3bkyazb6ncfzowolyhdkk4
*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. ...##
###
Modal Mu-Calculus
[chapter]

2001
*
Texts in Computer Science
*

During

doi:10.1007/978-1-4757-3550-5_5
fatcat:mfjlygtmd5e6lbmjdhr73oaisa
*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. ...##
###
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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