In this paper we show results on the combinatorial properties of shifted simplicial complexes. We prove two intrinsic characterization theorems for this class. The first theorem is in terms of a generalized vicinal preorder. It is shown that a complex is shifted if and only if the preorder is total. Building on this we characterize obstructions to shiftedness and prove there are finitely many i...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

The paper presents the essential connections between modal-like operators, topologies and fuzzy sets. We show, for example, that each fuzzy set determines a preorder and an Alexandrov topology, and that similar correspondences hold also for the other direction. Further, a category for preorder-based fuzzy sets is defined, and it is shown that its equivalent subcategory of representatives is iso...

The parametric lambda calculus subsumes different existing λ-calculi, in particular the classical λβ-calculus and the λβv-calculus of Plotkin. Previously established results on the parametric calculus, such as as confluence and standardization, are primarily syntactical. In this paper our attention is mainly addressed to semantics, although we start again from a syntactical point of view. We pr...

In this paper, we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the GSOS format of Bloom, Istrail and Meyer. The canonical model used for this purpose will be Abramsky’s domain of synchronization trees, and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract wi...

We define a language for Web services contracts as a parallelfree fragment of ccs and we study a natural notion of compliance between clients and services in terms of their corresponding contracts. The induced contract preorder turns out to be valuable in searching and querying registries of Web services, it shows interesting connections with the must preorder, and it exhibits good precongruenc...

We study the behavioural theory of πP, a π-calculus featuring restriction as the only binder. In contrast with calculi such as Fusions and Chi, reduction in πP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in πP: the first is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bri...

It is well known that the vertices of any graph can be put in a linear preorder so that for random walk on the graph vertices appearing earlier in the preorder are “easier to reach but more difficult to get out of”. We exhibit further such preorders corresponding to various functions related to random walk and study their relationships. These preorders coincide when the graph is a tree, but not...