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Structure Theorem and Strict Alternation Hierarchy for FO2 on Words
[chapter]
Lecture Notes in Computer Science
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For both languages, our structure theorems show exactly what is expressible using a given quantifier depth, n, and using m blocks of alternating quantifiers, for any m ≤ n. ...
We prove precise structure theorems that characterize the exact expressive power of first-order logic with two variables on words. ...
Alternation hierarchy for FO 2 [<] We define alternation rankers and prove our structure theorem (Theorem 4.5) for FO 2 m,n [<] . ...
doi:10.1007/978-3-540-74915-8_27
fatcat:43ff4bcaqvaixfannijp7wmoxu
On FO 2 Quantifier Alternation over Words
[chapter]
2009
Lecture Notes in Computer Science
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We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. ...
hierarchy -- and conjecturally equal to it. ...
Then M ∈ FO 2 m+1 \ FO 2 m−1 by Theorem 2.11. ⊓ ⊔ The fact that the R m and L m form strict hierarchies (Proposition 2.6), together with Theorem 2.11, proves that the F O 2 m hierarchy is infinite. ...
doi:10.1007/978-3-642-03816-7_44
fatcat:rnqstr6jrjf7tceibcyxr3btpi
The Half-Levels of the FO2 Alternation Hierarchy
2016
Theory of Computing Systems
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The alternation hierarchy in two-variable first-order logic FO 2 [<] over words was shown to be decidable by Kufleitner and Weil, and independently by Krebs and Straubing. ...
., for every integer m one can decide whether a given regular language is definable in Σ 2 m . Among other techniques, the proof relies on an extension of block products to ordered monoids. ...
It is known that the languages definable in FO 2 m form a strict hierarchy [43] . ...
doi:10.1007/s00224-016-9712-2
fatcat:aymcfkllrjbm7cwwatuiej6adq
The Regular Languages of First-Order Logic with One Alternation
[article]
2022
arXiv
pre-print
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The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. ...
This shows that the so-called Central Conjecture of Straubing holds for Σ_2 over languages with a neutral letter, the first progress on the Conjecture in more than 20 years. ...
Acknowledgments We wish to thank Nikhil Balaji and Sébastien Tavenas. The last author acknowledges financial support by the DFG grant ZE 1235/2-1. ...
arXiv:2203.06075v1
fatcat:bqmrgor3zzautkfdttpoqvrwaq
Block Products and Nesting Negations in FO2
[chapter]
2014
Lecture Notes in Computer Science
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The alternation hierarchy in two-variable first-order logic FO 2 [<] over words was recently shown to be decidable by Kufleitner and Weil, and independently by Krebs and Straubing. ...
Thus, the m th level of the FO 2 -alternation hierarchy is the Boolean closure of Σ 2 m . ...
It is known that the languages definable in FO 2 m form a strict hierarchy, see e.g. [16] . ...
doi:10.1007/978-3-319-06686-8_14
fatcat:avobzglq4vatphl46l35gg3q7q
First-Order Logic with Two Variables and Unary Temporal Logic
1997
BRICS Report Series
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We investigate the power of first-order logic with only two variables over<br />omega-words and finite words, a logic denoted by FO2. ...
Our proof of the small model property for unary-TL is based on an analysis of unary-TL types. ...
There are some remaining questions: (1) Is the FO 2 quantifier alternation hierarchy strict? ...
doi:10.7146/brics.v4i5.18784
fatcat:pvsnadu5kffk5j4dh45rfnksye
Understanding Semantic Web and Ontologies: Theory and Applications
[article]
2010
arXiv
pre-print
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Semantic Web is actually an extension of the current one in that it represents information more meaningfully for humans and computers alike. ...
In fact, Ontology is a key technique with which to annotate semantics and provide a common, comprehensible foundation for resources on the Semantic Web. ...
In other words, it is the process of change or modification of the structure of an ontology in order to make it suitable for purposes other than the original one. There are two types of translation. ...
arXiv:1006.4567v1
fatcat:ay2xkyhmlvdhheamib5ub5zzjm
The Regular Languages of First-Order Logic with One Alternation
2022
Proceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science
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The regular languages with a neutral letter expressible in firstorder logic with one alternation are characterized. ...
This shows that the so-called Central Conjecture of Straubing holds for Σ 2 over languages with a neutral letter, the first progress on the Conjecture in more than 20 years. ...
ACKNOWLEDGMENTS We wish to thank Nikhil Balaji and Sébastien Tavenas for fruitful discussions. ...
doi:10.1145/3531130.3533371
fatcat:44jaeoem7ffc3e4fzqaznlg53y
Ontology revision
[chapter]
1995
Lecture Notes in Computer Science
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This paper is partly a summary of early results, and partly an account of ongoing work in this area. ...
A number of sub-disciplines in artificial intelligence, philosophy and recursion theory have results that are relevant to ontology expansion even though their motivations were quite different. ...
ACKNOWLEDGEMENTS I am indebted to my colleagues in the Knowledge Systems Group for many discussions pertinent to this work. ...
doi:10.1007/3-540-60161-9_26
fatcat:rm53wk3lbvectjwtdewfunguay
Around Dot Depth Two
[chapter]
2010
Lecture Notes in Computer Science
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Automata for this class are not known, nor is its precise placement within the dot-depth hierarchy of starfree languages. ...
Using ideas from Straubing's "delay theorem", we extend our earlier work [LPS08] to propose partially-ordered two-way deterministic finite automata with look-around (po2dla) and a new interval temporal ...
KL would like to thank Manfred Kufleitner, Howard Straubing and Pascal Weil for discussions about the status of the logic FO 2 [<, S] within the dot-depth hierarchy during a visit in May-June '07 to LaBRI ...
doi:10.1007/978-3-642-14455-4_28
fatcat:s62bpy3t4bfvnoldrbcw5hf264
Deterministic Logics for UL
[article]
2014
arXiv
pre-print
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We revisit this language class with emphasis on notion of unambiguity and develop on the concept of Deterministic Logics for UL. ...
Logics such as TL[F,P], FO2[<] are not deterministic and have been shown to characterize UL using algebraic methods. ...
Since then, several diverse and unexpected characterizations have emerged for this language class: ∆ 2 [<] in the quantifier-alternation hierarchy of first-order definable languages [PW97] , the two variable ...
arXiv:1401.2714v1
fatcat:sxy5uh6fsncr7a46meb2eck6hq
Formal language theory of logic fragments
[article]
2015
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A combinatorial description in terms of so-called rankers is given for all full levels as well as all half levels of the quantifier alternation hierarchy of FO2 over the order predicate, both with and ...
Also in the second part, effective algebraic criteria describing all full levels as well as all half levels of the quantifier alternation hierarchy of FO2 over several signatures are given, yielding in ...
The structure of the quantifier alternation hierarchy is depicted in Figure 4 .2. ...
doi:10.18419/opus-3477
fatcat:xhpgb35uubadlmlroc5mk354j4
Abstracts of Working Papers in Economics
1997
Abstracts of Working Papers in Economics
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TI Report on the Investment Performance of Defaulted Bonds for 1994 and 1987-1994. AU Altman, Edward I.; ...
We prove the conjecture for n less than or equal to 3, and provide bounds on the number of NE's in m x n nondegenerate games when min (m,n) is less than or equal to 4. Money. ...
TI The Term Structure of Interest Rates: Alternative Approaches and Their Implications for the Valuation of Contingent Claims. AA New York University. ...
doi:10.1017/s0951007900003508
fatcat:sjk3leigpvgdfeuxuh5dsgiuaa
Membership and separation problems inside two-variable first order logic
2022
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variables, a fragment known as FO2[For languages of finite words, membership for these fragments has already been solved. ...
This thesis studies the expressive power of restricted fragments of first order logic on words with the order predicate. ...
FO 2 quantifier alternation hierarchy, in other words, for all levels of the ranker comparison hierarchy. ...
doi:10.26174/thesis.lboro.17872106
fatcat:xg6ajzwsh5hyxerq6kz6aengua
An Introduction to Model Versioning
[chapter]
2012
Lecture Notes in Computer Science
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Thereby, we aim at equipping students and researchers alike that are new to this domain with enough information for commencing to contribute to this challenging research area. P. Brosch et al. ...
In this tutorial, we give an introduction to the foundations of model versioning, the underlying technologies for processing models and their evolution, as well as the state of the art in model versioning ...
Merging textual languages with a strict syntactic structure (such as XML) might be more appropriate than merging languages which mix several properties of potentially independent concepts into one line ...
doi:10.1007/978-3-642-30982-3_10
fatcat:zqoem7stoja7fd32frq6s6hhca
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