Information Systems Theory

Mathematical foundation based on university-level IS theory.

Core Sets

P - Set of all predicators (roles)
O - Set of all objects (entities, labels, power types)
E ⊆ O - Set of entity types
F - Set of fact types
L ⊆ O - Set of label types
G ⊆ E - Set of power types
S ⊆ E - Set of sequence types

Key Functions

Base: P → O - Maps predicators to their object types
Pop: O → 𝒫(Ω) - Population function (instances)
Fact: F → 𝒫(P) - Maps fact types to their predicators

Constraints

Uniqueness: Ensures unique combinations (PRIMARY KEY)
Mandatory: Total role participation (NOT NULL)
Frequency: Min/max occurrence limits
Subset/Equality: Role relationships
Exclusion: Mutually exclusive facts
Custom: User-defined validation logic

Common Predicates

Use these in your formulas:

participates(e, p) - Entity e plays role p
connects(p, o) - Role p connects to object o
hasRole(x) - Object x has at least one role
related(x, y) - Objects x and y are related
arity(f) - Returns the arity of fact type f
size(s) - Returns the cardinality of set s
equals(x, y) - x and y are equal
subset(x, y) - x is a subset of y

You can also define custom predicates in your formulas.

🔷 Define Custom Sets

Define new types of sets for your information system model. Each set can have a custom shape and usage rules.

Set Name

Symbol

Shape

Usage Rule

Description (optional)

⚡ Define Custom Constraints

Define logical constraints using mathematical notation. Use quantifiers, logical operators, and set theory syntax.

Syntax Guide:

∀ or FORALL - Universal quantifier

∃ or EXISTS - Existential quantifier

∧ or && or /\ - AND

∨ or || or \/ - OR

¬ or ! or NOT - Negation

→ or => - Implies

forall_{x in S}[...] - Bounded quantifier

; - Statement separator

Example: forall_{x in E}[EXISTS_{y in P}[connected(x, y)]]

Constraint Name

Mathematical Formula

Description (optional)