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Semantical considerations on nonmonotonic logic

Robert C. Moore
<span title="">1985</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
Commonsense reasoning is "nonmonotonic" in  ...  This admits fixed points of nonmonotonic logic that contain P but not LP.  ...  in every fixed point of S5; hence there are no theorems of the form ~LP in any theory based on nonmonotonic S5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(85)90042-6">doi:10.1016/0004-3702(85)90042-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ja5havlclrhn3azysylysdrz7i">fatcat:ja5havlclrhn3azysylysdrz7i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20140806034800/http://ijcai.org/Past%20Proceedings/IJCAI-83-VOL-1/PDF/063.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/3f/bf/3fbf85a92d583f170a7a4af097717788840619e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(85)90042-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 4692 of Mathematical Reviews Vol. , Issue 93i [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;
In this paper, the author shows that for Reiter’s default logic, McDermott’s and Doyle’s nonmonotonic logic, and Moore’s au- toepistemic logic the first two reasoning tasks (existence of fixed points and  ...  Given a set of premises 2, three important decision problems arise in the context of nonmonotonic logics. The first is to decide whether a set of premises & has a corresponding fixed point at all.  ... 
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Definability and commonsense reasoning

Gianni Amati, Luigia Carlucci Aiello, Fiora Pirri
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
Implicit definability in nonmonotonic logic is always relative to the context-the current theory of the world.  ...  Theories expressed within this logical framework provide implicit definitions of concepts. Moreover, it is possible to derive these fixed points entirely within the logic. @ 1997 Elsevier Science B.V.  ...  Self-reference in nonmonotonic logic: the case of default logic We have shown that fixed points are explicitly definable in KD4Z.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0004-3702(96)00049-5">doi:10.1016/s0004-3702(96)00049-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hwuc4ywfuzabha3dfdvql2doiu">fatcat:hwuc4ywfuzabha3dfdvql2doiu</a> </span>
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Page 1234 of Mathematical Reviews Vol. , Issue 92c [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: “Default logic and autoepistemic logic are the two best- known fixed-point nonmonotonic logics.  ...  Helen Skala (Winona, MN) 92c:03031 03B60 68T27 Lin, Fang Zhen (1-STF-C); Shoham, Yoav (1-STF-C) Epistemic semantics for fixed-points nonmonotonic logics.  ... 
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Notes on Nonmonotonic Autoepistemic Propositional Logic

Marek A. Suchenek
<span title="">2011</span> <i title="Warsaw School of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zz2wmafuajfivcra5n7f75ueiu" style="color: black;">Zeszyty Naukowe</a> </i> &nbsp;
It begins with a brief review of semantics of common patterns of nonmonotonic deduction arising from a lack of knowledge, including autoepistemic deduction, in terms of the fixed-point equation φ(T,E)=  ...  This paper comprises an in-depth study of semantics of autoepistemic logic that is based on author's may years of research in the subject matter.  ...  a solution of the fixed-point equation (1).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.26348/znwwsi.6.74">doi:10.26348/znwwsi.6.74</a> <a target="_blank" rel="external noopener" href="https://doaj.org/article/c6340de35be34085b8bb73eec7d6a7e1">doaj:c6340de35be34085b8bb73eec7d6a7e1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/li3oy2wacfgffklqj7cpniycpy">fatcat:li3oy2wacfgffklqj7cpniycpy</a> </span>
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Chapter 6 Nonmonotonic Reasoning [chapter]

Gerhard Brewka, Ilkka Niemelä, Mirosław Truszczyński
<span title="">2008</span> <i title="Elsevier"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/knzhtkesqzhbzjhdqapu633m7i" style="color: black;">Foundations of Artificial Intelligence</a> </i> &nbsp;
In fact, casting these two and other fixed point logics in terms of the semantic approach to nonmonotonic inference we are about to present is one of major problems of nonmonotonic reasoning research.  ...  An open question is: can nonmonotonic inference relations defined by default logic (or other fixed point system) be characterized in semantic terms along the lines of preferential models?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1574-6526(07)03006-4">doi:10.1016/s1574-6526(07)03006-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7r4l7tqgn5hfjok7yqbuxj5xwa">fatcat:7r4l7tqgn5hfjok7yqbuxj5xwa</a> </span>
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Page 1422 of Mathematical Reviews Vol. , Issue 97C [page]

<span title="">1997</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;
In particular, an original modelization of the fixed point definition was proposed by K. J.  ...  Summary: “Two approaches for defining common knowledge co- exist in the literature: the infinite iteration definition and the circu- lar or fixed point one.  ... 
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A Minimal Model Semantics for Nonmonotonic Reasoning [chapter]

Laura Giordano, Valentina Gliozzi, Nicola Olivetti, Gian Luca Pozzato
<span title="">2012</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 two characterizations of rational closure: the first one in terms of minimal models where propositional interpretations associated to worlds are fixed along minimization, the second one where they  ...  This general framework can be instantiated in order to provide a semantic reconstruction within modal logic of the notion of rational closure, introduced by Lehmann and Magidor.  ...  In this first characterization we keep fixed the propositional interpretation associated to worlds.  ... 
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Ground Nonmonotonic Modal Logics

FRANCESCO M. DONINI, DANIELE NARDI, RICCARDO ROSATI
<span title="">1997</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;
In this paper we address ground logics, a family of nonmonotonic modal logics, and their usage in knowledge representation.  ...  They are characterized by a fix-point equation which determines the set of formulae derivable from the agent's initial knowledge and which can be applied to different normal modal systems to obtain a variety  ...  Acknowledgements We thank Marco Cadoli and Thomas Eiter for their careful reading of the paper, their comments and suggestions for the improvement of the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/7.4.523">doi:10.1093/logcom/7.4.523</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yyegn3jrvbh7bm7holtgof67vu">fatcat:yyegn3jrvbh7bm7holtgof67vu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090709160759/http://www.dis.uniroma1.it/~rosati/publications/Donini-Nardi-Rosati-JLC-97.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/85/5f/855fea6f88e0d36443bafb163bf39ab875cfb79b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/7.4.523"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

On embedding default logic into Moore's autoepistemic logic

Grigori Schwarz
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
Gottlob's translation, however, is indirect (it uses "nonmonotonic logic N" as an intermediate point), quite complex and exploitlj sophisticated encoding of proof theory in autoepistemic formulas.  ...  In addition, our argument is purely  ...  In particular, initially all the results were formulated for consistent extensions and consistent stable expansions; Georg noticed that the results remain true (and the proofs continue to hold) in the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(95)00117-4">doi:10.1016/0004-3702(95)00117-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4k6lkcrkvndedfyu5q4fibjfpi">fatcat:4k6lkcrkvndedfyu5q4fibjfpi</a> </span>
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Semantics-based Nonmonotonic Inference

Heinrich Wansing
<span title="">1995</span> <i title="Duke University Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/un57kpou5jawnm7yjqoeumbno4" style="color: black;">Notre Dame Journal of Formal Logic</a> </i> &nbsp;
In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic  ...  Moreover, in N a more general notion of consistency can be defined and nonmonotonic deduction can thus be based on a logical system satisfying the Deduction Theorem.  ...  In order to avoid fixed-point definitions of nonmonotonic inference, in [5] Gabbay suggested basing nonmonotonic deduction on semantic consequence in a logical system extended by a consistency operator  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1305/ndjfl/1040308828">doi:10.1305/ndjfl/1040308828</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/ndjfl/Wansing95.html">dblp:journals/ndjfl/Wansing95</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vui7sw2gh5g2vb33a3apq7vryq">fatcat:vui7sw2gh5g2vb33a3apq7vryq</a> </span>
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A natural semantics for modal logic over databases

W. Marek
<span title="">1988</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The resulting logic is related to the theory of updates in databases.  ...  Using mode1 theoretic forcing we give two interpretations of modal logic with nonmonotone, semantically defined, consequence operations.  ...  In fact, they are exactly the fixed points of the operator As. Proposition 2 . 11 . 211 If H is maximal in Sat(Z), then H is a fixed point for As, i.e.,As(H,X)cT(H).roof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(88)90077-1">doi:10.1016/0304-3975(88)90077-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o4iv3xgnobasvedi5i54rrqofa">fatcat:o4iv3xgnobasvedi5i54rrqofa</a> </span>
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Page 1971 of Mathematical Reviews Vol. , Issue 90D [page]

<span title="">1990</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;
Fixed points in the propositional nonmonotonic logic. Artificial Intelligence 38 (1989), no. 2, 199-206. This paper is a close study of some points arising in a paper by D. V. McDermott and J.  ...  Specifically, even when a set A of propositions is such that the function NM, (defined by McDermott and Doyle) has exactly one fixed point, that fixed point need not be the limit of successive applications  ... 
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From Turner's Logic of Universal Causation to the Logic of GK [chapter]

Jianmin Ji, Fangzhen Lin
<span title="">2012</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;
Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics.  ...  To date, it has been used to embed in it default logic, autoepistemic logic, and general logic programming under stable model semantics.  ...  Acknowledgements We want to thank Vladimir Lifschitz for his pioneering work in nonmonotonic logic and reasoning about action that makes this work possible.  ... 
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Belief, provability, and logic programs

José Júlio Alferes, Luís Moniz Pereira
<span title="">1995</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5dxceprzerhvngc2dulzkx45le" style="color: black;">Journal of Applied Non-Classical Logics</a> </i> &nbsp;
In particular we present here, for the first time, embeddings into epistemic logic of logic programs extended with a second kind of negation under the wellfounded semantics, and contrast them to the recent  ...  The main goal of this paper is to establish a nonmonotonic epistemic logic with two modalities -provability and belief -capable of expressing and comparing a variety of known semantics for extended logic  ...  Given a fix-point , objective literals in are true in the PSM, objective literals not in ! are false by default, and all others are undefined. Thus, objective literals in !  ... 
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