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Defaults as restrictions on classical Hilbert-style proofs

Gianni Amati, Luigia Carlucci Aiello, Fiora Pirri
<span title="">1994</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhs2rsfonnhrbntyqjovx333um" style="color: black;">Journal of Logic, Language and Information</a> </i> &nbsp;
We propose to describe default logic as a logic where the juxtaposition of default proofs is subordinate to a restriction condition .  ...  We also prove cumulativity for any default logic (L; ) by slightly modifying the notion of default proof.  ...  Finally, the new de nition of default logic (L; ) leads us to consider, in Section 5, a relation of re nement between default logics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01160020">doi:10.1007/bf01160020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4levomymdjeodk7npn33tueijm">fatcat:4levomymdjeodk7npn33tueijm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190307130542/http://pdfs.semanticscholar.org/e09d/b055efc99a2e47e1152411c7b4c4b8d270f0.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/e0/9d/e09db055efc99a2e47e1152411c7b4c4b8d270f0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01160020"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Yet some more complexity results for default logic

Rachel Ben-Eliyahu-Zohary
<span title="">2002</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 identify several new tractable subsets and several new intractable simple cases for reasoning in the propositional version of Reiter's default logic.  ...  By making some intuitive observations, most classes that we identify can be derived quite easily from some subsets of default logic already known in the literature.  ...  Later we need the notion of "default proof" for normal default theories [14] . Definition 2.6 (Default proof ; a special case of [14, Definition 3] ).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0004-3702(02)00189-3">doi:10.1016/s0004-3702(02)00189-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jhgzswqcqfev5jjpsz7ygr5kwu">fatcat:jhgzswqcqfev5jjpsz7ygr5kwu</a> </span>
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Default theories over monadic languages

Michael Kaminski, Julia Rubin-Mosin
<span title="">2006</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;
In this paper we compare the semantical and syntactical definitions of extensions for open default theories.  ...  We also show that, under the domain closure assumption, one free variable open default theories are decidable.  ...  Proof of Theorem 10 In this section we present the proof of Theorem 10 stating that for a uniterm default theory (D, A) there exists a finite set of new constant symbols b such that for any infinite set  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2006.08.007">doi:10.1016/j.tcs.2006.08.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zhzvvlqu6bccfefe3d5y3toii4">fatcat:zhzvvlqu6bccfefe3d5y3toii4</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;
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.  ...  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.  ...  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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A proof theoretical approach to default reasoning I: tableaux for default logic

G Amati
<span title="1996-04-01">1996</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;
The advantage of our approach, besides being simple and neat, is in its generality: it allows for the development of a default theory for any logic with a tableau formulation, such as intuitionistic logic  ...  Given a default theory W, D , the default rules D are simply understood as restrictions on the tableaux construction of the logic.  ...  Definition 5 (default tableau proof ) Let W, D be a default theory in some fixed logic L (whether the theory is defined in Reiter's system or in some of its variants), a default tableau proof in L for  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/6.2.205">doi:10.1093/logcom/6.2.205</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dpbdxncjd5gjjkuazl6ybzw6bm">fatcat:dpbdxncjd5gjjkuazl6ybzw6bm</a> </span>
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Redundancy in logic III: Non-monotonic reasoning

Paolo Liberatore
<span title="">2008</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 also considered the redundancy of defaults in a default theory. In this case, monotonic and unitary redundancy hold for justified default logic but not for the other three considered semantics.  ...  Checking redundancy, based on extensions, of a clause in the background theory is p 2 -complete for Reiter and justified default logics, and p 3 -complete for constrained and rational default logic; checking  ...  theory, four new defaults (each of size linear in the size of the background theory), and a new symbol in each default. 2 Theorem 25.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.artint.2008.02.003">doi:10.1016/j.artint.2008.02.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/faejhx352va2pi5gemiyt5rwby">fatcat:faejhx352va2pi5gemiyt5rwby</a> </span>
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Semi-representability of default theories in rational default logic [chapter]

Artur Mikitiuk
<span title="">1996</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;
They proved that an arbitrary default theory can be represented by a weak seminormal default theory provided the language L has been extended by new atoms.  ...  Marek and Truszczy nski studied the representability issue for default logic.  ...  default theory which can represent the original theory both in standard and in rational default logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-61630-6_13">doi:10.1007/3-540-61630-6_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r72wuq7wrfdwtndxe63hpwkik4">fatcat:r72wuq7wrfdwtndxe63hpwkik4</a> </span>
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Forthcoming papers

<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;
This article introduces a new method for continuous case-based reasoning, and discusses its application to the dynamic selection, modification, and acquisition of robot behaviors in an autonomous navigation  ...  Santamaria, Continuous case-based reasoning Case-based reasoning systems have traditionally been used to perform high-level reasoning in problem domains that can be adequately described using discrete,  ...  In this paper, we investigate how abduction can be performed from theories in default logic. In particular, we present a basic model of abduction from default theories.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0004-3702(97)90024-2">doi:10.1016/s0004-3702(97)90024-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uyydgdc44rhuvjxbftl5xcylpe">fatcat:uyydgdc44rhuvjxbftl5xcylpe</a> </span>
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A logic for default reasoning

R. Reiter
<span title="">1980</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
It is this property which leads to the non.monotonJcity of any logic of defaults. In this paper we propose a logic for default reasoning.  ...  For this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover.  ...  Alan Bundy and David Warren provided valuable insights into the relationship between default proofs and PROLOG.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0004-3702(80)90014-4">doi:10.1016/0004-3702(80)90014-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zajetvo6xndovbzbnhjdxkhwxe">fatcat:zajetvo6xndovbzbnhjdxkhwxe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809020036/http://www.cs.nott.ac.uk/~psznza/G52HPA/articles/Reiter:80a.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/93/bd/93bdca51c9c0477121ba9708ffe2747855b93aef.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(80)90014-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Default reasoning by deductive planning

Michael Thielscher, Torsten Schaub
<span title="">1995</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2ewief65xnegfh2slwulpgsnba" style="color: black;">Journal of automated reasoning</a> </i> &nbsp;
This interpretation supplies us with several interesting and valuable insights into the proof theory of Default Logics.  ...  From the very beginning, an important task was the development of proof theories in order to automate reasoning in Default Logic, preferably by adopting and extending methods known from classical automated  ...  Our examples provide new classes of default theories in which deciding credulous entailment is polynomial.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf00881829">doi:10.1007/bf00881829</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cegfbhgjcfcffccjth766745ue">fatcat:cegfbhgjcfcffccjth766745ue</a> </span>
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A New Research into Default Logic

Zhang Mingyi
<span title="">1996</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
In order to dedicate further research to default logic, a characterization of extensions is presented again and some new algorithms for reasoning tasks in default logic are presented in this paper.  ...  In previous papers some important properties of extensions of general default theories were given.  ...  Woo for comments on application of auto-compatibility to ELP in earlier drafts. We also thank the anonymous referees for their helpful comments to the previous versions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/inco.1996.0075">doi:10.1006/inco.1996.0075</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ywcuxj5nejc6jjlk5j2d4mfgrq">fatcat:ywcuxj5nejc6jjlk5j2d4mfgrq</a> </span>
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Proof Complexity of Propositional Default Logic [chapter]

Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, Heribert Vollmer
<span title="">2010</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 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic.  ...  Default logic is one of the most popular and successful formalisms for non-monotonic reasoning.  ...  Less is known about the complexity of proofs in default logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14186-7_5">doi:10.1007/978-3-642-14186-7_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m3j2j4evynb33ljd25w4ot234e">fatcat:m3j2j4evynb33ljd25w4ot234e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180518041601/http://drops.dagstuhl.de/opus/volltexte/2010/2526/pdf/10061.BeyersdorffOlaf.Paper.2626.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/07/70/0770b3dc1a3bdde5e4e2ccb99ba1b1c6425eeacb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14186-7_5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A note on the stable model semantics for logic programs

Michael Kaminski
<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;
This, in turn, leads to a natural translation of logic programs into open default theories. @ 1997 Elsevier Science B.V.  ...  The stable model semantics for logic programs is extended from ground literals onto open literals by augmenting the program language with an infinite set of new constants.  ...  •i Default theories and their extensions In this section we recall the definition of extensions for open default theories [ lo] needed for embeddings of logic programs into Reiter's default logic  ... 
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Default theories that always have extensions

Christos H. Papadimitriou, Martha Sideri
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
Determining whether a given default theory has an extension is the main computational problem pertinent to default logic, the analog of testing for validity and finding deductions in more classical logics  ...  We also give a proof that it is NP-complete to find extensions even for default theories with no prerequisites and at most two literals per default, a case substantially simpler than the NP-completeness  ...  Acknowledgment We are grateful to Yannis Dimopoulos, Nicole Bidoit, Christine Froidevaux, and Bart Selman for many interesting comments on the ideas and results in this paper.  ... 
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Page 4913 of Mathematical Reviews Vol. , Issue 95h [page]

<span title="">1995</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;
Mathematical proofs can thus be built by theorem proving both in the mathematical theory and in MT. This provides a very flexible way to perform mathematical reasoning on a computer.”  ...  Soundness, completeness, and decidability proofs for this class of preference logics are given in Appendix A (including results on first-order preference logics, introduced in Section 5).  ... 
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