The need to use partial functions arises frequently in formal descriptions of com puter systems However most proof assistants are based on logics of total func tions One way to address this mismatch is to invent and mechanize a new logic Another is to develop practical workarounds in existing settings In this paper we take the latter course we survey and compare methods used to support partiali...

Partial information is common in real-world databases. Yet the theoretical foundations of data models are not designed to support references to missing data (often termed nulls). Instead, we usually analyse a clean data model based on assumptions about complete information, and later retrofit support for nulls. The sketch data model is a recently developed approach to database specification bas...

We extend Bove’s technique for formalising simple general recursive algorithms in constructive type theory to nested recursive algorithms. The method consists in defining an inductive special-purpose accessibility predicate, that characterizes the inputs on which the algorithm terminates. As a result, the type-theoretic version of the algorithm can be defined by structural recursion on the proo...

Current human–computer interaction (HCI) paradigms are deeply rooted in a Western epistemology that attests its partiality and bias of its embedded assumptions, values, definitions, techniques, and derived frameworks and models. Thus tensions created between local cultures and HCI principles require researchers to pursue a more critical research agenda within an indigenous epistemology. In this...

The conceptual hierarchy represented in a concept lattice always refers to a formal context, that is, to a fixed section of data. In practice, there may be different choices for such an excerpt, for different reasons. The data may contain errors or omissions, it may differ from one observer to another. There are approaches that address such problems, building on notions like fuzziness, partiali...

Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation. A novel description of normalisation is given as a mathematically well-behaved total function. The output of this ‘hyper’ normalisation operation is a distr...

We argue that the evident utility of scenario-based modeling can be greatly enhanced when enriched with a mathematically precise notion of conditionality and partiality, such as that found in Triggered Message Sequence Charts (TMSCs). Unlike traditional Message Sequence Charts, the TMSC formalism allows scenarios to be conditional and partial, supports logical as well as behavioral operators fo...

We develop foundations for structuring behavioural specifications based on the logic tradition of hidden algebra. This includes an analysis of a number of important technical compositional properties for behavioural signatures, such as pushouts, inclusions and unions, as well as an investigation of algebraic rules for behavioural module composition. As a particularity of behavioural specificati...