We introduce a general theory of quantitative and metric rewriting systems, namely systems with relation enriched over quantales modelling abstract quantities. develop theories term-based refining cornerstone results (such as Newman’s Lemma, Church-Rosser Theorem, critical pair-like lemmas) to setting. To avoid distance trivialisation lack confluence issues, we non-expansive, linear term then g...

complete pseudogroups L∨ bb

The articles [12], [8], [13], [11], [14], [5], [4], [9], [16], [1], [2], [7], and [6] provide the notation and terminology for this paper. Let X be a set and let Y be a subset of 2X . Then ⋃ Y is a subset of X . In this article we present several logical schemes. The scheme DenestFraenkel deals with a non empty set A , a non empty set B, a unary functor F yielding a set, a unary functor G yield...

We present a dynamic form of observational logic for specifying concurrent systems on the basis of their observable behaviour, in particular without needing a language for describing states, which are regarded as non-observable. The logic is based on quantales. The models are labelled transition systems, and a weakly complete proof system is presented. We study the logic from the point of view ...

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued fram...

The ‘the’ in the title hides a subtlety. A metric space induces not one but four topologies - by means of open sets, closed closure, and interior they just so happen to coincide. agreement between these structures arising from function d:X×X→[0,∞] is due combination axioms lattice structure [0,∞]. Further motivation materializes Lawvere's observation 1973 effect that (slightly generalized) cate...

09h00 09h45 Zurab Janelidze Algebraic importance of “modus ponens” 09h50 10h20 Gareth Boxall NIP (Not the Independence Property) 10h25 10h55 James Gray Algebraic exponentiation 11h00 11h15 Tea/coffee Mathematics Tea Room 11h15 12h15 Alessandra Palmigiano Groupoid quantales beyond the étale setting 12h20 12h50 Willem Conradie Algorithmic canonicity and correspondence for (non-distributive) latti...

By introducing lattice-valued covers of a set, we present a general framework for uniform structures on very general L-valued spaces (for L an integral commutative quantale). By showing, via an intermediate L-valued structure of uniformity, how filters of covers may describe the uniform operators of Hutton, we prove that, when restricted to Girard quantales, this general framework captures Hutt...