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The Theory of the Generalised Real Numbers and Other Topics in Logic

Lorenzo Galeotti
<span title="">2019</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;
The classical Bolzano-Weierstraß and Heine-Borel theorems fail on generalisations of the real line.  ...  Moreover, we use generalisations of the real line to develop two new models of transfinite computability, one generalising type two Turing machines and one generalising a model of computation due to Blum  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/bsl.2019.47">doi:10.1017/bsl.2019.47</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2qz2plw6xrbhnijyv3agpqbr24">fatcat:2qz2plw6xrbhnijyv3agpqbr24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200214065638/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B53658C4D44B85F97FDBDB9C8323C3B9/S1079898619000477a.pdf/div-class-title-the-theory-of-the-generalised-real-numbers-and-other-topics-in-logic-div.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/d5/06/d50641dd1c32cdb8418e4543249ab2deb7759322.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/bsl.2019.47"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> cambridge.org </button> </a>

On Acyclic and Head-Cycle Free Nested Logic Programs [chapter]

Thomas Linke, Hans Tompits, Stefan Woltran
<span title="">2004</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 generalises different extensions of Fages' theorem, including a recent result by Erdem and Lifschitz for tight logic programs.  ...  We define the class of head-cycle free nested logic programs, and its proper subclass of acyclic nested programs, generalising similar classes originally defined for disjunctive logic programs.  ...  With the next results, we generalise Proposition 2 to HCF and acyclic nested programs. To begin with, we have the following theorem. Theorem 3 Let Π be a HCF nested logic program.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-27775-0_16">doi:10.1007/978-3-540-27775-0_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4k7pjlfpyngblpm6z2iuxrbwqy">fatcat:4k7pjlfpyngblpm6z2iuxrbwqy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060212160603/http://www.pims.math.ca:80/science/2004/NMR/papers/paper35.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/8c/80/8c8060300bf8f46896345800174da1dd836319fb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-27775-0_16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

L-Topology via Generalised Geometric Logic [article]

P. Jana
<span title="2019-08-25">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper introduces a notion of generalised geometric logic. Connections of generalised geometric logic with L-topological system and L-topological space are established.  ...  Generalised Geometric Logic In this section we will introduce the notion of generalised geometric logic which may be considered as a generalisation of fuzzy geometric logic and consequently of so called  ...  Hence A/ ≈ is L-Topology via Generalised Geometric Logic We first construct the L-topological system (X, |= ′ , A/ ≈ ) from generalised geometric logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1909.02106v1">arXiv:1909.02106v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6kcy5yh6nvgmbp5nysv2fmeax4">fatcat:6kcy5yh6nvgmbp5nysv2fmeax4</a> </span>
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The Unrestricted Combination of Temporal Logic Systems

M. Finger
<span title="2002-03-01">2002</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mwzmwwmscfe4vnzrjlt5itd2ju" style="color: black;">Logic Journal of the IGPL</a> </i> &nbsp;
This paper generalises and complements the work on combining temporal logics started by Finger and Gabbay [11, 10] .  ...  We also generalise such results to the external application of a multi-modal system containing any number of connectives with arbitrary arity, that respect normality.  ...  Does the transference of properties hold is such a generalised form? Let us first concentrate on the a combination of two generalised modal logics, M 1 and M 2 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/jigpal/10.2.165">doi:10.1093/jigpal/10.2.165</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n77fg3ak2rgcrgq4xnpy3yrxr4">fatcat:n77fg3ak2rgcrgq4xnpy3yrxr4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808071454/https://www.ime.usp.br/~mfinger/www-home/papers/FW02.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/fd/44/fd44b728a326f24a891d539c3d917d976629d758.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/jigpal/10.2.165"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Theorem Reuse by Proof Term Transformation [chapter]

Einar Broch Johnsen, Christoph Lüth
<span title="">2004</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 approach is based on a representation of proofs as logical framework proof terms, using the theorem prover Isabelle.  ...  This paper proposes an approach where theorems are generalised by abstracting their proofs from the original setting.  ...  We are grateful to Till Mossakowski and Burkhart Wolff for interesting discussions on the subject of abstraction in Isabelle, to Erwin R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30142-4_12">doi:10.1007/978-3-540-30142-4_12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zxrdadywandvliggfkfdhzwrsy">fatcat:zxrdadywandvliggfkfdhzwrsy</a> </span>
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An overview of Generalised Veltman Semantics [article]

Joost J. Joosten, Jan Mas Rovira, Luka Mikec, Mladen Vuković
<span title="2020-07-09">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Interpretability logics are endowed with relational semantics \'a la Kripke: Veltman semantics. For certain applications though, this semantics is not fine-grained enough.  ...  This paper aims to give an overview of results and applications of Generalised Veltman semantics up to the current date.  ...  Acknowledgements We thank Dick de Jongh, Volodya Shavrukov, VítěslavŠvejdar, and Rineke Verbrugge and Albert Visser for fruitful discussions and for comments on the origins  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.04722v1">arXiv:2007.04722v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yh7apvxvirgvhbr7oa3oludazm">fatcat:yh7apvxvirgvhbr7oa3oludazm</a> </span>
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Quasi-subtractive varieties

Tomasz Kowalski, Francesco Paoli, Matthew Spinks
<span title="">2011</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4l7nckgxmbcgvj5vxsioq6qwyq" style="color: black;">Journal of Symbolic Logic (JSL)</a> </i> &nbsp;
The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems.  ...  of deductive filters on A of the τ-assertional logic of .  ...  isomorphism between the lattice of V-V 0 congruences on A and the lattice of V-open lters on A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/jsl/1318338848">doi:10.2178/jsl/1318338848</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ygjejkr26veqxnhxp3iptujzoa">fatcat:ygjejkr26veqxnhxp3iptujzoa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160821102743/http://www.jaist.ac.jp/rcis/asubl4/abstracts/Kowalski-Paoli.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/e7/df/e7dfafa8354593a42c72ba3cfa5592ab8aafd7c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2178/jsl/1318338848"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A new continuous propositional logic [chapter]

Riccardo Poli, Mark Ryan, Aaron Sloman
<span title="">1995</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 this paper we present Minimal Polynomial Logic (MPL), a generalisation of classical propositional logic which allows truth values in the continuous interval 0; 1] and in which propositions are represented  ...  in Fuzzy Logic.  ...  Having de ned a set of generalised connectives any ordinary logic expression e can be generalised by simply replacing the ordinary connectives with the generalised ones.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-60428-6_2">doi:10.1007/3-540-60428-6_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tqaqvogeufdmhi3ex6nop462gm">fatcat:tqaqvogeufdmhi3ex6nop462gm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090625183716/http://www.cs.bham.ac.uk/~mdr/research/papers/pdf/CSRP-95-08.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/d4/fe/d4fe81748513ac749b34889cf66de84387a96ef5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-60428-6_2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the logical structure of choice and bar induction principles [article]

Nuria Brede, Hugo Herbelin
<span title="2021-06-28">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
of functions from A to B, a generalised form GDC_A,B,T of the axiom of dependent choice and dually a generalised bar induction principle GBI_A,B,T such that: GDC_A,B,T intuitionistically captures the  ...  B = 𝔹, ∙ bar induction when A = ℕ, ∙ the Weak Fan Theorem when A = ℕ and B = 𝔹.  ...  The second author thanks Valentin Blot and Étienne Miquey for numerous fruitful discussions on the axiom of dependent choice and bar induction.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08951v2">arXiv:2105.08951v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r7f62hxb2jd77aa6rmwlgdm74q">fatcat:r7f62hxb2jd77aa6rmwlgdm74q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210728210756/https://arxiv.org/pdf/2105.08951v2.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/ba/e0/bae05279b3e889d4b34568df7d3a4aa644ef2945.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2105.08951v2" 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 945 of Mathematical Reviews Vol. , Issue 82c [page]

<span title="">1982</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;
Theorem | characterizes when T,(Q)=T7,(Q) (there are five such theories); Theorem 2 gives further results on when T,(Q) C 7,(Q); and Theorem 3 says that 7,(Q) is decidable for all a (similarly for the  ...  To describe the generalisation of Morley’s theorem, the author introduces the notion of the complexity C( p) of an L-type p of T; C(p) is always a natural number.  ... 
<span class="external-identifiers"> </span>
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Strong Inconsistency in Nonmonotonic Reasoning

Gerhard Brewka, Matthias Thimm, Markus Ulbricht
<span title="">2017</span> <i title="International Joint Conferences on Artificial Intelligence Organization"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vfwwmrihanevtjbbkti2kc3nke" style="color: black;">Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence</a> </i> &nbsp;
We also demonstrate the potential of our new notion for applications, focusing on repair and inconsistency measurement.  ...  It turns out that for nonmonotonic reasoning a stronger notion is needed. In this paper we develop such a notion, called strong inconsistency.  ...  Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.24963/ijcai.2017/125">doi:10.24963/ijcai.2017/125</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/ijcai/BrewkaTU17.html">dblp:conf/ijcai/BrewkaTU17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pngjaohktfcudgdclqfrytvtzq">fatcat:pngjaohktfcudgdclqfrytvtzq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721030309/https://www.ijcai.org/proceedings/2017/0125.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/8f/fa/8ffa82d566c454546a22c65b336efd21ffceeda3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.24963/ijcai.2017/125"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 1633 of Mathematical Reviews Vol. 49, Issue 5 [page]

<span title="">1975</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;
Symbolic Logic 39 (1974), 57-66. This paper gives generalisations of some of the results in K. Kunen’s paper [Ann. Math. Logic 1 (1970), 179-227; MR 43 #3080].  ...  And under the assumption of co- herency, many of the known results about L[y] generalise to L[U]. For example, in Theorem 3.6 the author shows that for coherent U, L[U] GCH + + there is a A,?  ... 
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An illustration of the explanatory and discovery functions of proof

Michael De Villiers
<span title="2012-10-26">2012</span> <i title="AOSIS"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xwixhqgaujcebgrk2sc4hrcv4q" style="color: black;">Pythagoras</a> </i> &nbsp;
After logically explaining (proving) the result geometrically and algebraically, the result is generalised to other polygons by further reflection on the proof(s).  ...  This article provides an illustration of the explanatory and discovery functions of proof with an original geometric conjecture made by a Grade 11 student.  ...  With deductive generalisation is meant the logical reflection (looking back on) and consequent generalisation of a critical idea to more general or different cases by means of deductive reasoning.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4102/pythagoras.v33i3.193">doi:10.4102/pythagoras.v33i3.193</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ouirfjhjzfdgfb7caop7wiazga">fatcat:ouirfjhjzfdgfb7caop7wiazga</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160512173705/http://www.pythagoras.org.za:80/index.php/pythagoras/article/download/193/227" 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/4c/c6/4cc6d5ed7097564d418740f228d14c782502324a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4102/pythagoras.v33i3.193"> <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>

A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs

George Tourlakis
<span title="">2016</span> <i title="Uniwersytet Lodzki (University of Lodz)"> Bulletin of the Section of Logic </i> &nbsp;
first into Gentzen style logics in order to rely on cut elimination and the subformula property.  ...  Reference [12] introduced a novel formula to formula translation tool ("formulators") that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them  ...  The motivation for introducing M 3 in loc. cit. was to obtain a logic that acts as a provability logic for pure classical first-order logic in the sense that the conservation theorem holds, which in its  ... 
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Locality-preserving logical operators in topological stabilizer codes

Paul Webster, Stephen D. Bartlett
<span title="2018-01-24">2018</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z3u6fzrh4fdvhnzujueyvzipwi" style="color: black;">Physical Review A</a> </i> &nbsp;
In particular, we focus on those equivalent to a stack of a finite number of surface codes of any spatial dimension, where our procedure fully specifies the group of locality-preserving logical operators  ...  Using a correspondence between such operators and gapped domain walls, we describe a procedure for finding all locality-preserving logical operators admitted by a large and important class of topological  ...  of generalised domain walls in theorem 2.  ... 
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