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Theoretical Foundations of Value Withdrawal Explanations for Domain Reduction

G. Ferrand, W. Lesaint, A. Tessier
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
The linking of these rules inductively defines proof trees. Such a proof tree clearly explains the removal of a value (which is the root of the tree).  ...  Explanations can be considered as the essence of domain reduction.  ...  Acknowledgement This paper has benefitted from works and discussions with Patrice Boizumault and Narendra Jussien.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1571-0661(04)80788-6">doi:10.1016/s1571-0661(04)80788-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l2syxb22x5giporcsnatkx3fki">fatcat:l2syxb22x5giporcsnatkx3fki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20120124164709/http://www.univ-orleans.fr/lifo/Members/lesaint/publis/entcs2002.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/5b/86/5b8631409c3a6edbc2242c7ca21d47b97912763f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1571-0661(04)80788-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Value withdrawal explanations: a theoretical tool for programming environments [article]

Willy Lesaint
<span title="2002-07-12">2002</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Proof trees are built with respect to these rules. For each removed value, there exists such a proof tree which is the withdrawal explanation of this value.  ...  A value withdrawal explanation is a tree describing the withdrawal of a value during a domain reduction by local consistency notions and labeling.  ...  Finally, proof trees are built thanks to these rules. These proof trees are explanations for the removal of a value (their root).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0207050v2">arXiv:cs/0207050v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7e3n2rihnbbihcvbtysu3jpovy">fatcat:7e3n2rihnbbihcvbtysu3jpovy</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-cs0207050/cs0207050.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7a/7e/7a7e3b66a5736d6f1d9a0ec67be81d8b5d00167a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0207050v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

First order abduction via tableau and sequent calculi

MARTA CIALDEA MAYER, FIORA PIRRI
<span title="">1993</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mwzmwwmscfe4vnzrjlt5itd2ju" style="color: black;">Logic Journal of the IGPL</a> </i> &nbsp;
The reason why explanations are not required to be prenex is that this fact simpli es both de nitions and proofs.  ...  Tableaux and R-trees have properties that make them interesting from the standpoint of proof theory.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/jigpal/1.1.99">doi:10.1093/jigpal/1.1.99</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uvtwdb2gqvfy3i76eey2ud3sbi">fatcat:uvtwdb2gqvfy3i76eey2ud3sbi</a> </span>
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A Visualization System for Correctness Proofs of Graph Algorithms

P.A. Gloor, D.B. Johnson, F. Makedon, P. Metaxas
<span title="">1992</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tltvmmlbabcilpj6mmqsb6ncpe" style="color: black;">Computer Science Education</a> </i> &nbsp;
These examples can be referred to by the user interactively and alternatively with the visualization of the proof where the general case is portrayed abstractly.  ...  The system has been demonstrated for a greedy algorithm, Prim's algorithm for finding a minimum spanning tree of an undirected, weighted graph.  ...  The authors would like to thank the anonymous referees for the careful reading of an earlier draft of the paper and their constructive suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/0899340920030309">doi:10.1080/0899340920030309</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ev3aqctdanbjnoc4bp4ak423wy">fatcat:ev3aqctdanbjnoc4bp4ak423wy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20030831180919/http://www.wellesley.edu:80/CS/pmetaxas/visual_proofs.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/95/ae/95ae14be486811366ecd8cbf907323c68be62e1c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/0899340920030309"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Predicting the Understandability of OWL Inferences [chapter]

Tu Anh T. Nguyen, Richard Power, Paul Piwek, Sandra Williams
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
final explanation is generated.  ...  This model has been applied in our research on generating accessible explanations for an entailment of OWL ontologies, to determine the most understandable inference among alternatives, from which the  ...  We thank our colleagues and the anonymous viewers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38288-8_8">doi:10.1007/978-3-642-38288-8_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jzrgwj7d3bbm7c5ploxczbsz6i">fatcat:jzrgwj7d3bbm7c5ploxczbsz6i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705195147/http://oro.open.ac.uk/36692/1/piwek-36692.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ed/03/ed03a9761be7e0432214f5c00bd3277ca8f5683b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38288-8_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Web Explanations for Semantic Heterogeneity Discovery [chapter]

Pavel Shvaiko, Fausto Giunchiglia, Paulo Pinheiro da Silva, Deborah L. McGuinness
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
There, S-Match, a semantic matching system, produces proofs and explanations for mappings it has discovered.  ...  ., concept hierarchies or ontologies) and returns a mapping between the nodes of the graphs that correspond semantically to each other.  ...  Thus, we have modified the JSAT DPLL procedure and enabled it to generate proofs. Next, we discuss the IW proofs and explanations of the unit resolution rule in detail.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11431053_21">doi:10.1007/11431053_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7dgezfxlrbe7ppoagvwbkjwmzm">fatcat:7dgezfxlrbe7ppoagvwbkjwmzm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20131107030652/http://disi.unitn.it:80/~accord/Publications/35320303.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ee/ae/eeae6aace29d82e20f50b5a6647ed56c72ca1f8a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11431053_21"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Explanation-based generalisation = partial evaluation

Frank van Harmelen, Alan Bundy
<span title="">1988</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
We show this equivalence by analysing the definitions and underlying algorithms of both techniques, and by giving a Prolog program which can be interpreted as doing either explanation-based generalisation  ...  We argue that explanation-based generalisation as recently proposed in the machine learning literature is essentially equivalent to partial evaluation, a well known technique in the functional and logic  ...  in the proof tree.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(88)90088-4">doi:10.1016/0004-3702(88)90088-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5mw4vneci5fsno3qehcgd3siee">fatcat:5mw4vneci5fsno3qehcgd3siee</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180722074900/https://www.pure.ed.ac.uk/ws/files/408514/Explanation_BasedGeneralization_PartialEvaluation.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/9e/fb/9efb396336c5bec529414d1f7a141208115afa8b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(88)90088-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Generating explanations for biomedical queries

ESRA ERDEM, UMUT OZTOK
<span title="2013-12-17">2013</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yhwvj6mbzza5tfz766tokherka" style="color: black;">Theory and Practice of Logic Programming</a> </i> &nbsp;
AbstractWe introduce novel mathematical models and algorithms to generate (shortest orkdifferent) explanations for biomedical queries, using answer set programming.  ...  We implement these algorithms and integrate them inBioQuery-ASP.  ...  A.3.1 Proof of Proposition 10 -Soundness of Algorithm 7 In the proof of Proposition 10, the idea is to show that Algorithm 7 returns at Line 17 an explanation tree T in the and-or explanation tree for  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1471068413000598">doi:10.1017/s1471068413000598</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p4cbxg2mpncnla2uhgiuglbm6y">fatcat:p4cbxg2mpncnla2uhgiuglbm6y</a> </span>
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On Explanations for Non-Acceptable Arguments [chapter]

Xiuyi Fan, Francesca Toni
<span title="">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We give two different views (an argument-view and an attack-view) in explaining the non-acceptability of an argument and show the computation of explanations with debate trees.  ...  Finally, we say that an argument a is admissible if and only if a is in some admissible extension. Dispute Trees [11, 10] are used to compute our explanations.  ...  Let R be an att-explanation for a and (x, y) ∈ R. Then both x and y are related to a. Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-28460-6_7">doi:10.1007/978-3-319-28460-6_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6fw2yxx6hzh43aylfm4mpau3uu">fatcat:6fw2yxx6hzh43aylfm4mpau3uu</a> </span>
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Explainable Decision Making with Lean and Argumentative Explanations [article]

Xiuyi Fan, Francesca Toni
<span title="2022-01-24">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Specifically, we define ABA frameworks such that "good" decisions are admissible ABA arguments and draw argumentative explanations from dispute trees sanctioning this admissibility.  ...  to audiences with differing needs and competences: lean explanations, in terms of goals satisfied and, for some notions of "goodness", alternative decisions, and argumentative explanations, reflecting  ...  Proof of Theorem 5.4 The proof of this theorem is similar to the proofs of Theorems 5.1, 5.2 and 5.3. Let AF = L, R, A, C . (Part I.)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.06692v2">arXiv:2201.06692v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mrhhrtl5ynh4hoe276o4orlc7a">fatcat:mrhhrtl5ynh4hoe276o4orlc7a</a> </span>
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Generalizing multiple examples in explanation based learning [chapter]

Gunther Sablon, Luc Raedt, Maurice Bruynooghe
<span title="">1989</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a method to generalize rules by locating common parts and differences in order to obtain a more useful set of rules.  ...  Presenting multiple examples to an Explanation Based Learning system may lead to a lot of quite similar rules. This has a negative effect on the overall problem solving performance.  ...  for loves(_y,_u) (cf. 3 and 4) in the proof trees is more general than the subtree in the other proof tree. There are more clauses for loves/2 in the knowledge base (cf. 5 and 6).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-51734-0_60">doi:10.1007/3-540-51734-0_60</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bxjttgkhf5gyhc7uobvaz3ult4">fatcat:bxjttgkhf5gyhc7uobvaz3ult4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170816155211/https://lirias.kuleuven.be/bitstream/123456789/132881/1/AII89.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/73/53/7353283c4598f1bb1fb4ac9c787c41d90db3323b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-51734-0_60"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Proof-Producing Congruence Closure [chapter]

Robert Nieuwenhuis, Albert Oliveras
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This non-trivial (ground) equational reasoning result has been quite intensively sought after (see, e.g., [SD99, dMRS04, KS04]), and moreover has important applications to verification.  ...  Then, these are applied inside a congruence closure algorithm with Explain, where a k-step proof can be recovered in almost optimal time (quasi-linear in k), without increasing the overall O(n log n) runtime  ...  Each node in a tree is (labelled with) some element e i , and the root of a tree is the representative of that class.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-32033-3_33">doi:10.1007/978-3-540-32033-3_33</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/trdl5q2mwra7fcvausckav6vmu">fatcat:trdl5q2mwra7fcvausckav6vmu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809190020/http://www.cs.upc.edu/~roberto/papers/rta05.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ee/83/ee830577d00e4b1f503834cf419732b9ae25fe8c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-32033-3_33"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Rule Based Abduction [chapter]

Sai Kiran Lakkaraju, Yan Zhang
<span title="">2000</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A SLDNF resolution based proof procedure is employed to achieve this rule based abduction.  ...  It is shown that using this algorithm, one can always nd a minimal explanation for the observation if there exists such an explanation.  ...  F is consistent; and 3. E A and F A \ P. An explanation (E; F) of an observation G is minimal if for any explanation (E 0 ; F 0 ) of G, E 0 E and F 0 F imply E 0 = E and F 0 = F.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-39963-1_55">doi:10.1007/3-540-39963-1_55</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sqpufmw4wbdhpkgdhbfczy6yde">fatcat:sqpufmw4wbdhpkgdhbfczy6yde</a> </span>
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APPRENTICESHIP LEARNING IN IMPERFECT DOMAIN THEORIES [chapter]

Gheorghe Tecuci, Yves Kodratoff
<span title="">1990</span> <i title="Elsevier"> Machine Learning </i> &nbsp;
In the context of a weak theory about the example, it synergistically combines explanation-based learning, learning by analogy, empirical learning, and learning by questioning the user, developing its  ...  In the context of a complete theory about the example, DISCIPLE uses explanation-based learning to improve its performance.  ...  Acknowledgments This work has been sponsored by PRC-GRECO 'Intelligence Artificielle' and the Romanian CNST.  ... 
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Reconstructing proofs at the assertion level [chapter]

Xiaorong Huang
<span title="">1994</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Furthermore, these rules can be represented compactly in a tree structure.  ...  Finally, we describe a system called PROVERB, which substantially shortens ND proofs by abstracting them to the assertion level and then transforms them into natural language.  ...  Acknowledgment Thanks are due to Manfred Kerber and Daniel Nesmith, who read several drafts of this paper carefully, and to Armin Fiedler, who implemented the abstraction algorithm.  ... 
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