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Abstract rewriting internalized [article]

Maxime Lucas
2020 arXiv   pre-print
In the case of C= Set or C = Vect we recover classical results of abstract and algebraic rewriting in a slightly more general form, closer to von Oostrom's notion of decreasing diagrams.  ...  In traditional rewriting theory, one studies a set of terms up to a set of rewriting relations. In algebraic rewriting, one instead studies a vector space of terms, up to a vector space of relations.  ...  Abstract and algebraic rewriting In this section, we recall some of the standard results of abstract and algebraic rewriting.  ... 
arXiv:2002.06004v1 fatcat:wlfy7zyftnhx7jt4tzfsd7dhba

Introducing Abstractions via Rewriting [chapter]

William D. Young
2005 Lecture Notes in Computer Science  
The abstractions are introduced through semantics-preserving rewrite rules.  ...  We outline techniques for automatically "retrofitting" a detailed low-level model with abstractions that facilitate reasoning about the properties of a model.  ...  The abstracted version, on the other hand, reveals obvious simplifications that can be implemented as rewrites.  ... 
doi:10.1007/11560548_41 fatcat:ncorxe6earg4bmzekk42p6admy

Structures for Abstract Rewriting

Marc Aiguier, Diane Bahrami
2007 Journal of automated reasoning  
In this paper, we investigate an abstract form of rewriting, by following the paradigm of "logical-system independency".  ...  Finally, we introduce convergent rewrite systems that enable one to describe deduction procedures for their corresponding theory, and propose a Knuth-Bendix style completion procedure in this abstract  ...  Abstract rewriting modulo theories and more This section is devoted to generalize, in our abstract framework, the notion of rewriting modulo theories.  ... 
doi:10.1007/s10817-006-9065-7 fatcat:xqjib73s35efdcz3aq2hhgmvle

From Abstract Rewriting Systems to Abstract Proof Systems [article]

Clemens Grabmayer
2013 arXiv   pre-print
With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract rewriting systems.  ...  Some personal recollections on the introduction of 'abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility.  ...  I thank Vincent van Oostrom for discussions, for explaining to me the origins of abstract rewriting systems in the work of Newman, and for his comments about previous versions of this text.  ... 
arXiv:0911.1412v2 fatcat:tnual6eejzggfma7lhvroz5cku

An abstract concurrent machine for rewriting [chapter]

Nachum Dershowitz, Naomi Lindenstrauss
1990 Lecture Notes in Computer Science  
Term rewriting corresponds to reduction in applicative languages; narrowing of terms corresponds to goal reduction in logic languages. An abstract machine is described for rewriting and narrowing.  ...  The way our abstract machine works for rewriting is that any given term t that we wish to rewrite has a process assigned to it.  ...  In this paper, we show how different rewriting and narrowing strategies can be implemented on an abstract concurrent machine.  ... 
doi:10.1007/3-540-53162-9_48 fatcat:zj662ceq6zbfdgod32ckojx4gu

Rewriting Abstract Structures: Materialization Explained Categorically [chapter]

Andrea Corradini, Tobias Heindel, Barbara König, Dennis Nolte, Arend Rensink
2019 Green Chemistry and Sustainable Technology  
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects.  ...  The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work.  ...  obtained by rewriting an abstract object. → Sect. 3 We decorate abstract objects with annotations from an ordered monoid and extend abstract rewriting to abstract objects with annotations.  ... 
doi:10.1007/978-3-030-17127-8_10 dblp:conf/fossacs/CorradiniHKNR19 fatcat:bxe7khmssbenfjrmgehlauwzoy

Rewriting Abstract Structures: Materialization Explained Categorically [article]

Andrea Corradini and Tobias Heindel and Barbara König and Dennis Nolte and Arend Rensink
2019 arXiv   pre-print
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects.  ...  The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work.  ...  Definition 35 (Abstract rewriting step ↪).  ... 
arXiv:1902.04809v1 fatcat:anph56vyhbgz3c477i53jwgrq4

Finding small counterexamples for abstract rewriting properties

2018 Mathematical Structures in Computer Science  
Rewriting notions like termination, normal forms and confluence can be described in an abstract way referring to rewriting only as a binary relation.  ...  Several theorems on rewriting, like Newman's lemma, can be proved in this abstract setting.  ...  As our abstract rewrite relations are just binary relations on a set A, in this paper we will mainly speak about binary relations rather than rewrite systems.  ... 
doi:10.1017/s0960129518000221 fatcat:gbj6elu7kreo5dunggttvv6m64

An Abstract Way to Define Rewriting Logic

Marc Aiguier, Diane Bahrami, Delphine Longuet
2006 Electronical Notes in Theoretical Computer Science  
Keywords: Rewriting formal system, abstract rewrite system, abstract rewriting logic, reachability and provability models, soundness and completeness results 1  ...  To achieve this purpose, we will show that there exists a valid and useful notion of rewriting logic associated to any rewriting theory fitting an abstract framework developed by two of the authors in  ...  This requires first to give an abstract form of logics which parameterize rewriting logic, and then to study rewriting in this abstract framework of logics.  ... 
doi:10.1016/j.entcs.2005.09.033 fatcat:tedzcb3f3nebtiaayairp5wlsa

Categorical Abstract Rewriting Systems and Functoriality of Graph Transformation [article]

Dominique Duval and Rachid Echahed and Frédéric Prost
2011 arXiv   pre-print
In this paper, we introduce a new notion of abstract rewriting in the framework of categories. Then, we define the functoriality property of rewriting systems.  ...  Rewriting systems are often defined as binary relations over a given set of objects.  ...  Introduction Various properties of rewriting systems can be defined on an abstract level by using the notion of abstract rewriting systems (see e.g., [1] ).  ... 
arXiv:1101.3417v3 fatcat:sr7qnb2t4bggtag4vewonf2vam

Summary Level Training of Sentence Rewriting for Abstractive Summarization [article]

Sanghwan Bae, Taeuk Kim, Jihoon Kim, Sang-goo Lee
2019 arXiv   pre-print
As an attempt to combine extractive and abstractive summarization, Sentence Rewriting models adopt the strategy of extracting salient sentences from a document first and then paraphrasing the selected  ...  Background Sentence Rewriting In this paper, we focus on single-document multisentence summarization and propose a neural abstractive model based on the Sentence Rewriting framework (Chen and Bansal  ...  The abstractor rewrites each of the selected sentences to form a summary S = {f (ŝ 1 ), f (ŝ 2 ), • • • , f (ŝ k )}, where f is an abstracting function.  ... 
arXiv:1909.08752v3 fatcat:vrsc6uaf7zbnhbr663y7jbqi6i

Rewriting ALCHIQ to Disjunctive Existential Rules (Extended Abstract)

David Carral, Markus Krötzsch
2020 International Workshop on Description Logics  
If such a rewriting can always be computed, then L 1 is (effectively, fact-entailment preserving) rewritable to L 2 .  ...  The result are two new rewriting approaches for the DL ALCHIQ: a rewriting to Datalog ∨ that (unavoidably) requires unbounded (but still linear) rule sizes, and a rewriting to Datalog ∨∃ that achieves  ... 
dblp:conf/dlog/CarralK20 fatcat:4xudtrbkqnbhbfqjjjyctllzby

Symbolic Abstract Contract Synthesis in a Rewriting Framework [article]

María Alpuente, Daniel Pardo, Alicia Villanueva
2016 arXiv   pre-print
Roughly speaking, we define an abstract symbolic technique that explains the execution of a (modifier) C function by using other (observer) routines in the same program.  ...  Starting from the semantic definition of KernelC in the K framework, we enrich the symbolic execution facilities recently provided by K with novel capabilities for assertion synthesis that are based on abstract  ...  Expected postcondition axioms for the insert method 3 The (symbolic) K Framework K is a rewriting-based framework for engineering language semantics [19] .  ... 
arXiv:1608.05619v1 fatcat:szggkkgk2zbwfc2g47vepyym5a

Text Rewriting Improves Semantic Role Labeling (Extended Abstract)

Kristian Woodsend, Mirella Lapata
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
In this paper we use text rewriting as a means of increasing the amount of labeled data available for model training.  ...  Our method uses automatically extracted rewrite rules from comparable corpora and bitexts to generate multiple versions of sentences annotated with gold standard labels.  ...  Examples of rewrites are given in Table 1 .  ... 
doi:10.24963/ijcai.2017/729 dblp:conf/ijcai/WoodsendL17 fatcat:os5wjnlau5dj7em5acts36v62e

Fast Abstractive Summarization with Reinforce-Selected Sentence Rewriting

Yen-Chun Chen, Mohit Bansal
2018 Proceedings of the 56th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)  
Inspired by how humans summarize long documents, we propose an accurate and fast summarization model that first selects salient sentences and then rewrites them abstractively (i.e., compresses and paraphrases  ...  Empirically, we achieve the new state-of-theart on all metrics (including human evaluation) on the CNN/Daily Mail dataset, as well as significantly higher abstractiveness scores.  ...  The results are shown in Table 6 : our model rewrites substantially more abstractive summaries than previous work.  ... 
doi:10.18653/v1/p18-1063 dblp:conf/acl/BansalC18 fatcat:7zhltuzqq5frdfhnkzyjmmdhia
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