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First-Order Logic Definability of Free Languages [chapter]

Violetta Lonati, Dino Mandrioli, Federica Panella, Matteo Pradella
2015 Lecture Notes in Computer Science  
Operator Precedence Grammars (OPGs) define a deterministic class of context-free languages, which extend input-driven languages and still enjoy many properties: they are closed w.r.t.  ...  FrGs were originally introduced for grammatical inference of programming languages.  ...  In this paper, instead, we will exploit the fact that FrLs can be defined in terms of first-order logic sentences, but first-order logic can also be used to define further, even more sophisticated, constraints  ... 
doi:10.1007/978-3-319-20297-6_20 fatcat:atvrg2dplfeyjkkiy7mfxiqtta

Aperiodicity, Star-freeness, and First-order Definability of Structured Context-Free Languages [article]

Dino Mandrioli
2021 arXiv   pre-print
A classic result in formal language theory is the equivalence among noncounting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic.  ...  Together with first-order completeness of linear temporal logic these results constitute a theoretical foundation for model-checking algorithms.  ...  An RE E defines a language over Σ, denoted by L(E). Monadic second and first order logics to define languages [48] .  ... 
arXiv:2006.01236v3 fatcat:c4n3yzumkjeutctgshukzheddm

Non-definability of languages by generalized first-order formulas over (N,+) [article]

Andreas Krebs, A. V. Sreejith
2012 arXiv   pre-print
We consider first-order logic with monoidal quantifiers over words.  ...  We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical predicate.  ...  We know that the set of languages accepted by uniform-AC 0 circuits are exactly those definable by first order logic using order, addition and multiplication relations.  ... 
arXiv:1204.6179v2 fatcat:k7imom23ozatdjuoadgwpknnpq

Proving that a Tree Language is not First-Order Definable [article]

Martin Beaudry
2018 arXiv   pre-print
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized  ...  We show that a recursive proof exists for the syntactic algebra of every non-definable language. We also investigate certain types of uniform recursive proofs.  ...  The language of those trees where λ(root) = ∩ and val(root) = 1 is not first-order definable.  ... 
arXiv:1812.01674v1 fatcat:beb5kttocjdenkeebx2ljcsuje

Tree Languages Defined in First-Order Logic with One Quantifier Alternation

Mikolaj Bojanczyk, Luc Segoufin, unknown Anonymous
2010 Logical Methods in Computer Science  
These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is .  ...  We study tree languages that can be defined in \Delta_2 .  ...  Among them one can find [11, 15, 13, 7] : a) word languages that can be defined in the temporal logic with operators F and F −1 ; b) word languages that can be defined by a first-order formula with two  ... 
doi:10.2168/lmcs-6(4:1)2010 fatcat:27ect4obrrheha75za2up6t57e

Definable relations and first-order query languages over strings

Michael Benedikt, Leonid Libkin, Thomas Schwentick, Luc Segoufin
2003 Journal of the ACM  
Two classical results on logic and language theory state that languages thus definable in monadic second-order logic (MSO) are precisely the regular languages [20] , and the languages definable in first-order  ...  One can then look at definable sets, those of the form fã j M j = '(ã)g, where ' is a first-order formula in the language of M.  ...  Matching with LIKE can be expressed in first-order logic over S: indeed, with LIKE one can only define star-free languages, which are FO-definable in S.  ... 
doi:10.1145/876638.876642 fatcat:dnyytdskv5holgdahoekdxucki

Definability of Languages by Generalized First-Order Formulas over (N,+) [chapter]

Amitabha Roy, Howard Straubing
2006 Lecture Notes in Computer Science  
We consider an extension of first-order logic by modular quantifiers of a fixed modulus q.  ...  More generally, we completely characterize the regular languages definable in this logic.  ...  We do know, for example, thanks to the circuit lower bounds, that regular languages definable by first-order sentences with arbitrary numerical predicates are all definable in F O[<, {≡ s : s > 1}], and  ... 
doi:10.1007/11672142_40 fatcat:perekogksbabhgf3dgtgskhr5q

First-Order Definability of Transition Structures

Antje Rumberg, Alberto Zanardo
2018 Journal of Logic, Language and Information  
In this paper, we provide a class of first-order definable Kripke structures that preserves L t -validity w.r.t. transition structures.  ...  In that framework, sentences of the transition language L t are evaluated on transition structures at pairs consisting of a moment and a set of transitions.  ...  The first-order definability of index structures is essentially a result of that correspondence: the prunings of a given branching time structure are first-order definable substructures.  ... 
doi:10.1007/s10849-018-9276-4 fatcat:wocsnw7dnrc6dadmdz3xzpym2q

On Existentially First-Order Definable Languages and Their Relation to NP

Bernd Borchert, Dietrich Kuske, Frank Stephan
1999 RAIRO - Theoretical Informatics and Applications  
The proofs rely on a result of Pin and Weil characterizing the automata of existentially first-order definable languages. Résumé.  ...  but not quantifierfree definable in FO[<, min, max, +1, −1].  ...  It can be considered to be the first result about the close relation of leaf languages for NP and existentially first-order definable languages.  ... 
doi:10.1051/ita:1999116 fatcat:hl6kcxk2c5coth2m6trkcqv2oa

Definability of Languages by Generalized First-Order Formulas over $(\mathbb{N},+)$

Amitabha Roy, Howard Straubing
2007 SIAM journal on computing (Print)  
ACC(q) has a model-theoretic characterization as the family of languages definable in an extension of first-order logic which contains predicate symbols for arbitrary relations on the natural numbers,  ...  We consider an extension of first-order logic by modular quantifiers of a fixed modulus q.  ...  In this section, we consider definability of languages in first-order logic with modular quantifiers when we allow monadic (i.e., arity 1) numerical predicates.  ... 
doi:10.1137/060658035 fatcat:koehhopovnae7dyvcpvdyq4bgm

Tree Languages Defined in First-Order Logic with One Quantifier Alternation [chapter]

Mikołaj Bojańczyk, Luc Segoufin
Lecture Notes in Computer Science  
These are tree languages definable by a first-order formula whose quantifier prefix is ∃ * ∀ * , and simultaneously by a first-order formula whose quantifier prefix is ∀ * ∃ * , both formulas over the  ...  We study tree languages that can be defined in ∆2.  ...  Among them one can find [11, 15, 13, 7] : a) word languages that can be defined in the temporal logic with operators F and F −1 ; b) word languages that can be defined by a first-order formula with two  ... 
doi:10.1007/978-3-540-70583-3_20 fatcat:s3jvpvpoyvgtjjg3x6cakllvsy

Use of language elements in the process of social communication

O Muhammadiyeva
2022 Zamonaviy lingvistik tadqiqotlar: xorijiy tajribalar, istiqbolli izlanishlar va tillarni o'qitishning innovatsion usullari  
The research focuses on cognitive linguistics, as well as one of the most pressing problems in German lexicology and stylistics – the study of figurative words in the language of German youth.  ...  The goals and objectives of the study are to study the level of use of figurative words in the language of German youth and to classify the cognitive and semantic meanings of such words.  ...  In conclusion, it is often the case that the state of public consciousness or language is assessed, and this is usually defined as a "bad" language condition.  ... 
doi:10.47689/linguistic-research-vol-iss1-pp321-323 fatcat:o24dwxd7gjh6pbcfzxq2isea7q

Self-study in learning foreign language

D Dauletova, G Dauletbaeva
2022 Ренессанс в парадигме новаций образования и технологий в XXI веке  
The use of technology has received increasing recognition as a means capable of bridging formal and informal settings in the target language learning and enabling students to actively and effectively use  ...  Subsequent Confirmatory factory analysis -CFA with data from university students confirmed a secondorder common factor with these four first-order latent constructs:  ...  Although the importance of the role of the strategic and motivational factors in first and second language contexts has been well documented, how these factors function in relation to students' learning  ... 
doi:10.47689/innovations-in-edu-vol-iss1-pp191-193 fatcat:tonl3kicszdqrnp54zer4hbz4m

Teaching grammar material by jokes and games

G Mardieva
2022 Zamonaviy lingvistik tadqiqotlar: xorijiy tajribalar, istiqbolli izlanishlar va tillarni o'qitishning innovatsion usullari  
At first, theoretical principles of teaching grammar are analyzed, then, recommendation how to teach grammar material by games and jokes are offered.  ...  Defining and non-defining clauses [4].  ...  Any idea has to be expressed mostly in the usual grammatical order of SUBJECT + PREDICATE + OBJECT.  ... 
doi:10.47689/linguistic-research-vol-iss1-pp308-310 fatcat:7pzaafptn5dwnh7fpzvunfd7kq

Teaching writing essay to intermediate level learners

Sh Seytnazarova
2022 Ренессанс в парадигме новаций образования и технологий в XXI веке  
In English essay first meant "a trial" or "an attempt", and this is still an alternative meaning.  ...  The Frenchman Michel de Montaigne (1533–1592) was the first author to describe his work as essays; he used the term to characterize these as "attempts" to put his thoughts into writing, and his essays  ...  Clearly define the claims, write out the reasons, the evidence. Look for weaknesses of logic, and also strengths.  ... 
doi:10.47689/innovations-in-edu-vol-iss1-pp213-214 fatcat:vcraupymb5fzvpetktwrbmtup4
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