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A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract)

Ingo Battenfeld
2010 Electronic Proceedings in Theoretical Computer Science  
Here we show that the posets of sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic properties and that our counterexamples can be applied to the set of smooth equivalence relations  ...  In recent work, Doberkat has examined lattice properties of posets of congruences on a stochastic relation and motivated a domain-theoretic investigation of these ordered sets.  ...  In this paper we attempt a domain-theoretic investigation of posets of sub-σ -algebras.  ... 
doi:10.4204/eptcs.24.7 fatcat:4dadtw2ev5b4bczicap2qj73km

Topos-Theoretic Approaches to Quantum Theory [article]

Matthijs Vákár
2021 arXiv   pre-print
It aims to provide a synthesized account of their various approaches.  ...  This review paper surveys work by Isham, Butterfield, Doering, Landsman, Spitters, Heunen et al. about topos-theoretic analyses of quantum theory.  ...  This interval domain IR (in Set) as a poset is defined as the set of all non-empty compact intervals of real numbers ordered by inclusion.  ... 
arXiv:2110.06793v1 fatcat:skv7oblsofhbfcqwr4zaws2ugy

Comparing Dependencies in Probability Theory and General Rough Sets: Part-A [article]

A Mani
2018 arXiv   pre-print
Comparison of ideas of dependence in the approaches had been attempted from a set-valuation based minimalist perspective by the present author.  ...  In this research, duality results are adapted to demonstrate the possibility of improved comparisons across implications between ontologically distinct concepts in a common logic-based framework by the  ...  in a suitable semantic domain, • object level properties of indiscernibility in a suitable semantic domain, • properties of abstractions from approximations, • properties of abstractions of indiscernibility  ... 
arXiv:1804.02322v1 fatcat:qje2sgjzczgfdpajbeiz7pfrfy

The causal set approach to quantum gravity

Sumati Surya
2019 Living Reviews in Relativity  
CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset.  ...  a finite number of causal set elements.  ...  A Notation and terminology We list some of the more widely used definitions as well as the abbreviations used in the paper.  ... 
doi:10.1007/s41114-019-0023-1 fatcat:2zjxw2hmang27dlhga2mcapvqm

Representation and duality of the untyped lambda-calculus in nominal lattice and topological semantics, with a proof of topological completeness [article]

Murdoch J. Gabbay, Michael J. Gabbay
2016 arXiv   pre-print
A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is necessary).  ...  We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets.  ...  Also, Figure 1 does not mention ∀ and Figure A.6 (the algebraic presentation of ∀; the body of the paper uses nominal lattices instead, but this is equivalent) does not mention σ.  ... 
arXiv:1305.5968v3 fatcat:6qgfin25sfcixhat5y2o4nkcze

Representation and duality of the untyped λ-calculus in nominal lattice and topological semantics, with a proof of topological completeness

Murdoch J. Gabbay, Michael Gabbay
2017 Annals of Pure and Applied Logic  
A novel interpretation of λ is given in terms of adjoints, and λ-terms are interpreted absolutely as sets (no valuation is necessary).  ...  We give a semantics for the λ-calculus based on a topological duality theorem in nominal sets.  ...  NOMINAL DISTRIBUTIVE LATTICES WITH QUANTIFICATION NOMINAL ALGEBRAS OVER NOMINAL SETS Definition of a sigma-algebra (σ-algebra) 3.1.1. A termlike σ-algebra.  ... 
doi:10.1016/j.apal.2016.10.001 fatcat:mippteqe7benxkey2kqo4mka24

The causal set approach to quantum gravity [article]

Sumati Surya
2019 arXiv   pre-print
CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset.  ...  In the continuum approximation the former corresponds to the spacetime causality relation and the latter ensures that finite volume regions in a spacetime contain only a finite number of "fundamental"  ...  Again, in order to obtain covariant observables one has to pass to the full sigma algebra S associated with A. However, unlike a classical measureD need not extend to a full sigma algebra.  ... 
arXiv:1903.11544v1 fatcat:mfsx425lczfnjkvbdnfhsi42pm

Fibrations, Logical Predicates and Indeterminates

Claudio Alberto Hermida
1993 DAIMI Report Series  
<p>Within the framework of categorical logic/type theory, we provide a category-theoretic account of some logical concepts, i.e. first-order logical predicates for simply typed lambda-calculus, structural  ...  of a fibration with that of the fibres.  ...  The abovementioned fact about Aw-fibrations therefore allow us to extend Pitts' result to topos-theoretic models of )tW.  ... 
doi:10.7146/dpb.v22i462.6935 fatcat:ntn5t54vfzh6dp4da47e5fjucy

Theorem Proving and Algebra [article]

Joseph A. Goguen
2021 arXiv   pre-print
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem  ...  ; deduction for conditional equations; the theorem of constants; interpretation and equivalence of theories; term rewriting, termination, confluence and normal form; abstract rewrite systems; standard  ...  (Σ, B) be a terminat- ing sub-CTRS of (Σ, A), let P be a poset, and let N = A−B.  ... 
arXiv:2101.02690v2 fatcat:2unv7ebr7zdprpjrcme5pmgkvi

On path-based coalgebras and weak notions of bisimulation [article]

Harsh Beohar, Sebastian Küpper
2017 arXiv   pre-print
It is well known that the theory of coalgebras provides an abstract definition of behavioural equivalence that coincides with strong bisimulation across a wide variety of state-based systems.  ...  It is shown that recording executions (up to a notion of stuttering), rather than the set of successor states, from a state is sufficient to characterise branching bisimulation in both cases.  ...  Acknowledgements The authors thank the anonymous reviewers of the conference CALCO'17 for their feedbacks on an earlier draft of this paper.  ... 
arXiv:1705.08715v2 fatcat:fppxof3gtvhdrcrkebtdwjkk4e

Pathlike Co/bialgebras and their antipodes with applications to bi- and Hopf algebras appearing in topology, number theory and physics [article]

Ralph M. Kaufmann, Yang Mo
2021 arXiv   pre-print
We develop an algebraic theory of flavored and pathlike co-, bi- and Hopf algebras.  ...  In particular, we can precisely give conditions the invertibility of characters needed for renormalization in the formulation of Connes and Kreimer and in the canonical examples these conditions are met  ...  A full treatment is in §6.2. Example 2.20 (Non-Sigma operads and Posets).  ... 
arXiv:2104.08895v1 fatcat:nt6hkqvscfcbzcri46fdyliiy4

Non-Parametric Methods Applied to the N-Sample Series Comparison [article]

Paolo D'Alberto and Chris Drome and Ali Dasdan
2012 arXiv   pre-print
In summary, we have two contributions: First, we present a self-contained survey of the most promising methods being used in the fields of machine learning, statistics, and bio-informatics today.  ...  Through a combination of data organization and statistical tests, we describe extensions that scale well with increased dimensionality.  ...  The final result of this work is a stochastic library that the authors will provide to interested affiliations.  ... 
arXiv:1205.1880v1 fatcat:oe4cxyrma5hodetwxamagcgdsu

The trascendence of Kac-Moody algebras

Desamparados Fernández-Ternero, Juan Núñez-Valdés
2021 Filomat  
Indeed, lot of references in the literature on these algebras are analyzed and a study of the most relevant topics regarding them is shown.  ...  present state-of-the-art developments and results on these algebras at various levels of analysis and fields of application in different disciplines.  ...  Acknowledgement In the beginnings of the present century the authors began to research in Kac-Moody algebras under the guidance of Prof. Louis Santharoubane.  ... 
doi:10.2298/fil2110445f fatcat:z7qcuelomrd6fg3s5pt3oxzhpu

Collaborating institutions [chapter]

2016 The Financial System We Need  
An abstract of this talk will be handed at the congress.  ...  General Topology and its Applications Exponentiable monomorphism in the category of DCPO CAGLIARI, FRANCESCA BOLOGNA UNIVERSITY (ITALY) A poset D is said to be a directed complete poset, or dcpo, if every  ...  a new special family for associating suitable primitives for any function of L 2 .  ... 
doi:10.18356/b4968a28-en fatcat:v75hvlhqebfglfsx7q4qwwlc34

Categorical Quantum Dynamics [article]

Stefano Gogioso
2017 arXiv   pre-print
which open the way to a wealth of new applications.  ...  We use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinite-dimensional separable Hilbert spaces: these were long-missing features,  ...  Let G := ( , ) be a coherent group on an object G of a †-SMC. Then the category-theoretic way of talking about abstract operations in algebra 13 .  ... 
arXiv:1709.09772v1 fatcat:idax6g6zkfdwdksdh3zwea3mpa
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