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Geometry and Meaning

C. J. "Keith" van Rijsbergen
2006 Computational Linguistics  
One of the major goals of the book is to argue that non-classical logic, in the form of a quantum logic, is a candidate for analyzing language and its underlying logic, with a promise that such an approach  ...  -Plato Geometry and Meaning is an interesting book about a relationship between geometry and logic defined on certain types of abstract spaces and how that intimate relationship might be exploited when  ...  On the other hand, Grassmann was recognized for his foundational work on analytical geometry; for example, Hermann Weyl (1949) comments: Today probably the best approach to analytic geometry is by  ... 
doi:10.1162/coli.2006.32.1.155 fatcat:dbgxycinrrg6ndkpgcbborhhke

Symmetries and Symmetry-Breakings: The Fabric of Physical Interactions and the Flow of Time

Giuseppe Longo
2010 Foundations of Science  
Causes become interactions and these interactions themselves constitute the fabric of the universe of their manifestations, its geometry: modifying this fabric appears to cause the interactions to change  ...  For example, it is the choice of the Lorentz gauge, which enables to produce the potential for electromagnetic interactions as correlates to gauge invariance.  ...  Causes become interactions and these interactions themselves constitute the fabric of the universe of their manifestations, its geometry: modifying this fabric appears to cause the interactions to change  ... 
doi:10.1007/s10699-010-9210-y fatcat:7k5j4jotn5by3mlboybe2ww34u

Towards An Approach to Hilbert's Sixth Problem: A Brief Review

Yuri Ximenes Martins, Rodney Josué Biezuner
2020 Zenodo  
Furthermore, following the Atiyah-Witten functorial style of topological quantum field theories, it provides a nonperturbative quantization for classical field theories whose underlying cohomology satisfies  ...  In this work we will give a gentle introduction and a brief review to one of the most recent and formal approaches to this problem, based on synthetic higher categorical languages.  ...  Acknowledgements Both authors would like to thank Fernando Pereira Paulucio Reis and Maico Felipe Silva Ribeiro for reading a version of the text.  ... 
doi:10.5281/zenodo.4031161 fatcat:iw4rt5wesndelixelfmcwpwbiy

DR. GEO II: Adding Interactivity Planes in Interactive Dynamic Geometry

Hilaire Fernandes,, Stephane Ducasse, Thibault Carron
2007 Fifth International Conference on Creating, Connecting and Collaborating through Computing (C5 '07)  
This rigidity is therefore a source of internal tension for the learner and it can reduce the pedagogical added value of the interactive geometry environments.  ...  Interactive geometry environments support the creation and exploitation of interactive geometric sketches.  ...  It is the classic interactivity plane of the interactive geometry software, it enables the user to construct logically different objects: point, line, value; construction with geometric transformations  ... 
doi:10.1109/c5.2007.12 dblp:conf/c5/FernandeDC07 fatcat:6xkepuekcbfgrioty2ebvmvvnu

The Labyrinth of Quantum Logic [article]

Tim Maudlin
2018 arXiv   pre-print
But the meaning of "classical" is often not precisely specified. One might, for example, interpret it as "classical physics" or "classical logic" or "classical probability theory".  ...  Early in his career, Hilary Putnam believed that modifications of classical logic could both solve the measurement problem and account for the two-slit phenomena.  ...  for classical logic.  ... 
arXiv:1802.01834v1 fatcat:s55qmzmkzjh3fooehnimkksyei

Granular computing as a basis of human–data interaction: a cognitive cities use case

Gwendolin Wilke, Edy Portmann
2016 Granular Computing  
As a basis for automated human-oriented data processing, we use the spatial granular calculus of granular geometry.  ...  The article proposes granular computing as a theoretical, formal and methodological basis for the newly emerging research field of human-data interaction (HDI).  ...  To see that heuristic constructions usually do not comply with classical geometry, consider the following: In classical geometry, if three points lie on the same line, it is implied that all lines that  ... 
doi:10.1007/s41066-016-0015-4 fatcat:vvytxw3qz5djjateuinidbbgmi

Exotic topological order in fractal spin liquids

Beni Yoshida
2013 Physical Review B  
group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries.  ...  A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.  ...  One may see that logical operators commute with all the interaction terms by computing commutation polynomials.  ... 
doi:10.1103/physrevb.88.125122 fatcat:lso6f57cebd3xluduzm4hf6r3a

New logical perspectives on physics

Johan van Benthem, Sonja Smets
2011 Synthese  
Inspired by the grand traditions of algebraic logic and classical model theory in the study of geometry, the authors present a detailed first-order analysis of the structure of both Special and general  ...  While the preceding paper opts for the intuitionistic approach of weakening classical logic, the paper "The Dynamic Turn in Quantum Logic" by A. Baltag and S.  ... 
doi:10.1007/s11229-011-9911-y fatcat:qbekpistevbw3nafzbfdcqdme4

Preface to special issue: LINEARITY 2014

2016 Mathematical Structures in Computer Science  
The workshop was a one-day satellite event of FLoC 2014, the sixth Federated Logic Conference, which was held as part of the 2014 Vienna Summer of Logic.  ...  This special issue collects selected articles from the Third International Workshop on Linearity (LINEARITY 2014), which was held in Vienna, on July 13th, 2014.  ...  The workshop was a one-day satellite event of FLoC 2014, the sixth Federated Logic Conference, which was held as part of the 2014 Vienna Summer of Logic.  ... 
doi:10.1017/s0960129516000359 fatcat:eu3xvw5zfnbw5npacashyykvxy

G-CPT Symmetry of Quantum Emergence and Submergence—An Information Conservational Multiagent Cellular Automata Unification of CPT Symmetry and CP Violation for Equilibrium-Based Many-World Causal Analysis of Quantum Coherence and Decoherence

Wen-Ran Zhang
2016 Journal of Quantum Information Science  
In turn, BQAs can submerge from one world but emerge in another within YinYang bipolar quantum geometry. It is suggested that all logical, physical, social, biological and W.-R.  ...  It is suggested that the crux of the problem can trace its origin back to the incompleteness of CPT symmetry due to the lack of holistic representation for equilibrium-based bipolar coexistence.  ...  Acknowledgements This paper was reviewed and accepted for publication by Journal of Modern Physics (JMP). It was transferred to JQIS on the author's request.  ... 
doi:10.4236/jqis.2016.62008 fatcat:qvgsvzgzm5h5hbirov7ucjqp5m

Around logical perfection [article]

John Alexander Cruz Morales, Andrés Villaveces, Boris Zilber
2019 arXiv   pre-print
We draw on various notions of perfection from mathematics of the 19th and 20th centuries and then trace the relation to the concept of categoricity in power as a logical notion of what a "mathematically  ...  In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity.  ...  of model theory (its interactions with geometry) and its links with the analytic world.  ... 
arXiv:1803.04909v2 fatcat:gmd4giuiazhmni7jet36is3yta

Page 1991 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
for second order logic based upon dual linear decompositions of classical im- plication (211-224); Yves Lafont, From proof-nets to interaction nets (225-247); G.  ...  Purdy, A variable-free logic for anaphora (41-70); J. Moravesik, Is snow white? (71-87); Paul Weingartner, Can there be reasons for putting limitations on classical logic?  ... 

Page 2865 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
The aim of the present paper is to relate unification theory to classical work on equation solving in algebra and mathematical logic.  ...  production of traditional proofs for constructive geometry theorems.  ... 

Page 4688 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
Louis, MO, 1996 Staffordshire, 1993 Sugaku Expositions Symposium: Classical Analysis, 8th International Cocycle Conjugacy Problems for Shifts on the Hyperfinite II; Factor Logic Programming, 1996 Joint  ...  for the Interaction Fluid-structure in Biomechanics, 2nd Proof Theory of Modal Logic Random Matrices and Operator Algebra Free Representation Theory of Groups, Algebras, and * 00023 Rough Sets and Knowledge  ... 

A Brief Guide to Linear Logic [chapter]

1993 Current Trends in Theoretical Computer Science  
Informally, on the level of basic intuition, one might say that classical logic is about truth, that intuitionistic logic is about construction of proofs, and that linear logic is about process states,  ...  A convenient way to present the syntax of linear logic is by modifying the traditional Gentzen-style sequent calculus axiomatization of classical logic,  ...  Geometry of interaction is further investigated in the work of Danos Linear logic continues to be a very active eld of research.  ... 
doi:10.1142/9789812794499_0027 dblp:series/wsscs/Scedrov93 fatcat:zbt4262y5rdx3kg57bhfq7mrua
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