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A model-theoretic characterization of monadic second order logic on infinite words
[article]

2016
*
arXiv
*
pre-print

*Monadic*

*second*

*order*

*logic*and linear temporal

*logic*are two

*logical*formalisms that can be used to describe classes

*of*

*infinite*

*words*, i.e., first-

*order*

*models*based

*on*the natural numbers with

*order*, ...

*Monadic*

*second*

*order*

*logic*over

*infinite*

*words*(S1S) can alternatively be described as

*a*first-

*order*

*logic*interpreted in P(ω), the power set Boolean algebra

*of*the natural numbers, equipped with modal ... We thank the referee for their valuable comments

*on*an earlier version

*of*this paper. ...

##
###
A MODEL-THEORETIC CHARACTERIZATION OF MONADIC SECOND ORDER LOGIC ON INFINITE WORDS

2017
*
Journal of Symbolic Logic (JSL)
*

*Monadic*

*second*

*order*

*logic*and linear temporal

*logic*are two

*logical*formalisms that can be used to describe classes

*of*

*infinite*

*words*, i.e., first-

*order*

*models*based

*on*the natural numbers with

*order*, ...

*Monadic*

*second*

*order*

*logic*over

*infinite*

*words*(S1S) can alternatively be described as

*a*first-

*order*

*logic*interpreted in ${\cal P}\left( \omega \right)$ , the power set Boolean algebra

*of*the natural ... We thank the referee for their valuable comments

*on*an earlier version

*of*this paper. ...

##
###
Monadic Second-Order Logic for Graphs: Algorithmic and Language Theoretical Applications
[chapter]

2009
*
Lecture Notes in Computer Science
*

This tutorial will present an overview

doi:10.1007/978-3-642-00982-2_2
fatcat:ryjvoaa7dnefrcruygfnpqso2i
*of*the use*of**Monadic**Second*-*Order**Logic*to describe sets*of*finite graphs and graph transformations, in relation with the notions*of*tree-width and clique-width. ... It will review applications to the construction*of*algorithms, to Graph Theory and to the extension to graphs*of*Formal Language Theory concepts. ...*A*graph, either finite or*infinite*, can be considered as*a**logical*structure whose domain (the ground set*of*the*logical*structure) consists*of*the set*of*vertices ;*a*binary relation*on*this set represents ...##
###
Page 2568 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

In other

*words*, satisfiability*of**a**monadic**second*-*order*property in the behaviour*of**a*machine can be expressed as*a**monadic**second*-*order*property*of*the machine itself. ... The key notion*of*the paper is “*monadic**second*-*order*compatibility”:*A*transduction f is called*monadic**second*-*order*compatible if every*monadic**second*-*order*sentence*A*in the signature*of*the labelled ...##
###
The monadic theory of finite representations of infinite words

2007
*
Information Processing Letters
*

This result can be seen as

doi:10.1016/j.ipl.2007.02.014
fatcat:nvdw46e7wzfa3b5qbllnc76vve
*a*translation, onto finite representations*of**infinite**words*,*of*Büchi's automata-*theoretic**characterization**of*S1S. ... In this paper, we consider existential*monadic**second*-*order**logic*(*monadic*Σ1)*on*finite unary graphs, that is finite graphs with functional edge relation. ... The*monadic**second**order*theory*of*lassos In this section, we consider*monadic**second**order**logic**on*lassos, i.e. unary graphs that are canonical encodings*of*ultimately periodic*words*. ...##
###
Page 7076 of Mathematical Reviews Vol. , Issue 99j
[page]

1999
*
Mathematical Reviews
*

Later, in work

*of*Biichi, McNaughton, and Rabin, such an equivalence was shown also between finite automata and*monadic**second*-*order**logic*over*infinite**words*and trees. ... It was shown that many complexity classes could be*characterized*by different versions*of**second*-*order**logic*. ...##
###
Page 6793 of Mathematical Reviews Vol. , Issue 2000j
[page]

2000
*
Mathematical Reviews
*

The primary objective

*of*this paper is to develop*a*general theory*of**logical*systems and*a*general theory*of*equivalence between*logics*in*order*to*characterize*algebraizable*logics*. ... Soc. 141 (1969), 1-35; MR 40 #30] to show the decidability*of*the*monadic**second*-*order*theory*of*two successors. Here the automaton worked over labeled*infinite*binary trees. ...##
###
Limited Set quantifiers over Countable Linear Orderings
[chapter]

2015
*
Lecture Notes in Computer Science
*

In this paper, we study several sublogics

doi:10.1007/978-3-662-47666-6_12
fatcat:dv6ak7eqgrh2fhs6ncjafwffve
*of**monadic*secondorder*logic*over countable linear*orderings*, such as first-*order**logic*, firstorder*logic**on*cuts, weak*monadic**second*-*order**logic*, weak*monadic*...*second*-*order**logic*with cuts, as well as fragments*of**monadic*secondorder*logic*in which sets have to be well*ordered*or scattered. ... Given*a*language V ⊆ {∈, ∈} • that represents the range*of**a*restricted set quantifier, we define the restricted projection*of*L as: This operation is the language*theoretic*counterpart to the*logical*...##
###
A Defense of Second-Order Logic

2010
*
Axiomathes
*

, in the following sense: if first-

doi:10.1007/s10516-010-9101-4
fatcat:hdqksz4hzvg6phufemkb5owfya
*order**logic*does not*characterize*adequately mathematical systems, given the existence*of*non-isomorphic firstorder interpretations,*second*-*order**logic*does not*characterize*... In this paper, I argue that the*second*-*order*theorist can solve each*of*these difficulties. As*a*result, secondorder*logic*provides the benefits*of**a*rich framework without the associated costs. ... The last step is to provide*a**one*-*one*mapping*of**monadic**second*-*order**logic*onto the truncated*model*theory. Azzouni's definition is as follows (Azzouni 1994, p. 15) . ...##
###
Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
[chapter]

2008
*
Lecture Notes in Computer Science
*

Hierarchical decompositions yielding the notions

doi:10.1007/978-3-540-70575-8_1
fatcat:ftpcqszcb5fs5nswbqnbnmy5ja
*of*tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with*Monadic**Second*-*order**Logic*are important ... Graph structure is*a*flexible concept covering many different types*of*graph properties. ... I thank*A*. Blumensath, M. Fellows and I. Walukiewicz for many useful comments*on**a*first draft*of*this overview. The first 11 references are books and survey articles. ...##
###
Remarks on Second-Order Consequence

2010
*
THEORIA : an International Journal for Theory, History and Fundations of Science
*

Tarski's definition

doi:10.1387/theoria.421
doaj:0fd8f87adda94489bca490f8727ddb5d
fatcat:efbtngjivjhobkvioh7llx76ya
*of**logical*consequence can take different forms when implemented in*second**order*languages, depending*on*what counts as*a**model*. ... In the canonical, or standard, version,*a**model*is just an ordinary structure and the (*monadic*)*second*-*order*variables are meant to range over all subsets*of*its domain. ... In other*words*, it presupposes*a*realist conception*of*set theory. Thus,*a*prerequisite to use canonical*second*-*order**logic*as*logic*is*a*commitment to some form*of*set-*theoretical*realism. ...##
###
Monadic Second-Order Logic with Arbitrary Monadic Predicates
[article]

2017
*
arXiv
*
pre-print

We study

arXiv:1709.03117v1
fatcat:bbhqfmurlnepfkzarzrc4tmpyi
*Monadic**Second*-*Order**Logic*(MSO) over finite*words*, extended with (non-uniform arbitrary)*monadic*predicates. ... We show that it defines*a*class*of*languages that has algebraic, automata-*theoretic*and machine-independent*characterizations*. ... all*of*weak*monadic**second*-*order**logic*, which coincides with*monadic**second*-*order**logic*. ...##
###
Logical definability on infinite traces

1996
*
Theoretical Computer Science
*

This generalizes results

doi:10.1016/0304-3975(95)00130-1
fatcat:4qsekf35zvftjbxixwoot2ie6y
*on**infinite**words*and*on*finite traces to*infinite*traces. It closes an important gap in the different*characterizations**of*recognizable languages*of**infinite*traces. ... The main results*of*the present paper are the equivalence*of*definability by*monadic*secondorder*logic*and recognizability for real trace languages, and that first-*order*definable, star-free, and aperiodic ... We also thank the anonymous referees from ICALP and especially from*Theoretical*Computer Science for the valuable comments which helped improving the presentation*of*this paper. ...##
###
Page 3 of Mathematical Reviews Vol. , Issue 94c
[page]

1994
*
Mathematical Reviews
*

It is shown that (1)

*a*Z- language L is Z-regular iff L is definable by*a**monadic**second*-*order*sentence, (2) the*monadic**second*-*order*theory*of*Z and the weak*monadic**second*-*order*theory*of*Z are equivalent ... In the article under review, the authors study the generalizations, from w to Z,*of*the weak and full*monadic**second*-*order*theory*of*the integers,*of*temporal*logic*,*of*regular grammars, and*of*finite ...##
###
Page 4947 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

We give

*a*correspondence (in the style*of*the Buchi theorem for regular languages) between L(SBTA) and MSOf[Sig], i.e.*a*decidable*monadic**second*-*order**logic*over*a*suitable*infinite*signature Sig. ... We also introduce*a*nat- ural subclass*of*Y(SBTA) which still properly contains the class*of*regular languages and which is proved to be*characterized*by*monadic**second*-*order**logic*over*a*finite signature ...
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