Diagrammatic logics were introduced in 2002, with emphasis on the notions of specifications and models. In this paper we improve the description of the inference process, which is seen as a Yoneda functor on a bicategory of fractions. A diagrammatic logic is defined from a morphism of limit sketches (called a propagator) which gives rise to an adjunction, which in turn determines a bicategory o...

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced ‘stateand-effect’ triangles which capture this situation categorically, involving an adjunction between stateand predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck’s monadicity theorem, to ...

Given a coalgebra p for HG, an algebra s for GH and the obvious notion of morphism from coalgebra to algebra, we observe that morphisms from Gp to s correspond to morphisms from p to Hs in the manner of an adjunction even when there is no adjunction between G and H. This appears to be one of the basic phenomena underlying the transport of special algebras. A proof of Freyd’s Iterated Square The...

In this paper, we present a knowledge representation which is focused on the correspondence of adjunction strl!cture between English and Korean. We acquire the knowledge available in machine translation, from the linguistic structures and data in the two languages. The adjunction stucture is the constituent representing the relation between the modifier and the modifiee. Our approach is based o...

We give a general theorem that provides examples of n-random reals à la Chaitin, for every n ≥ 1; these are halting probabilities of partial computable functions that are universal by adjunction for the class of all partial computable functions, The same result holds for the class functions of partial computable functions with prefix-free domain. Thus, the usual technical requirement of prefix-...

The category of effect algebras is the Eilenberg-Moore category for the monad arising from the free-forgetful adjunction between categories of bounded posets and orthomodular posets. In the category of effect algebras, an observable is a morphism whose domain is a Boolean algebra. The characterization of subsets of ranges of observables is an open problem. For an interval effect algebra E, a wi...