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On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Marjon Blondeel, Tommaso Flaminio, Steven Schockaert, Lluís Godo, Martine De Cock
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wcbukkuh2vbrpcbz2f4z2a2g6u" style="color: black;">Fuzzy sets and systems (Print)</a> </i> &nbsp;
Besides being related to answer set programming, autoepistemic logic is also closely related to several modal logics.  ...  Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent's rational beliefs on gradable propositions.  ...  Relating fuzzy modal logic and fuzzy autoepistemic logic The aim of Moore's autoepistemic logic [1] is to characterize the set of beliefs of a rational agent with introspection capabilities by means  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2015.02.018">doi:10.1016/j.fss.2015.02.018</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tedcqm4f6rd2fepmzkgby4pbva">fatcat:tedcqm4f6rd2fepmzkgby4pbva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922063726/http://digital.csic.es/bitstream/10261/130287/1/FSS,2015,v276,pp.74-99..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/bd/6c/bd6c189559c6a0120a95cfc56aba82ea28559ee0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.fss.2015.02.018"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

REPRESENTING AUTOEPISTEMIC LOGIC IN MODAL LOGIC

Frank Brown
<i > International Journal &#34;Information Theories &amp; Applications </i> &nbsp; <span class="release-stage">unpublished</span>
The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5.  ...  This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to  ...  Autoepistemic Logic Represented in Modal Logic The fixed-point equation for Autoepistemic Logic may be expressed in S5 Modal Quantificational Logic by the necessary equivalence: κ≡(AEL κ Γ) where AEL is  ... 
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From Carnap's modal logic to autoepistemic logic [chapter]

Georg Gottlob
<i title="Springer-Verlag"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rkyvgfejkrep5atcgejp4ymf5y" style="color: black;">Logics in Artificial Intelligence</a> </i> &nbsp;
Recently, it turned out that there are interesting connections between Carnap's modal logic and finite model theory for modal logics.  ...  Finally, we explain the relationship between Carnap's logic and autoepistemic logic and show that autoepistemic reasoning corresponds to solving problems equivalent to (possibly cyclic) graphs of interdependent  ...  Carnap's Modal Logic In 1947 the philosopher and logician Rudolf Carnap published "Meaning and Necessity", a study containing a new approach to semantics and modal logic [3] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0021961">doi:10.1007/bfb0021961</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/jelia/Gottlob94.html">dblp:conf/jelia/Gottlob94</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hcz7qf6byjauzma5iwumde7xsa">fatcat:hcz7qf6byjauzma5iwumde7xsa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190225172250/http://pdfs.semanticscholar.org/71bf/92fa5b599ca37cabb8a978353dc7776cd1a2.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/71/bf/71bf92fa5b599ca37cabb8a978353dc7776cd1a2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0021961"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Separating disbeliefs from beliefs in autoepistemic reasoning [chapter]

Tomi Janhunen
<span title="">1997</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 paper investigates separated autoepistemic logic which is a generalization of Moore's autoepistemic logic with separate modalities for belief and disbelief.  ...  Along the separation of beliefs and disbeliefs, the relationship between autoepistemic logic and default logic becomes very intuitive.  ...  Moore proposed autoepistemic logic as a reconstruction of Non-monotonic modal logic I (NML I) by McDermott and Doyle 16] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-63255-7_10">doi:10.1007/3-540-63255-7_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zjdag5igk5alxkzn4tlerafl6e">fatcat:zjdag5igk5alxkzn4tlerafl6e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190222085922/http://pdfs.semanticscholar.org/3411/0651ad816ccc3e6b08732aaf065fb43ff3ae.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/34/11/34110651ad816ccc3e6b08732aaf065fb43ff3ae.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-63255-7_10"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 701 of Mathematical Reviews Vol. , Issue 98B [page]

<span title="">1998</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 generalize Moore’s autoepistemic logic to multi- valued autoepistemic logic, where the set of truth-values can be any complete lattice.  ...  The first deals with arrow logic and the second with some methodological issues surround- ing modal logic and arrow logic. Arrow logic is the modal logic  ... 
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Fixpoint 3-valued semantics for autoepistemic logic [article]

M. Denecker and V. Marek and M. Truszczynski
<span title="1999-01-12">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory.  ...  In the case of modal representations of logic programs our least fixpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used).  ...  Autoepistemic logic -preliminaries The language of autoepistemic logic is the standard language of propositional modal logic over a set of atoms Σ and with a single modal operator K.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/9901003v1">arXiv:cs/9901003v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fccqhyscj5fkjenbik3daxka6q">fatcat:fccqhyscj5fkjenbik3daxka6q</a> </span>
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Fixpoint 3-valued semantics for autoepistemic logic [chapter]

Marc Denecker, V. Wiktor Marek, Mirosław Truszczyński
<span title="">1999</span> <i title="Springer Berlin Heidelberg"> Logical Foundations for Cognitive Agents </i> &nbsp;
The paper presents a constructive 3-valued semantics for autoepistemic logic (AEL). We introduce a derivation operator and de ne the semantics as its least xpoint.  ...  In the case of modal representations of logic programs our least xpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen semantics (depending on the embedding used).  ...  Autoepistemic logic | preliminaries The language of autoepistemic logic is the standard language of propositional modal logic over a set of atoms and with a single modal operator K.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-60211-5_10">doi:10.1007/978-3-642-60211-5_10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oncr6mcxyvcolc4r6yv43asss4">fatcat:oncr6mcxyvcolc4r6yv43asss4</a> </span>
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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;
Recently Gottlob proved [2] that there does not exist a faithful modular translation of default logic into autoepistemic logic, and presented a non-modular translation.  ...  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.  ...  Nevertheless, Moore's autoepistemic logic still remains the most popular among nonmonotonic modal logics.  ... 
<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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Page 5737 of Mathematical Reviews Vol. , Issue 92j [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;
Here we look at quantification in autoepistemic logic, which is a modal logic of self-knowledge.  ...  Summary: “We study a family of modal nonmonotonic logics closely related to the family of modal nonmonotonic logics pro- posed by McDermott and Doyle.  ... 
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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;
We will call our logic, naturally enough, autoepistemic logic. The language will be much like McDermott and Doyle's, an ordinary logical language augmented by autoepistemic modal operators.  ...  on modal logic rather than classical logic.  ... 
<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>

On the relation between default and modal nonmonotonic reasoning

Alexander Bochman
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
The notion of a default consequence relation is introduced as a generalization of both default and modal formalizations of nonmonotonic reasoning.  ...  A nonmodular translation of a modal theory into an autoepistemic theory has been given, in fact, in [ 121 as part of a general translation of default logic into an autoepistemic logic.  ...  Autoepistemic consequence relations We will begin with autoepistemic logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0004-3702(98)00011-3">doi:10.1016/s0004-3702(98)00011-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xehewctilbho5ch3vm6wn3zdze">fatcat:xehewctilbho5ch3vm6wn3zdze</a> </span>
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Uniform semantic treatment of default and autoepistemic logics [article]

Marc Denecker, Victor W. Marek, Miroslaw Truszczynski
<span title="2000-02-03">2000</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, we show that the interpretation of defaults as modal formulas proposed by Konolige allows us to represent all semantics for default logic in terms of the corresponding semantics for autoepistemic  ...  We revisit the issue of connections between two leading formalisms in nonmonotonic reasoning: autoepistemic logic and default logic.  ...  Marek and Truszczynski related default logic to two modal nonmonotonic logics related but different from autoepistemic logic: the nonmonotonic modal logic N [MT89a] and nonmonotonic modal logic S4F  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0002002v1">arXiv:cs/0002002v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mmzapua3cbhjvkrmsq4jbo3pfm">fatcat:mmzapua3cbhjvkrmsq4jbo3pfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171008194242/https://core.ac.uk/download/pdf/2417244.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/95/68/9568bfbf188e544bfc76d68fcf0f897a0265a61d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0002002v1" 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>

Uniform semantic treatment of default and autoepistemic logics

Marc Denecker, Victor W. Marek, Mirosław Truszczyński
<span title="">2003</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
The correspondence exploits the modal interpretation of a default proposed by Konolige.  ...  Our results establish conclusively that default logic can be viewed as a fragment of autoepistemic logic, a result that has been long anticipated.  ...  In [29] Schwarz proved that reflexive autoepistemic logic can similarly be obtained from modal logic SW5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0004-3702(02)00293-x">doi:10.1016/s0004-3702(02)00293-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zpyvjdfugngkxloqxh6ma4pl7m">fatcat:zpyvjdfugngkxloqxh6ma4pl7m</a> </span>
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Page 753 of Mathematical Reviews Vol. , Issue 99b [page]

<span title="">1991</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: “This paper investigates separated autoepistemic logic, which is a generalization of Moore’s autoepistemic logic with sep- arate modalities for belief and disbelief.  ...  A normal modal logic is a modal logic with the necessitation rule and the axiom K: O(A — B) — (OA — OB), a regular modal logic is one with the inference rule RR by which from A, + B we can infer the sequent  ... 
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Reiter's Default Logic Is a Logic of Autoepistemic Reasoning And a Good One, Too [article]

Marc Denecker, Victor W. Marek, Miroslaw Truszczynski
<span title="2011-08-16">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We argue that Reiter's default logic is a better formalization of Moore's intuitions about autoepistemic propositions than Moore's own autoepistemic logic.  ...  Thus, Reiter had developed his default logic as a formalization of autoepistemic propositions rather than of defaults.  ...  Table 1 : 1 Lattice operators and the corresponding semantics Table 2 : 2 The alignment of default and autoepistemic logics the modal logic S5 can be used to translate any autoepistemic logic theory  ... 
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