Results 11 to 20 of about 419,838 (64)

Unitless Frobenius quantales [PDF]

, 2022
It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales that may not have a unit. We develop the elementary theory of these structures and show, in particular, how
Santocanale, Luigi, de Lacroix, Cédric
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Simple Involutive Quantales [PDF]

, 1997
Involutive quantales were introduced in [7] as complete lattices equipped with a multiplication and an involution. Such structures are well known from the calculus of relations: the set Rel(X) of binary relations on any setXforms an involutive quantale ...
Pelletier, J.Wick, Rosický, J.
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Quotients and colimits of κ-quantales [PDF]

, 2011
Let κQnt be the category of κ-quantales, quantales closed under κ-joins in which the monoid identity is the largest element. (κ is an infinite regular cardinal.) Although the lack of lattice completeness in this setting would seem to mitigate against the
Aleš Pultr, Richard N. Ball, Pultr, Aleš, Ball, Richard N.   +3 more
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Relational Representation of Groupoid Quantales [PDF]

, 2013
In Palmigiano and Re (J Pure Appl Algebra 215(8):1945-1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial
Re, R., Re, Riccardo, Palmigiano, A., Palmigiano, Alessandra   +3 more
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Quantales and temporal logics [PDF]

, 2006
We propose an algebraic semantics for the temporal logic CTL∗ and simplify it for its sublogics CTL and LTL. We abstractly represent state and path formulas over transition systems in Boolean left quantales.
Höfner, Peter, Möller, Bernhard (Prof.), Bernhard Möller, Georg Struth, Peter Höfner, Möller, Bernhard (Prof. Dr.), Struth, Georg   +6 more
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A representation theorem for quantales [PDF]

, 1993
We define a relational quantale to be a quantale whose elements are relations on a set A, ordered by inclusion and forming a monoid under relational composition.
Gurr, Doug, Brown, Carolyn
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Semigroups in complete lattices: quantales, modules and related topics

, 2018
This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer ...
Gutiérrez García, Javier,, Eklund, Patrik, Höhle, Ulrich,, Gutiérrez García, Javier, Patrik Eklund, Jari Kortelainen, Ulrich Höhle, Höhle, Ulrich, Kortelainen, Jari, Javier Gutiérrez García, Eklund, Patrik,, Kortelainen, Jari,   +11 more
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Reflectors to quantales

, 2022
In this paper, we show that marked quantales have a reflection into quantales. To obtain the reflection we construct free quantales over marked quantales using appropriate lower sets.
Chen, Yudong, Feng, Jianjun, Paseka, Jan, Zhang, Xia   +3 more
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$$\ell r$$-Multisemigroups, Modal Quantales and the Origin of Locality

, 2021
International audienceWe introduce lr-multisemigroups as duals of modal quantales and study modal correspondences between equations in these multisemigroups and the domain and codomain axioms of modal quantales.
Christian Johansen, Uli Fahrenberg, Georg Struth, Krzysztof Ziemiański, Ziemiański, Krzysztof, Calk, Cameron, Cameron Calk, Fahrenberg, Uli, Struth, Georg, Johansen, Christian   +9 more
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Groupoid quantales: A non-étale setting [PDF]

, 2011
We establish a bijective correspondence involving a class of unital involutive quantales and a class of groupoids whose space of units is a sober space. This class includes equivalence relations that arise from group actions. The resulting axiomatization
Alessandra Palmigiano, Re, R., Re, Riccardo, Riccardo Re, Palmigiano, A., Palmigiano, Alessandra   +5 more
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