Let X be a dcpo and let L be a complete lattice. The family σL(X) of all Scott continuous mappings from X to L is a complete lattice under pointwise order, we call it the L-fuzzy Scott structure on X. Let E be a dcpo. A mapping g : σL(E) −> M is called an LM-fuzzy possibility valuation of E if it preserves arbitrary unions. Denote by πLM(E) the set of all LM-fuzzy possibility valuations of E. T...

This paper can be seen as a continuation of the works contained in the recent preprints [Za], of the second author, and [Mi], of Juan Migliore. Our results are: 1). There exist codimension three artinian level algebras of type two which do not enjoy the Weak Lefschetz Property (WLP). In fact, for e ≫ 0, we will construct a codimension three, type two h-vector of socle degree e such that all the...

The algebraic relationship between predicates and predicate transformers is considered. A canonical decomposition property of transformers is used to develop a typing mechanism for predicate transformer process models based on the input and output interfaces of the processes. Predicate transformers are typed according to the variables read from or written to by the process described by the pred...

0 Introduction In modern treatments of predicate calculus [2], no mention is made of states or variables up until the point where substitution is introduced. There, suddenly, the abstraction that reigned before is cast to the winds, and a substitution is defined as the result of a textual replacement of variable names by expressions. It is the purpose of this note to remedy this breach of style...

This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These def...

Abstract Construction and analysis of distributed systems is difficult; choreographic programming a deadlock-freedom-by-construction approach to simplify it. In this paper, we present new theory programming. It supports for the first time: construction that require decentralised decision making (i.e., if/while-statements with multiparty conditions); provide not only deadlock freedom but also fu...

A state transformation semantics and a predicate transformer semantics for programs built from atomic actions, sequential composition, nondeterministic choice, parallel composition, atomisation, and recursion are presented. Both semantic models are derived from some SOS-style labelled transition system. The state transformation semantics and the predicate transformer semantics are shown to be i...

Moreover the term predicate fuzzy logic L∀ will denote the predicate calculus obtained from the propositional core fuzzy logic L by adding the “classical” quantifiers (∀ and ∃) together with the same axioms and rule of generalization used by Hàjek in his book [7] when defining BL∀. On the other hand, given a left-continuous t-norm ∗, if L∗ denotes the (propositional) fuzzy logic which is standa...

For a completely distributive quantale L, L-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous L-idempotent semimodules of L-fuzzy monotonic predicates. © 2012 Elsevier B.V. All rights reserved.