A Set-Theoretic and Transition-System Model of Computation for Semantic Interoperability Across Heterogeneous Laboratory Interfaces

Abstract

Laboratory computing environments increasingly combine scientific programming languages, symbolic computation systems, instrument-control protocols, graphical automation environments, distributed control middleware, and structured scientific data formats. Python, MATLAB, IDL, Julia, Maple, Mathematica, LabVIEW, SCPI/VISA, EPICS, Tango, SPEC, PLC languages, HDF5, NetCDF, FITS, XML, JSON, and related interfaces are often used within the same laboratory ecosystem, yet they are based on different computational models and different representations of data, state, units, metadata, control flow, and physical-device behaviour. This paper proposes a theory-based semantic interoperability framework for heterogeneous laboratory workflows and instrument-control interfaces. The framework models each laboratory interface as a structured computational system and interprets its constructs into a shared laboratory semantic domain. Laboratory commands are represented as state transforming semantic objects carrying operation, artefact, data, unit, metadata, event, and constraint information. Workflows are modelled as typed, partially ordered semantic graphs. Translation is defined not as a total syntactic function, but as a partial semantic relation between source and target construct sequences mediated by abstraction maps, concretisation maps, semantic equivalence, observational refinement, and preservation conditions. The
paper develops a mathematical model of computation based on set theory, labelled transition systems, trace semantics, partial orders, quotient structures, semantic algebras, Galois-style abstraction, typed operation signatures, unit algebra, workflow homomorphisms, bisimulation, simulation, and safety invariants. The framework provides formal conditions for classifying exact, equivalent, approximate, composite, wrapper-dependent, unsafe, and unsupported translations across heterogeneous laboratory systems