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A strong normalization result for classical logic

Franco Barbanera, Stefano Berardi
<span title="">1995</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;
In this paper we give a strong normalization proof for a set of reduction rules for classical logic.  ...  Acknowledgements We are grateful to Mariangiola Dezani for her constant support and gentle guidance, and to Mario Coppo for helpful discussions and his careful reading of an earlier draft.  ...  The first author wishes to express his gratitude also to Paola Francis for her steadfast encouragement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(95)00004-z">doi:10.1016/0168-0072(95)00004-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zamayiq2dbhjtpinm6t44r5fwu">fatcat:zamayiq2dbhjtpinm6t44r5fwu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170927052132/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/4c5/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY4MDA3Mjk1MDAwMDR6.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/a6/74/a674a1d64f97f5e99558daab288588ec2020942c.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(95)00004-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A Notion of Classical Pure Type System (Preliminary version)

Gilles Barthe, John Hatcliff, Morten Heine Sørensen
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
Gri n's discoveries were followed by a series of papers on classical logic, control operators and the Curry-Howard isomorphism, see for example 3,4,18,24,42,62 66,69 72,82].  ...  In classical proof theory, Girard noticed that cut-elimination in classical sequent calculus was not con uent di erent strategies for reduction gives di erent proofs in normal form, i.e. proof normalization  ...  As a result, it is not possible to prove strong normalization l a Harper-Honsell-Plotkin for P.  ... 
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On the Relation between Weak Completion Semantics and Answer Set Semantics [article]

Emmanuelle-Anna Dietz Saldanha, Jorge Fandinno
<span title="2019-10-16">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
After that, we will provide a translation from logic programs understood under the WCS into logic programs understood under the ASP.  ...  In particular, we will show that logic programs under the WCS can be represented as logic programs under the ASP by means of a definition completion, where all defined atoms in a program must be false  ...  We are thankful to David Pearce for pointing to Vakarelov's work on the relation between Lukasiewicz logic and classical logic with strong negation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.07278v1">arXiv:1910.07278v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6rxp6msgfnbvfealxlwfgeii6q">fatcat:6rxp6msgfnbvfealxlwfgeii6q</a> </span>
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Equivalence for the G3′-stable models semantics

José Luis Carballido, Mauricio Osorio, José Ramón Arrazola
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gyhc4ppmyjfm5a64dneqesv7ka" style="color: black;">Journal of Applied Logic</a> </i> &nbsp;
strong equivalence between programs can be reduced to checking whether a formula is a theorem in some paraconsistent logic, or in some cases in classical logic.  ...  We also present some program transformations for disjunctive programs which can be used to reduce the size of a program.  ...  Table 2 2 The Loop transformation was defined only for normal programs. The RD − transformation does preserve strong p-stable equivalence for normal programs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jal.2009.12.001">doi:10.1016/j.jal.2009.12.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pgkghgvzgrgihlu5kwigcxnija">fatcat:pgkghgvzgrgihlu5kwigcxnija</a> </span>
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P-stable models of strong kernel programs

Claudia Zepeda, José Luis Carballido
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anp7kqfyerdljfxydqb4objj6a" style="color: black;">Journal of Algorithms</a> </i> &nbsp;
We introduce three different formats for normal programs: Negative normal programs, Restricted negative normal programs and Strong kernel programs.  ...  One of the main results of this paper indicates that the p-stable semantics for strong-kernel programs agrees with the stable semantics for kernel programs as defined in [2] .  ...  Now, it is easy to see that for each rule r ∈ P , the rule RED(r, M ) is a logical consequence (in classical logic) of the rule We also introduce another format for normal program called Strong Kernel  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jalgor.2009.02.004">doi:10.1016/j.jalgor.2009.02.004</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t42okwvl7bbkbe4frw4wcvsn54">fatcat:t42okwvl7bbkbe4frw4wcvsn54</a> </span>
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Page 4306 of Mathematical Reviews Vol. , Issue 94h [page]

<span title="">1994</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;
Mariko Yasugi (J-KSUS; Kyoto) 94h:03112 03F05 03B15 03B40 Parigot, Michel (F-PARIS7-ML; Paris) Strong normalization for second order classical natural deduction.  ...  Summary: “We prove the strong normalization theorem for second- order classical natural deduction. The method used is an adapta- tion of the method of reducibility candidates introduced by J.-Y.  ... 
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Basic proof theory

Lev Gordeev
<span title="">1998</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hq6x4whtd5hhlhsxzculyeamey" style="color: black;">Science of Computer Programming</a> </i> &nbsp;
Analogous (weaker) results about strong normalization in the corres- ponding N-systems were obtained by Crabbe.  ...  Second-order logic. 1. Intuitionistic N-system. Normal deductions. 2. Typed polymorphic lambda calculus. 3. Girard's strong normalization proof. 4-5.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0167-6423(98)00002-1">doi:10.1016/s0167-6423(98)00002-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zaujpt3oybegxplm2wqphdgchq">fatcat:zaujpt3oybegxplm2wqphdgchq</a> </span>
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Page 7603 of Mathematical Reviews Vol. , Issue 2004j [page]

<span title="">2004</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;
Strong normalization for Au-calculus followed from strong normalization for intuitionistic logic and the property: if wu reduces to v, then (1) u* reduces to v*; (2) the reduction is non-trivial, that  ...  The goal of this paper is to fill gaps in several strong normaliza- tion proofs for classical logic [M. Parigot, J.  ... 
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Page 620 of Mathematical Reviews Vol. , Issue 96b [page]

<span title="">1996</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;
“This paper studies the existence of storage operators which give a normal form as result (strong storage operators) for recursive and iterative representation of data in A-calculus.  ...  This reduction relation satisfies sev- eral properties of interest, among others, the property of strong normalization. We prove this last result by using a reducibility argument a la Tait.”  ... 
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Page 8925 of Mathematical Reviews Vol. , Issue 2003m [page]

<span title="">2003</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;
Nour [“A short proof of the strong normalization of classical natural deduction with disjunction”, J. Symbolic Logic, to appear]) and the local confluence.  ...  In this way strong normalization for detour conversions is reduced to strong normal- ization for the simply typed lambda calculus.  ... 
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Page 582 of Mathematical Reviews Vol. , Issue 93b [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;
it in a sys- tem of second order logic and proving strong normalization for the latter by strongly impredicative means, and to carry this out he had to restrict his elimination rules for V and 3 to have  ...  The au- thor of this paper proves both weak normalization (that there is a reduction sequence to a normalized deduction) and strong normal- ization (that every reduction sequence terminates) for a natural  ... 
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On Negation, Completeness and Consistency [chapter]

Arnon Avron
<span title="">2002</span> <i title="Springer Netherlands"> Handbook of Philosophical Logic </i> &nbsp;
One can argue that this strong normality characterizes classical logic.  ...  the two standard formulations of the \strong consistency" of classical logic are not equivalent in general.9 Classical logic is obtained from it by adding :A ! (A !  ...  The converse is obvious. 2 In view of the last proposition, the strong c-normality of RMI m and its two obvious corollaries (weak normality and c-normality) can be reformulated in terms of the algebraic  ... 
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Towards a Fuzzy Answer Set Semantics for Residuated Logic Programs

Nicolás Madrid, Manuel Ojeda-Aciego
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wl6t75bdqrdlrgsukwo2coosly" style="color: black;">2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology</a> </i> &nbsp;
In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation.  ...  As a result, I is a stable model of P if and only if I(p) = ϑ * ¬I(0). Fuzzy answer sets In this section, we concentrate on strong negation and we will consider normal residuated logic programs.  ...  • normal if it does not contain default negation but it might contain strong negation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/wiiat.2008.357">doi:10.1109/wiiat.2008.357</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iat/MadridO08.html">dblp:conf/iat/MadridO08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4a4g7hdpuzeerc5l5agj6six54">fatcat:4a4g7hdpuzeerc5l5agj6six54</a> </span>
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Page 1995 of Mathematical Reviews Vol. , Issue 96d [page]

<span title="">1996</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;
The classical notion of strong normal form in combinatory logic is also generalized, yielding yet another description of these translates.  ...  Their resulting tripartite characterization extends to the combined first-order algebraic and higher-order setting the classical combinatory logic descriptions of the translates of long #-normal forms  ... 
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Strong and explicit negation in non-monotonic reasoning and logic programming [chapter]

José Júlio Alferes, Luís Moniz Pereira, Teodor C. Przymusinski
<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;
It is worth noting that the well-founded semantics for normal logic programs 12] obeys relevance (cf. 10]).  ...  Then, for no atom A: T j = A^A The following result shows that the relevant logic program semantics WFSX (de ned in 23]) is embeddable in AEBX.  ...  A Autoepistemic Logic of Beliefs Here we brie y recall the de nition of the Autoepistemic Logic of Beliefs, AEB, introduced by Przymusinski in 29].  ... 
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