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Coalgebra Learning via Duality [chapter]

Simone Barlocco, Clemens Kupke, Jurriaan Rot
<span title="">2019</span> <i title="Springer Singapore"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lliksjpywfcx3dtw7aj2vkybvi" style="color: black;">Green Chemistry and Sustainable Technology</a> </i> &nbsp;
The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories.  ...  Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras.  ...  We are grateful to Joshua Moerman, Nick Bezhanishvili, Gerco van Heerdt, Aleks Kissinger and Stefan Milius for valuable discussions and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-17127-8_4">doi:10.1007/978-3-030-17127-8_4</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/fossacs/BarloccoKR19.html">dblp:conf/fossacs/BarloccoKR19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u5iwwtmzi5fx7h3pwqcjr6odmy">fatcat:u5iwwtmzi5fx7h3pwqcjr6odmy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503142841/https://link.springer.com/content/pdf/10.1007%2F978-3-030-17127-8_4.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/c3/f0/c3f0809edcfe4cb79c9d10883ee167e9d9176445.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-17127-8_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Coalgebra Learning via Duality [article]

Simone Barlocco, Clemens Kupke, Jurriaan Rot
<span title="2019-08-08">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The approach relies on the use of logical formulas as tests, based on a dual adjunction between states and logical theories.  ...  Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras.  ...  We are grateful to Joshua Moerman, Nick Bezhanishvili, Gerco van Heerdt, Aleks Kissinger and Stefan Milius for valuable discussions and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.05762v2">arXiv:1902.05762v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lcwbjokgrjavvm7jvxbtobnurq">fatcat:lcwbjokgrjavvm7jvxbtobnurq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200908085517/https://arxiv.org/pdf/1902.05762v1.pdf" title="fulltext PDF download [not primary version]" 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] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/33/6e/336ec08e8fa031c99f3f5cbd43d86dfcfee9a386.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.05762v2" 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>

Admissibility via natural dualities

Leonardo Cabrer, George Metcalfe
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/74pjbehpfraq5ogj3loetdwp7m" style="color: black;">Journal of Pure and Applied Algebra</a> </i> &nbsp;
In particular, axiomatizations are obtained for the admissible clauses and quasi-identities of bounded distributive lattices, Stone algebras, Kleene algebras and lattices, and De Morgan algebras and lattices  ...  quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be characterized using natural dualities  ...  We thank Christoph Röthlisberger for his helpful comments, and are grateful also to two anonymous referees who noted several inconsistencies in the original version of this paper and suggested many valuable  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jpaa.2015.02.015">doi:10.1016/j.jpaa.2015.02.015</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sswkmjjv6jhv7nvo4vfa5mdkg4">fatcat:sswkmjjv6jhv7nvo4vfa5mdkg4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719043033/https://boris.unibe.ch/68284/1/CabrerMetcalfe2014final.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/ca/fa/cafa60b22e0eae485960065068d4f316fade0474.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jpaa.2015.02.015"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Admissibility via Natural Dualities [article]

Leonardo Manuel Cabrer, George Metcalfe
<span title="2015-01-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, axiomatizations are obtained for the admissible clauses and quasi-identities of bounded distributive lattices, Stone algebras, Kleene algebras and lattices, and De Morgan algebras and lattices  ...  quasivarieties generated by a single finite algebra, or equivalently, the quasiequational and universal theories of their free algebras on countably infinitely many generators, may be characterized using natural dualities  ...  Axiomatizations (called bases) of the admissible rules for this logic were later provided, independently, by Iemhoff [20] and Rozière [36] , and subsequently for other intermediate logics by Iemhoff  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.06141v1">arXiv:1501.06141v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nvtipj7jgjcwjbo3kdeceuebdu">fatcat:nvtipj7jgjcwjbo3kdeceuebdu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200824003513/https://arxiv.org/pdf/1501.06141v1.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/e4/31/e43177d549b10ba2e6386207a7b1f715970ce755.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1501.06141v1" 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>

Taking Degrees of Truth Seriously

Josep Maria Font
<span title="2009-03-28">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nzzezfqw65bhpbeksnoskjzuza" style="color: black;">Studia Logica: An International Journal for Symbolic Logic</a> </i> &nbsp;
Some recent works studying these in the particular cases of Lukasiewicz's many-valued logics and of logics associated with varieties of residuated lattices are also presented.  ...  Then the alternative usage of truth-values in order to define logics that preserve degrees of truth is presented and discussed.  ...  The many interesting talks in Dresden's Workshop on Truth Values (May-June 2008) and in Siena's Conference on Logic, Algebra and Truth Degrees (September 2008) also contributed in the same direction.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11225-009-9180-7">doi:10.1007/s11225-009-9180-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4jocuegwkneqdpaql77ukajhhy">fatcat:4jocuegwkneqdpaql77ukajhhy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090116002622/http://www.mat.ub.edu/~jmfont/docs/Seriously.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/e6/31/e631967796d8cbb7fe1839fb7c9912728b2e0f24.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11225-009-9180-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Truth Functionality and Measure-Based Logics [chapter]

Luca Boldrin, Claudio Sossai
<span title="">1999</span> <i title="Springer Netherlands"> Applied Logic Series </i> &nbsp;
We present a truth-functional semantics for necessity-valued logics, based on the forcing technique.  ...  The subsequent step is the definition of a many-valued truth-functional semantics, by simply taking the truth value of a formula to be the set of all informational states that force the truth of the formula  ...  Thanks also to Giovanni Sambin, Silvio Valentini and Alessandro Saffiotti for their acute observations. We are gratefull to Nino Trainito for his carefull reading of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-017-1652-9_23">doi:10.1007/978-94-017-1652-9_23</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mkkosr2bcbhftdkoxkdwsx42sq">fatcat:mkkosr2bcbhftdkoxkdwsx42sq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20051222083716/http://www.ladseb.pd.cnr.it:80/infor/papers/kluwer99preprint.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/46/3f/463f8c4482c9865789919579b8674b4e875ea84c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-017-1652-9_23"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Theory of Truth that Prefers Falsehood

Melvin Fitting
<span title="">1997</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ankkynzqs5dqbo4lk5zcpua7rq" style="color: black;">Journal of Philosophical Logic</a> </i> &nbsp;
There is often a close relationship between theories of truth and the semantics of logic programming. Generally speaking, the same mathematical machinery is appropriate for both.  ...  The present paper can be seen as shifting the mechanism of stable model semantics for logic programming back to the philosophical arena, repaying the debt incurred to Kripke years ago.  ...  Of course this can not be done in the framework of classical, two-valued logic because of liar sentences.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/a:1004217812355">doi:10.1023/a:1004217812355</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ibipfnho5vegpdpdokgjtsrjbq">fatcat:ibipfnho5vegpdpdokgjtsrjbq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100614111202/http://comet.lehman.cuny.edu/fitting/bookspapers/pdf/papers/TruthFalse.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/92/dd/92ddf126c76a4ba7f138ec2d35d0dae2d1486a56.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1023/a:1004217812355"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures

Yoshihiro Maruyama
<span title="2014-12-27">2014</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
The set-theoretical hyperdoctrinal models of quantum logic, as well as all quantum hyperdoctrines with cartesian base categories, turn out to give sound and complete semantics for Faggian-Sambin's first-order  ...  We systematically investigate into the categorical logics of dual adjunctions by utilising Johnstone-Dimov-Tholen's duality-theoretic framework.  ...  Objects in Set give domains of discourse for semantics, and the dualising object Ω a set of truth values.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.171.10">doi:10.4204/eptcs.171.10</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cpjr7g6yh5b77pkow4gzgzts2e">fatcat:cpjr7g6yh5b77pkow4gzgzts2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809063327/http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPLX.10.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/70/02/700287ee122b277d56e31197fc0fe9e7417eed86.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.171.10"> <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 Representation Theorem for Many-valued Modal Logics [article]

Zoran Majkic
<span title="2011-03-01">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Such a new framework offers a new semantics for many-valued logics based on the truth-invariance entailment.  ...  In the case when the many-valued modal logics are based on the set of truth-values that are complete distributive lattices we obtain a compact autoreferential Kripke-style canonical representation.  ...  In Section 4 we apply this new Representation theorem framework to modal many-valued logics, in the particular case when it is based on complete distributive lattices of truth values (an autoreferential  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1103.0217v1">arXiv:1103.0217v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xxz4xjrwtnczrgewv463oazqai">fatcat:xxz4xjrwtnczrgewv463oazqai</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1103.0217/1103.0217.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> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/45/b2/45b20db95f979857b2a5335af83f9de3496ee1d4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1103.0217v1" 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>

Testing Semantics: Connecting Processes and Process Logics [chapter]

Dusko Pavlovic, Michael Mislove, James B. Worrell
<span title="">2006</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 approach is based on generalizing from duality theories that now are common in semantics to logical connections, which are simply contravariant adjunctions.  ...  We propose a methodology based on testing as a framework to capture the interactions of a machine represented in a denotational model and the data it manipulates.  ...  This approach is based on generalizing from duality theories that now are common in semantics to logical connections, which are simply contravariant adjunctions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11784180_24">doi:10.1007/11784180_24</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ba75kgvhsncpvdp6bcu7zijp74">fatcat:ba75kgvhsncpvdp6bcu7zijp74</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121114205221/http://www.isg.rhul.ac.uk/dusko/papers/2006-AMAST.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/fc/99/fc99f315daee6645dad56ac0d20b1df2c6a30bb5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11784180_24"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Paraconsistent Foundations for Probabilistic Reasoning, Programming and Concept Formation [article]

Ben Goertzel
<span title="2021-01-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Then variations on the Curry-Howard correspondence are used to map these paraconsistent and probabilistic logics into probabilistic types suitable for use within dependent type based programming languages  ...  It is argued that 4-valued paraconsistent truth values (called here "p-bits") can serve as a conceptual, mathematical and practical foundation for highly AI-relevant forms of probabilistic logic and probabilistic  ...  Constructible Duality Logic The variant of formal logic that appears to best match the natural semantics of experiential learning based AI systems is the constructible duality logic articulated by Patterson  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.14474v2">arXiv:2012.14474v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4zfsz3taqnbfjayux7zly7w2ia">fatcat:4zfsz3taqnbfjayux7zly7w2ia</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210119064333/https://arxiv.org/pdf/2012.14474v2.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/41/84/41849ec7b7f9f70931559eb75e172d3b94237e17.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.14474v2" 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>

Relational Semantics Through Duality [chapter]

Ewa Orłowska, Ingrid Rewitzky, Ivo Düntsch
<span title="">2006</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 show how the classical duality results extended to a Duality via Truth contribute to development of a relational semantics for various modal-like logics.  ...  In particular, we present a Duality via Truth for some classes of information algebras and frames.  ...  Duality via Truth results for a language of lattice-based relation algebras and for languages of substructural logics can be easily developed based on the representation results presented in [OrR05, DOR03  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11734673_2">doi:10.1007/11734673_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tplwvjg3ejecrjiwzkqgsjwmmm">fatcat:tplwvjg3ejecrjiwzkqgsjwmmm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190217093422/http://pdfs.semanticscholar.org/0549/82bf11200e37df9a8b8f74ad4aa33ee55f64.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/05/49/054982bf11200e37df9a8b8f74ad4aa33ee55f64.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11734673_2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Back and forth between algebraic geometry, algebraic logic, sheaves and forcing [article]

Trek Sayed Ahmed
<span title="2018-11-02">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We also study topoi as semantics for higher order logic of many sorted theories in connection to set theory, and the quasi-topoi based on MV algebras, for fuzzy logic.  ...  We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos.  ...  The natural thing to do is to replace Set, by Monoid, which has a tensor product, and define the semantics of ⊗ using this tensor product. (4) Now we have a semantics for V L , via forcing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.01754v1">arXiv:1811.01754v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qxlowihguzhpdpw7jxaqwxx5vu">fatcat:qxlowihguzhpdpw7jxaqwxx5vu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826033313/https://arxiv.org/pdf/1811.01754v1.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/b3/31/b331fe6ec652aaf8845ba430488018a8c5927157.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.01754v1" 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>

Natural duality, modality, and coalgebra

Yoshihiro Maruyama
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/74pjbehpfraq5ogj3loetdwp7m" style="color: black;">Journal of Pure and Applied Algebra</a> </i> &nbsp;
ISP M provides a natural framework for the universal algebra of modalities, and as such, for the theory of modal natural dualities.  ...  The main results are topological and coalgebraic dualities for ISP M (L) where L is a semi-primal algebra with a bounded lattice reduct.  ...  My heartfelt thanks are due to Piet Hut for his illuminating discussion on philosophical ideas. This work was supported by the Nakajima foundation and by Grant-in-Aid for JSPS Fellows (236509).  ... 
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Some remarks on semantics and expressiveness of the Sentential Calculus with Identity [article]

Steffen Lewitzka
<span title="2021-12-05">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Furthermore, we define a general framework of dualities between certain SCI-theories and Lewis-style modal systems in the vicinity of S3.  ...  We reformulate the original semantics of SCI in terms of Boolean prealgebras establishing a connection to 'hyperintensional semantics'.  ...  We then get the hierarchy S1SP ( S3 ( S4 ( S5 of Lewis (-style) modal logics for which we can use the same framework of algebraic semantics based on Boolean algebras (we shall explore this kind of semantics  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.02696v1">arXiv:2112.02696v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ej27q6htjzci3eqtfgni7yk7py">fatcat:ej27q6htjzci3eqtfgni7yk7py</a> </span>
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