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Classical field theory via Cohesive homotopy types [article]

Urs Schreiber
2013 arXiv   pre-print
Extended Conference Abstract submitted to the proceedings of the Conference on Type Theory, Homotopy Theory and Univalent Foundations in Barcelona, Fall 2013  ...  A brief survey of how classical field theory emerges synthetically in cohesive homotopy type theory.  ...  With hindsight one finds that this modal type theory is essentially what Lawvere was envisioning in [Law91] , where it is referred to as encoding "being and becoming", and later more formally in [Law94  ... 
arXiv:1311.1172v1 fatcat:icc7zcuevfg7vnqugfkbi6vimu

A spatial similarity measure based on games: theory and practice

M Aiello
2002 Logic Journal of the IGPL  
We show how this is possible in the case of the spatial modal logic S4u of Bennett. The approach results in a spatial similarity measure based on topological model comparison games.  ...  Model comparison games can be used not only to decide whether two specific models are equivalent or not, but also to establish a measurement of difference among a whole class of models.  ...  Aknowledgements The author is thankful to Johan van Benthem for fruitful discussions on the topic, to Kees Doets for feedback on a previous version of the proof of Theorem 4.4, and to Michael Zakharyaschev  ... 
doi:10.1093/jigpal/10.1.1 fatcat:ubnlxqwx3zf3bl7doemwsfkvxe

Topo-distance: Measuring the Difference between Spatial Patterns [chapter]

Marco Aiello
2000 Lecture Notes in Computer Science  
Model theoretic notions such as topological bisimulations and topological model comparison games are introduced to define a distance on the space of all topological models for the language S4u.  ...  The framework uses a multi-modal language S4u interpreted on topological spaces (rather than Kripke semantics) to describe the spatial patterns.  ...  Acknowledgments The author is thankful to Johan van Benthem for fruitful discussions on the topic and to Kees Doets for feedback on a previous version of the proof of Theorem 4.  ... 
doi:10.1007/3-540-40006-0_6 fatcat:fl2svirudbeermhkizkfmpvmyq

Topos Semantics for a Higher-Order Temporal Logic of Actions

Philip Johnson-Freyd, Jon Aytac, Geoffrey Hulette
2020 Electronic Proceedings in Theoretical Computer Science  
We use categorical techniques to recast a real-time semantics for TLA in terms of the actions of a group of time dilations, or "stutters," and an extension by a monoid incorporating delays, or "falters  ...  TLA is a popular temporal logic for writing stuttering-invariant specifications of digital systems.  ...  In this topos-theoretic setting, we can apply a simple recipe for constructing a topos together with internal complete modal algebras.  ... 
doi:10.4204/eptcs.323.11 fatcat:bq2osbihkbeinlhqbchdh4eaza

Page 6608 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
Kosta Dosen (Belgrade) 92m:03039 03B65 03B45 03G30 Reyes, Gonzalo E. (3-MTRL) A topos-theoretic approach to reference and modality. Notre Dame J. Formal Logic 32 (1991), no. 3, 359-391.  ...  An approach to modal logic is presented that is based on the notion of kind.  ... 

The theory of descriptions revisited

Alberto Peruzzi
1988 Notre Dame Journal of Formal Logic  
Fourman and D. Scott, is presented with reference to sheaves.  ...  Russell until now, and its most important advantages and disadvantages are sketched. TD is studied in the context of model theory (in A.  ...  It is just the proof-theoretic approach to TD which comes next, the first version of which was presented by Hubert and Bernays in [7] .  ... 
doi:10.1305/ndjfl/1093634997 fatcat:ehi3lr73fbhr7aiwzy3tmtugdu

Logical Relations as Types: Proof-Relevant Parametricity for Program Modules [article]

Jonathan Sterling, Robert Harper
2021 arXiv   pre-print
are rendered as derived notions in terms of a modal type-theoretic account of the phase distinction.  ...  Using the insight that logical relations/parametricity is itself a form of phase distinction between the syntactic and the semantic, we contribute a new synthetic approach to phase separated parametricity  ...  Acknowledgments anks to Mathieu Anel, Carlo Angiuli, Steve Awodey, Karl Crary, Daniel Gratzer, Gordon Plotkin, and Michael Shulman for their advice and comments, and to Tristan Nguyen at AFOSR for support  ... 
arXiv:2010.08599v3 fatcat:egvxsje5qbhzbgguct6cv47sjy

Does Category Theory Provide a Framework for Mathematical Structuralism?†

GEOFFREY HELLMAN
2003 Philosophia Mathematica  
We propose a synthesis of Bell's "many-topoi" view and modal-structuralism.  ...  Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis à vis set theory.  ...  This leads Bell to pursue an analogy with (special) relativity in physics: a particular topos corresponds to an inertial frame of reference, and a shift of frames is analogous to applying an admissible  ... 
doi:10.1093/philmat/11.2.129 fatcat:2ucbthjpdjf53om5jkv4dymole

Beyond Transcendentalism and Naturalization: A Categorial Framework for the Semiotic Phenomenology

Martina Properzi
2019 International Journal of Philosophy  
approach of phenomenology to the categorial study with the "in the third person" objective approach distinctive of semiotics, sharing in principle with the former a common pre-logical and hence ante-predicative  ...  and the contemporary trend to re-orient phenomenology naturalistically excluding the foundational perspective.  ...  Such a pair of categories and triple of functors is a unity-and-identity-of-opposites [62] . Let 5 be a topos. A level in 5 is the right adjoint's inclusion of an adjoint modality.  ... 
doi:10.11648/j.ijp.20190703.14 fatcat:s4mkjkd3lrhn7j43zzmo2uo36q

A Generalized Blakers-Massey Theorem [article]

Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal
2020 arXiv   pre-print
We prove a generalization of the classical connectivity theorem of Blakers-Massey, valid in an arbitrary higher topos and with respect to an arbitrary modality, that is, a factorization system (L,R) in  ...  We explain how to rederive the classical result, as well as a recent generalization by Chach\'olski-Scherer-Werndli. Our proof is inspired by the one given in Homotopy Type Theory.  ...  Of course, for a more precise discussion of the relationship between the higher categorical approach and the model category theoretic one, we refer the reader to [Lur09] .  ... 
arXiv:1703.09050v5 fatcat:swh2zmjfsfcu5jjhihrmkemabq

Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics

H. Freytes, G. Domenech, C. de Ronde
2014 Foundations of physics  
In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras.  ...  It allows us to introduce a classical type study of the mentioned properties.  ...  Acknowledgements This work was partially supported by the following grants: VUB project GOA67; FWO-research community W0.030.06; CONICET RES. 4541-12 (2013-2014) and PIP 112-201101-00636, CONICET.  ... 
doi:10.1007/s10701-014-9842-9 fatcat:cadl26cx5zhrjkn2l2foyr4wea

A Formal Ontology for a Computational Approach of Time and Aspect [chapter]

Aurélien Arena, Jean-Pierre Desclés
2010 Lecture Notes in Computer Science  
This linguistic model yields a conceptualisation reused for the definition of a formal ontology of time and aspect.  ...  This paper provides a linguistic semantic analysis of time and aspect in natural languages.  ...  This interval-based semantics is in line with a model-theoretic approach.  ... 
doi:10.1007/978-3-642-14770-8_7 fatcat:pe3udufkmbg33bwcfrxwipigbm

CrossLoc: Scalable Aerial Localization Assisted by Multimodal Synthetic Data [article]

Qi Yan, Jianhao Zheng, Simon Reding, Shanci Li, Iordan Doytchinov
2022 arXiv   pre-print
Despite significant progress in recent years, most learning-based approaches to visual localization target at a single domain and require a dense database of geo-tagged images to function well.  ...  Furthermore, we introduce CrossLoc, a cross-modal visual representation learning approach to pose estimation that makes full use of the scene coordinate ground truth via self-supervision.  ...  We thank Théophile Schenker and Alexis Roger for their projects work, which helped set the spark of this research. Finally, we would like to thank Dr.  ... 
arXiv:2112.09081v5 fatcat:4hfazjabhnbfjhv2emdysyara4

Upsetting the Foundations for Mathematics

Lawrence Neff Stout
2005 Philosophia Scientiæ  
categorical foundations would be an improvement, and a way of recovering set theory within a categorical approach.  ...  Abstract: Starting with a review of the kinds of questions a foundation for mathematics should address, this paper provides a critique of set theoretical foundations, a proposal that multiple interconnected  ...  For many parts of mathematics, but not all, category theoretic approaches have provided a methodological foundation and a guide to practice.  ... 
doi:10.4000/philosophiascientiae.515 fatcat:felwcldhx5dapcqvychqaauacm

Modality and Contextuality in Topos Quantum Theory

Benjamin Eva
2016 Studia Logica: An International Journal for Symbolic Logic  
Topos quantum theory (TQT) represents a whole new approach to the formalization of non-relativistic quantum theory.  ...  It is well known that TQT replaces the orthomodular quantum logic of the traditional Hilbert space formalism with a new intuitionistic logic that arises naturally from the topos theoretic structure of  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11225-016-9668-x fatcat:dquhux3hifee5fivobujyiqpwa
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