Heterogeneous algebras

Lattice Logic Properly Displayed

“…In the present section, we introduce a class of heterogeneous algebras [7] which equivalently encodes complete lattices, and which will be useful to motivate the design of the calculus for lattice logic from a semantic viewpoint, as well as to establish its properties. This presentation takes its move from very well known facts in the representation theory of complete lattices, which can be found e.g.…”

Towards Pervasive Intelligence: Reflections on the Evolution of the Agent Factory Framework

“…It differed from other similar frameworks available at the time in its use of an algebraic specification technique (the UMIST Paradox System) that could be directly executed. The system was underpinned by the theory associated with heterogeneous algebras that was developed by Birkhoff and Lispson [5]. The environment drew heavily from Communicating Sequential Processes [23] (CSP) and viewed multi-agent systems as a specific class of complex distributed systems, namely Communicating Intentional Processes (CIP).…”

Semirigid spaces

“…This is one way how to describe it. Another (equivalent) approach is to view it as an (y-sorted algebra (many sorted algebras = heterogeneous algebras, see [2]) Clo(X) = ({C"}"6û), {S?\n ,m£co}U {n\j)\j £co,l<i<j}) where the underlying set of its nth sort C" is the set of all continuous maps X" -» X, each S"" is the operation sending the set Cm x C" x ■ ■ • x C" (Cn appears here m times) into C" by the rule This description allows the use of all common notions introduced for manysorted algebras, such as isomorphisms, homomorphisms, etc. In particular, it allows the introduction of first-order language of the many-sorted algebras and investigations of the first-order sentences about the clone.…”