Input-Output Relations as Ordered Concepts

Diagrammatic encoding of program behavior via concept lattices reveals reachability structure and non-determinism without fixed calculational rules.

Source paper

extracted_from

(2002) · Priestley, Hilary A.

community

Design principles for care-centered systems
members_of
Cross-scale frameworks linking spatial patterns, diagrams, and simplicity as expressions of care in design.
Relational semantics through spatial and narrative representation
members_of
Frameworks treating meaning-making as emergent from relational configurations—spatial diagrams, image schemas, and narrative structures—rather than essential properties, drawing on systems theory and cognitive linguistics.
Order theory in computer science
members_of
Partial orders unify size, information, and definedness across CS domains via lattice-theoretic models.

framework

Concept Lattice (Formal Concept Analysis)
supports
Theory developed by R. Wille and TH Darmstadt group; reveals hierarchical structure in binary relations through lattices of formal concepts.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Input-Output Relations Diagrammaticallymethod0.881
Input-Output Specificationconcept0.830
Specification relating a program's inputs and outputs, analogous to illocutionary correctness.
Order provides terminology, notation, and models across diverse areas of computer science including comparisons of size, information content, and definedness.claim0.785
Order (general mathematical structure of space)concept0.762
A most general system of mathematical structures arising from the nature of space, which has degrees of life.
Perhaps we will need three levels of specification, internal, input-output and accomplishment.hypothesis0.758
Speculation about specification hierarchy.
What is the relationship between order and function?question0.755
Opening question that drives the chapter's enquiry.
Rectilinear Orderconcept0.754
The straight, orthogonal geometries that arise naturally from structural and functional forces in built forms.
How can order relations in posets provide semantic models for data and computation?question0.750
Motivating question throughout: using order theory to capture information flow, approximation, and program behavior.