Working definition
A constraint-satisfaction problem defines variables, domains, and constraints, then seeks assignments satisfying all hard constraints. Soft constraints and weighted preferences require a separate optimization or ranking layer so that exceptions and disagreements remain visible.
Notation
find x such that Cᵢ(x)=true for all hard constraintsxᵢ ∈ DᵢAssumptions
- Variables and domains are finite or searchable.
- Hard and soft rules are distinguished.
- Conflicts have a declared resolution policy.
Invariants
- Every returned assignment satisfies all active hard constraints.
- An unsatisfiable core identifies jointly conflicting constraints.
- Removing constraints cannot reduce the feasible set.
Reproducible procedure
- Compile rules into typed predicates.
- Check consistency and extract conflicts.
- Enumerate or optimize feasible assignments with a complete audit trail.
Error and boundary controls
- Natural-language rules may be mistranscribed.
- Incomplete constraints create false feasibility.
- Search cutoffs can hide valid assignments.
What this does not establish
Faithfully satisfying traditional rules establishes internal consistency, not that those rules predict or cause the desired outcome.
Explicit applications
2 cross-domain bridges
Rule conflict and satisfiability audit
Expose incompatible conditions, exceptions, and precedence policies across named traditions.
Inputs
- typed rules
- active chart facts
- conflict policy
Outputs
- applicable set
- conflict set
- resolution trace
Transformation: Evaluate hard predicates and extract unsatisfied or conflicting cores.
Limit: Logical consistency is not empirical confirmation.
Open connected system →Muhūrta eligibility compiler
Find candidate windows satisfying a named tradition’s hard conditions while exposing withheld and conflicting rules.
Inputs
- candidate intervals
- tradition rule pack
- activity type
Outputs
- eligible windows
- failed conditions
- conflicts
Transformation: Evaluate typed predicates and compute feasible interval intersections.
Limit: Eligibility means conformity to encoded tradition, not demonstrated outcome improvement.
Open connected system →Authoritative references
- [1]Dictionary of Algorithms and Data Structures · National Institute of Standards and Technology
Establishes: Reference vocabulary for graphs, optimization, search, data structures, complexity, and computational methods used to make algorithms explicit.
Boundary: A formal data structure can represent domain relationships without establishing that the represented causal or interpretive relationships are true.
Direct answer
- A constraint-satisfaction problem defines variables, domains, and constraints, then seeks assignments satisfying all hard constraints. Soft constraints and weighted preferences require a separate optimization or ranking layer so that exceptions and disagreements remain visible.
Mechanism and method
- Compile rules into typed predicates.
- Check consistency and extract conflicts.
- Enumerate or optimize feasible assignments with a complete audit trail.
What is measured
- Every returned assignment satisfies all active hard constraints.
- An unsatisfiable core identifies jointly conflicting constraints.
- Removing constraints cannot reduce the feasible set.
Limitations
- Natural-language rules may be mistranscribed.
- Incomplete constraints create false feasibility.
- Search cutoffs can hide valid assignments.
- Variables and domains are finite or searchable.
- Hard and soft rules are distinguished.
- Conflicts have a declared resolution policy.
What this does not establish
- Faithfully satisfying traditional rules establishes internal consistency, not that those rules predict or cause the desired outcome.
Bridge: Rule conflict and satisfiability audit
- Expose incompatible conditions, exceptions, and precedence policies across named traditions.
- Input: typed rules
- Input: active chart facts
- Input: conflict policy
- Output: applicable set
- Output: conflict set
- Output: resolution trace
- Limit: Logical consistency is not empirical confirmation.
Bridge: Muhūrta eligibility compiler
- Find candidate windows satisfying a named tradition’s hard conditions while exposing withheld and conflicting rules.
- Input: candidate intervals
- Input: tradition rule pack
- Input: activity type
- Output: eligible windows
- Output: failed conditions
- Output: conflicts
- Limit: Eligibility means conformity to encoded tradition, not demonstrated outcome improvement.