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Page 5759 of Mathematical Reviews Vol. , Issue 2000h [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(F-EVRY-LMI; Evry) A full formalization of SLD-resolution in the calculus of inductive constructions. (English summary) J. Automat. Reason. 23 (1999), no. 3-4, 347-371.  ...  Summary: “This paper presents a full formalization of the seman- tics of definite programs in the calculus of inductive constructions.  ... 
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On the Complexity of Disjunction and Explicit Definability Properties in Some Intermediate Logics [chapter]

Mauro Ferrari, Camillo Fiorentini, Guido Fiorino
<span title="">2002</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;
In this paper we provide a uniform framework, based on extraction calculi, where to study the complexity of the problem to decide the disjunction and the explicit definability properties for Intuitionistic  ...  Unlike the previous approaches, our framework is independent of structural properties of the proof systems and it can be applied to Natural Deduction systems, Hilbert style systems and Gentzen sequent  ...  Here the term "simple" mainly refers to the intuitionistic nature of these rules. As a matter of fact, the main rule of our extraction calculi is an inference rule formalizing SLD-resolution.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36078-6_12">doi:10.1007/3-540-36078-6_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vwbpnolic5aopfpee6owomep34">fatcat:vwbpnolic5aopfpee6owomep34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830062742/https://air.unimi.it/retrieve/handle/2434/170714/253251/2002_lpar.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/7c/79/7c792a5968bfe3f1ce95cb90f6c16743ad513b26.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-36078-6_12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 4129 of Mathematical Reviews Vol. , Issue 92h [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “We present a fragment of (positive) relevant logic which can be computed by a straightforward extension to SLD resolution while allowing full nesting of implications.  ...  This allows one to construct a special stable retraction the range of which consists of all retractions. This stable retraction is used as an interpretation of the constant p in the Afp-calculus.  ... 
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Page 6940 of Mathematical Reviews Vol. , Issue 93m [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We start from the SLD-resolution calculus and a simple abstract Prolog machine to realize the SLD-resolution calculus.  ...  The formal specification of the composite protocol is constructed from the formal specification of the two protocols from which it is composed, and the proof of the composite protocol is an expansion of  ... 
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On the complexity of the disjunction property in intuitionistic and modal logics

Mauro Ferrari, Camillo Fiorentini, Guido Fiorino
<span title="2005-07-01">2005</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3kjjbv4edjbezl2w37ipy5lo5a" style="color: black;">ACM Transactions on Computational Logic</a> </i> &nbsp;
For S4 we even prove the feasible interpolation theorem and we provide a lower bound for the length of proofs.  ...  In this article we study the complexity of disjunction property for intuitionistic logic, the modal logics S4, S4.1, Grzegorczyk logic, Gödel-Löb logic, and the intuitionistic counterpart of the modal  ...  For instance, let ND Int be the natural deduction calculus for intuitionistic logic and let SLD be the following inference rule formalizing SLD-resolution: A 1 . . .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1071596.1071598">doi:10.1145/1071596.1071598</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jwyvwet5hrhmxgtknx2ya3gq24">fatcat:jwyvwet5hrhmxgtknx2ya3gq24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813203928/https://air.unimi.it/retrieve/handle/2434/4800/252422/2005_tocl.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/f4/79/f47988e0f434058da2cf6115f72d2e216066b35b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1071596.1071598"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen

Peter Schroeder-Heister
<span title="">2002</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nxnim3i24fhcvkvgruk2dej7yu" style="color: black;">Bulletin of Symbolic Logic</a> </i> &nbsp;
Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of propositional SLD-resolution in logic  ...  It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory.  ...  This is a full-fledged completeness proof for propositional SLD-resolution, invalidating Γ → A by constructing the closure Γ * of Γ under the clauses given.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1182353872">doi:10.2178/bsl/1182353872</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lumupxmagzhlnbpvebdhlxc2ee">fatcat:lumupxmagzhlnbpvebdhlxc2ee</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121114192803/http://ls.informatik.uni-tuebingen.de/psh/forschung/publikationen/HertzResolution00long.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/6d/d4/6dd4a056421ffdc7c61cc79957877a364507cbcf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1182353872"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Infinite Computation, Co-induction and Computational Logic [chapter]

Gopal Gupta, Neda Saeedloei, Brian DeVries, Richard Min, Kyle Marple, Feliks Kluźniak
<span title="">2011</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 give an overview of the coinductive logic programming paradigm.  ...  In such cases, it is typical to augment SLD resolution with tabling (called SLG resolution), which memoizes calls and solutions to inductive predicates and by extension prevents construction of (rational  ...  Negation in Co-LP As mentioned earlier, SLD resolution extended with the coinductive hypothesis rule is called co-SLD resolution.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-22944-2_4">doi:10.1007/978-3-642-22944-2_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v2klxrhr6vfpfagwncfzpg56v4">fatcat:v2klxrhr6vfpfagwncfzpg56v4</a> </span>
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A Proof-Theoretic Approach to Logic Programming. I. Clauses as Rules

LARS HALLNÄS, PETER SCHROEDER-HEISTER
<span title="">1990</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/crzmi3qeiramtlvcrfycib3qg4" style="color: black;">Journal of Logic and Computation</a> </i> &nbsp;
Based on this approach, the soundness and completeness of SLD-resolution is established by purely proof-theoretic methods.  ...  The sequent calculus with the general elimination schema even permits the introduction of a genuine notion of falsity which is not defined via a meta-rule.  ...  SLD-resolution independently of the generalizations considered.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/1.2.261">doi:10.1093/logcom/1.2.261</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k2szlx3k75gozlwb7lmc5ppj4i">fatcat:k2szlx3k75gozlwb7lmc5ppj4i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190227004834/http://pdfs.semanticscholar.org/87a9/d1b7241a3c1bda0b4dea81ff706d981ed77f.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/87/a9/87a9d1b7241a3c1bda0b4dea81ff706d981ed77f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/1.2.261"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Structural Resolution for Logic Programming [article]

P. Johann and E. Komendantskaya and V. Komendantskiy
<span title="2015-07-21">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce a Three Tier Tree Calculus (3TC) that defines in a systematic way three tiers of tree structures underlying proof search in logic programming.  ...  We use 3TC to define a new -- structural -- version of resolution for logic programming.  ...  A calculus for the operation can be formulated in terms of a suitable unification algorithm. We give formal definitions in Sections 2 and 3.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.06010v1">arXiv:1507.06010v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yhooydkaevckfagxlh52qu7dja">fatcat:yhooydkaevckfagxlh52qu7dja</a> </span>
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Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

FRANCESCA A. LISI
<span title="2008-01-04">2008</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;
We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of$\mathcal{AL}$-log.  ...  In this paper, we consider the problem of automating the acquisition of these rules for the Semantic Web.  ...  Reasoning for AL-log knowledge bases is based on constrained SLD-resolution, i.e. an extension of SLD-resolution with a tableau calculus for ALC to deal with constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1471068407003195">doi:10.1017/s1471068407003195</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ncsy2pl35holhip7j5xdtgcam">fatcat:2ncsy2pl35holhip7j5xdtgcam</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171116204906/http://ceur-ws.org/Vol-314/42.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/85/a0/85a043c831564b087f3c20db1efe22c737b51ac1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s1471068407003195"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Reasoning About Epistemic States of Agents by Modal Logic Programming [chapter]

Linh Anh Nguyen
<span title="">2006</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 prove that the presented SLD-resolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4Ig5a.  ...  We specify here the least model semantics, the fixpoint semantics, and an SLD-resolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended for reasoning about belief  ...  Acknowledgements I would like to thank the reviewers for helpful comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11750734_3">doi:10.1007/11750734_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fnzle2g6orhkjjszrqritxn3se">fatcat:fnzle2g6orhkjjszrqritxn3se</a> </span>
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Structural Resolution: a Framework for Coinductive Proof Search and Proof Construction in Horn Clause Logic [article]

Ekaterina Komendantskaya, Patricia Johann, Martin Schmidt
<span title="2017-05-04">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Structural resolution is a newly proposed alternative to SLD-resolution that makes it possible to define and semi-decide a notion of productivity appropriate to LP.  ...  In this paper, we prove soundness of structural resolution relative to Herbrand model semantics for productive inductive, coinductive, and mixed inductive-coinductive logic programs.  ...  We particularly thank Vladimir Komendantskiy and Frantiŝek Farka, who at different times implemented prototypes of CoAlgebraic Logic Programming (CoALP) and S-Resolution: their input has been invaluable  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.07865v2">arXiv:1511.07865v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6lqbu7vyqzegnchxtiws7ty3fu">fatcat:6lqbu7vyqzegnchxtiws7ty3fu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200907052008/https://arxiv.org/pdf/1511.07865v2.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/7c/5a/7c5ad5f799379b6aa3b82b0e562a9b2a08db920e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1511.07865v2" 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>

Regular search spaces as a foundation of logic programming [chapter]

Alberto Momigliano, Mario Ornaghi
<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;
Secondly, we embark on a generalization and abstraction of the nice properties of SLD-resolution. The outcome is our formulation of the concept of regular search space.  ...  Our ambition is to show that almost everything in the vulgate of logic programming can be carried out in a style close to natural deduction, and in particular in a restricted fragment of minimal logic.  ...  We would like to thank Roy Dyckhoff and Frank Pfenning for their valuable comments on earlier versions of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-58025-5_59">doi:10.1007/3-540-58025-5_59</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7okk6khlq5gozo7wydffw5hqxe">fatcat:7okk6khlq5gozo7wydffw5hqxe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180729210316/https://link.springer.com/content/pdf/10.1007%2F3-540-58025-5_59.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/bc/38/bc38d7708f54a3cc0041023eb156c110c5d9ca24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-58025-5_59"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Logic programming and model checking [chapter]

Baoqiu Cui, Yifei Dong, Xiaoqun Du, K. Narayan Kumar, C. R. Ramakrishnan, I. V. Ramakrishnan, Abhik Roychoudhury, Scott A. Smolka, David S. Warren
<span title="">1998</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;
In particular, the XMC model checker for value-passing CCS and the modal mu-calculus is discussed, as well as the XSB tabled logic programming system, on which XMC is based.  ...  We report on the current status of the LMC project, which seeks to deploy the latest developments in logic-programming technology to advance the state of the art of system speci cation and veri cation.  ...  The XSB system implements SLG resolution CW96a], which t o a r s t a p p r o ximation can be understood as a tabled version of SLD resolution.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0056604">doi:10.1007/bfb0056604</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k5q3x4d6ubfovb4ddmw6hfsyhm">fatcat:k5q3x4d6ubfovb4ddmw6hfsyhm</a> </span>
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A framework for computing finite SLD trees

Naoki Nishida, Germán Vidal
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/75odiq25o5gtzcy4h7mdcztb5y" style="color: black;">Journal of Logical and Algebraic Methods in Programming</a> </i> &nbsp;
The search space of SLD resolution, usually represented by means of a socalled SLD tree, is often infinite.  ...  In this work, we introduce a framework to construct a finite data structure representing the (possibly infinite) SLD derivations for a goal.  ...  Computations in logic programming are formalized by means of SLD resolution. The notion of computation rule R is used to select an atom within a goal for its evaluation.  ... 
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