We present a framework for conceptual blending – a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process, and we show how our approach fits within a generalised conceptual blending workflow. Speci...

The Distributed Ontology, Model, and Specification Language DOL provides logic-independent structuring, linking, and modularity constructs. Its homogeneous OWL fragment, DOWL, we argue, can be seen as an ideal language for formalising ontology patterns in description logics. It naturally consumes earlier formalisms such as C-OWL or DDL, and extends these with various expressive means useful for...

In this paper we characterize those accessible V-categories that have limits of a specified class. We do by introducing the notion companion C for class weights Ψ, as collection special types colimit diagrams are compatible with Ψ. then Ψ-limits accessibly embedded and C-virtually reflective in presheaf V-category, C-models sketches. This allows us to recover standard theorems locally presentab...

The ergodic decomposition theorem is a cornerstone result of dynamical systems and theory. It states that every invariant measure on system mixture ones. Here we formulate prove the in terms string diagrams, using formalism Markov categories. We recover usual measure-theoretic statement by instantiating our category stochastic kernels. Along way give conceptual treatment several concepts theory...

The general methodology of “algebraizing” logics (cf. [2], [4]) is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved. In this paper we tran...

We propose to detect isomorphisms of algebraic modular speci cations, by representing speci cations as diagrams over a category C0 of base speci cations and speci cation morphisms. We start with a formulation of modular speci cations as terms, which are interpreted as diagrams. This representation has the advantage of being more abstract, i.e. less dependent of one speci c construction than ter...

The main source of inspiration for the present paper is the work of R. Rosebrugh and R.J. Wood on constructively completely distributive lattices where the authors elegantly employ the concepts of adjunction and module. Both notions (suitably adapted) are available in topology too, which permits us to investigate topological, metric and other kinds of spaces in a similar spirit. We introduce he...

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity...

Using the well-known categorical notion of ‘functor’ one may define the concept of datatype (algebra) without being forced to introduce a signature, that is, names and typings for the individual sorts (types) and operations involved. This has proved to be advantageous for those theory developments where one is not interested in the syntactic appearance of an algebra. The categorical notion of ‘...

Ensuring that specifications are consistent is an important part of specification development and testing. In this paper we introduce the ConsVISor tool for consistency checking of RM-ODP specifications. This tool is a category theory based consistency checker for formal specifications in a variety of languages, including both graphical and non-graphical modeling languages. Because RM-ODP suppo...