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

Silvio Ghilardi, Samuel J. van Gool
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.  ... 
arXiv:1503.08936v2 fatcat:l75wkjekljdvnkyuqrfoae7ita

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

SILVIO GHILARDI, SAMUEL J. VAN GOOL
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.  ... 
doi:10.1017/jsl.2016.70 fatcat:i7ndwyefhnhupdichkaz2econu

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

Bruno Courcelle
2009 Lecture Notes in Computer Science  
This tutorial will present an overview 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  ... 
doi:10.1007/978-3-642-00982-2_2 fatcat:ryjvoaa7dnefrcruygfnpqso2i

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

Anuj Dawar, David Janin
2007 Information Processing Letters  
This result can be seen as 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.  ... 
doi:10.1016/j.ipl.2007.02.014 fatcat:nvdw46e7wzfa3b5qbllnc76vve

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]

Thomas Colcombet, A. V. Sreejith
2015 Lecture Notes in Computer Science  
In this paper, we study several sublogics 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  ... 
doi:10.1007/978-3-662-47666-6_12 fatcat:dv6ak7eqgrh2fhs6ncjafwffve

A Defense of Second-Order Logic

Otávio Bueno
2010 Axiomathes  
, in the following sense: if first-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) .  ... 
doi:10.1007/s10516-010-9101-4 fatcat:hdqksz4hzvg6phufemkb5owfya

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects [chapter]

Bruno Courcelle
2008 Lecture Notes in Computer Science  
Hierarchical decompositions yielding the notions 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.  ... 
doi:10.1007/978-3-540-70575-8_1 fatcat:ftpcqszcb5fs5nswbqnbnmy5ja

Remarks on Second-Order Consequence

Ignacio Jané
2010 THEORIA : an International Journal for Theory, History and Fundations of Science  
Tarski's definition 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.  ... 
doi:10.1387/theoria.421 doaj:0fd8f87adda94489bca490f8727ddb5d fatcat:efbtngjivjhobkvioh7llx76ya

Monadic Second-Order Logic with Arbitrary Monadic Predicates [article]

Nathanaël Fijalkow, Charles Paperman
2017 arXiv   pre-print
We study 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.  ... 
arXiv:1709.03117v1 fatcat:bbhqfmurlnepfkzarzrc4tmpyi

Logical definability on infinite traces

Werner Ebinger, Anca Muscholl
1996 Theoretical Computer Science  
This generalizes results 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.  ... 
doi:10.1016/0304-3975(95)00130-1 fatcat:4qsekf35zvftjbxixwoot2ie6y

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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