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Henkin quantifiers and complete problems

Andreas Blass, Yuri Gurevich
<span title="">1986</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
an N~-complete predicate.  ...  The remaining non-linear quantifiers expJ exactly co-NLe predicates.  ...  Q~, with Q a Henkin quantifier and ~ a quantifier-free first-order formula, can be Y~-complete.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(86)90040-0">doi:10.1016/0168-0072(86)90040-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/opxpt5xq7be2fn73jspwocmrjy">fatcat:opxpt5xq7be2fn73jspwocmrjy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200313090440/https://deepblue.lib.umich.edu/bitstream/handle/2027.42/26312/0000397.pdf;jsessionid=C50338AA6C68C4D30295FEFE22C5C893?sequence=1" 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/0c/c6/0cc6344f3ab9e6ade2812877ec05abd89448f2fb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(86)90040-0"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Degrees of logics with Henkin quantifiers in poor vocabularies

Marcin Mostowski, Konrad Zdanowski
<span title="2004-04-23">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3egevcnserbbni4tcigsztdici" style="color: black;">Archive for Mathematical Logic</a> </i> &nbsp;
We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 .  ...  We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)?  ...  Additionally, the problem whether the class E ω is weaker than H ω is also open.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00153-004-0220-8">doi:10.1007/s00153-004-0220-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kwp3gn7tbbgcvkpbjznurxq2vu">fatcat:kwp3gn7tbbgcvkpbjznurxq2vu</a> </span>
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Complexity of syntactical tree fragments of Independence-Friendly logic [article]

Fausto Barbero
<span title="2019-09-29">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
express NP-complete problems and other second-order concepts; and b) we give more general criteria for checking the first-orderness of an IF sentence.  ...  On one hand, prefixes that contain "Henkin" or "signalling" patterns were shown to characterize fragments of IF logic that capture NP-complete problems; all the remaining prefixes were shown instead to  ...  Acknowledgements Many thanks are due to Lauri Hella, for at least three reasons: 1) the key ideas of theorems 9.3 and 10.1, 2) the suggestion of re-reading Jarmo Kontinen's complexity results, and 3) many  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1610.03406v2">arXiv:1610.03406v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gzeyfif2arghrhn7fjnjtxnkeu">fatcat:gzeyfif2arghrhn7fjnjtxnkeu</a> </span>
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A Bit of History Related to Logic Based on Equality [chapter]

Peter B. Andrews
<span title="">2014</span> <i title="Springer International Publishing"> Studies in Universal Logic </i> &nbsp;
Keywords Type theory • Equality • Henkin • Axiom • Extensionality Leon Henkin and I were both students of Alonzo Church, but he finished his Ph.D. thesis in 1947, and I did not arrive at Princeton for  ...  However, Henkin was at the Institute for Advanced Study in Princeton on a Guggenheim Fellowship during the 1961-1962 academic year.  ...  and completeness.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-09719-0_8">doi:10.1007/978-3-319-09719-0_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4h3w5soorrglnj7dgsqyckgpn4">fatcat:4h3w5soorrglnj7dgsqyckgpn4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813115103/http://www.springer.com/cda/content/document/cda_downloaddocument/9783319097183-c8.pdf?SGWID=0-0-45-1484205-p176862602" 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/11/80/1180e35e1eba4b6ab7b1a03c77f06f46051d2bf2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-09719-0_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Independence-Friendly Logic Without Henkin Quantification [chapter]

Fausto Barbero, Lauri Hella, Raine Rönnholm
<span title="">2017</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;
The proof shows that a complete set of Henkin prefixes is explicitly definable in the fragment of Action Recall.  ...  by the IF rendition of the H 1 2 prefix, shown above: its "slash set" {x 1 1 , y1} contains an existentially quantified variable, y1.  ...  , yet allow describing NP-complete problems such as SAT and SET PARTITIONING ( [2] ); the problem of a complete classification of such patterns is still open.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-55386-2_2">doi:10.1007/978-3-662-55386-2_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lkrodjvexrfhlost2fhurdzeqa">fatcat:lkrodjvexrfhlost2fhurdzeqa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200307044252/https://trepo.tuni.fi/bitstream/handle/10024/116929/independence-friendly_logic_2017.pdf;jsessionid=2E509F08B3852007A4C89EC732683E18?sequence=2" 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/98/80/9880d0d372146b1c0dc3e86d3909cf1ebf2dac59.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-55386-2_2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Function Symbols in Tuple-Generating Dependencies

Georg Gottlob, Reinhard Pichler, Emanuel Sallinger
<span title="">2015</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xtq6wnwaszaebg4qf7aw6mllwi" style="color: black;">Proceedings of the 34th ACM Symposium on Principles of Database Systems - PODS &#39;15</a> </i> &nbsp;
When studying dependencies, existential quantifiers and -in their Skolemized form -function symbols are often seen as two ways to express the same concept.  ...  More concretely, the function f dm representing the department manager depends on both the department and the employee.  ...  Science Fund (FWF):P25207-N23 and (FWF):P25518-N23.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2745754.2745756">doi:10.1145/2745754.2745756</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/pods/GottlobPS15.html">dblp:conf/pods/GottlobPS15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fbzgn2k2vrba5lagn4vhbv5mfm">fatcat:fbzgn2k2vrba5lagn4vhbv5mfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191115134251/http://ceur-ws.org/Vol-1912/paper31.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/18/df/18dff00622701fc1f96d60f7043a58306212742c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2745754.2745756"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

In Memoriam: Leon Albert Henkin 1921–2006

J. Donald Monk
<span title="">2009</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;
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive.  ...  We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.  ...  A problem which Henkin formulated in JSL, vol. 17, has led to an important field of research in logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1246453978">doi:10.2178/bsl/1246453978</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qfwwyh3tb5dfdmhzdglsaq73au">fatcat:qfwwyh3tb5dfdmhzdglsaq73au</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160422121541/http://euclid.colorado.edu/~monkd/henkin.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/e5/95/e595c0ff033e9ce124bb808a91e6ed27615c5981.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/bsl/1246453978"> <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>

On the Innocence and Determinacy of Plural Quantification [chapter]

Salvatore Florio, Øystein Linnebo
<span title="2021-07-22">2021</span> <i title="Oxford University Press"> The Many and the One </i> &nbsp;
Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy.  ...  Both assumptions are problematic, as is shown by providing a Henkin-style semantics for plural logic that does not resort to sets but takes a plural term to have plural reference.  ...  As is well known, the standard deductive system for second-order logic is sound and complete with respect to set-based Henkin semantics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/oso/9780198791522.003.0008">doi:10.1093/oso/9780198791522.003.0008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/l3z7wwkmarak3hb2x2q4zll5k4">fatcat:l3z7wwkmarak3hb2x2q4zll5k4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210924162538/https://oxford.universitypressscholarship.com/downloadpdf/10.1093/oso/9780198791522.001.0001/oso-9780198791522-chapter-8.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/06/52/06521aa49cee5bdc8bef977702741f0a1bc691df.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/oso/9780198791522.003.0008"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

On the Innocence and Determinacy of Plural Quantification

Salvatore Florio, Øystein Linnebo
<span title="2015-03-09">2015</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pyrfyab2zva6lmpkx2bzn2vz2y" style="color: black;">Noûs</a> </i> &nbsp;
B Completeness of the Henkin semantics Here we describe a standard proof system S for plural logic and we prove that it is sound and complete with respect to the plurality-based Henkin semantics formulated  ...  We want to show that S is (sound and) complete with respect to the plurality-based Henkin semantics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/nous.12091">doi:10.1111/nous.12091</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/im5ja33x45dndjmo7aa2ymn7jy">fatcat:im5ja33x45dndjmo7aa2ymn7jy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200310165025/https://research.birmingham.ac.uk/portal/files/31922650/On_the_Innocence_and_Determinacy_Nous_FINAL.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/db/20/db200c745ab192a88ea896a1ce82c0909e3f6201.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/nous.12091"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Second-Order Logic and Set Theory

Jouko Väänänen
<span title="">2015</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fftrkw4bpjbflpnbaznwmotdbi" style="color: black;">Philosophy Compass</a> </i> &nbsp;
Both second order logic and set theory can be used as a foundation for mathematics, that is, as a formal language in which propositions of mathematics can be expressed and proved.  ...  We take it upon ourselves in this paper to compare the two approaches, second order logic on one hand and set theory on the other hand, evaluating their merits and weaknesses.  ...  The apparent problem that second order logic has second order quantifiers while set theory is presented in a first order language, is really only an apparent problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/phc3.12229">doi:10.1111/phc3.12229</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2vq3iweyxzckbfbhtooe73hs5a">fatcat:2vq3iweyxzckbfbhtooe73hs5a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180627171331/http://www.math.helsinki.fi/logic/people/jouko.vaananen/Vaananen_Compass.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/bb/a3/bba3b13a685f9deab976fc2cf33050876d6c4501.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/phc3.12229"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Quantified Multimodal Logics in Simple Type Theory [article]

Christoph Benzmueller, Lawrence C. Paulson
<span title="2009-05-14">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness.  ...  This entails further soundness and completeness results of our embedding for fragments of quantified multimodal logics.  ...  This leads to a simpler definition of a quantified multimodal language QML ST T below, and it does not affect our soundness and completeness results.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0905.2435v1">arXiv:0905.2435v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pq6athk3bfb43d7wrllpu2ho7y">fatcat:pq6athk3bfb43d7wrllpu2ho7y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130703180101/http://www.cl.cam.ac.uk/~lp15/papers/Reports/SR%E2%80%932009%E2%80%9302.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/50/1b/501bbda9f911396e2482f8293a96265a3613f4da.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0905.2435v1" 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>

Page 84 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 92, Issue 1 [page]

<span title="">1959</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_american-mathematical-society-transactions" style="color: black;">American Mathematical Society. Transactions of the American Mathematical Society </a> </i> &nbsp;
Henkin, The completeness of the first order functional calculus, J. Symb. Logic vol. 14 (1949) pp. 159-166. a , Completeness in the theory of types, J. Symb.  ...  Robinson, On the metamathematics of algebra, Amsterdam, North Holland, 1952. a. , Note on a problem of L. Henkin, J. Symb. Logic, vol. 21 (1956) pp. 33-35. UNIVERSITY OF MINNESOTA, MINNEAPOLIs, MINN.  ... 
<span class="external-identifiers"> </span>
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Page 84 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 92, Issue 1 [page]

<span title="">1959</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_american-mathematical-society-transactions" style="color: black;">American Mathematical Society. Transactions of the American Mathematical Society </a> </i> &nbsp;
Henkin, The completeness of the first order functional calculus, J. Symb. Logic vol. 14 (1949) pp. 159-166. , Completeness in the theory of types, J. Symb.  ...  Note on a problem of L. Henkin, J. Symb. Logic, vol. 21 (1956) pp. 33-35. UNIVERSITY OF MINNESOTA, MINNEAPOLIS, MINN. UNIVERSITY OF CALIFORNIA, BERKELEY, CALIF.  ... 
<span class="external-identifiers"> </span>
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Decidability problems in languages with Henkin quantifiers

Michał Krynicki, Marcin Mostowski
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers  ...  We know that every nonlinear Henkin quantifier has to contain H, therefore the problem is reduced to the question: are there any decidable classes of Henkin quantifiers A such that the theory of unary  ...  so-called the Henkin quantifier).  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928005805/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/5b8/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY4MDA3MjkyOTAwMDNp.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/d5/34/d534a7ea4bdcf2f77ba17c7c17fb20dae5dfa3f9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(92)90003-i"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Efficient elimination of Skolem functions in LK^h [article]

Ján Komara
<span title="2020-06-15">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We have r (π) = 0 if and only if the proof π is cut-free. 4.5 The characterization problem. We give here a brief outline of soundness and completeness for the LK h -calculus.  ...  It is obvious that if a Henkin constant c QxA occurs in a quantifier L(C)-formula Q yB, then rk(c QxA ) < rk(c Q yB ). Henkin and quantifier axioms.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1909.01697v4">arXiv:1909.01697v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/27aimhi3t5h2hdw4ihpu56jmpa">fatcat:27aimhi3t5h2hdw4ihpu56jmpa</a> </span>
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