The process of computing models of a theory or specification that are minimal with respect to set inclusion or a given ordering, often intended to capture canonical, parsimonious, or intended solutions among many models.

Principle

Select models that do not properly contain any other model (or that are minimal under a chosen ordering), on the heuristic that minimality corresponds to parsimony or intended interpretation in the target domain.

Demonstration

Compute minimal Herbrand models of a definite logic program to obtain the least set of ground atoms entailed by the program, or compute minimal repairs of an inconsistent database by selecting tuples whose removal yields consistency with minimal change.

Misapplication

Assuming minimal models always represent the intended semantics when the domain requires maximality, default preferences, or probabilistic weighting; relying on minimality can exclude legitimate behaviours or overconstrain solutions.

Consequence

Gives canonical, often unique solutions in monotone settings (e.g., least Herbrand model) and supports nonmonotonic semantics where minimality encodes default assumptions, but may produce multiple incomparable minimal models requiring further selection criteria.

Reversal

Maximal model selection or arbitrary model acceptance: choosing largest models or any model without preference eliminates the parsimony bias and can capture alternatives the minimal approach excludes.

Boundary

Depends on the ordering chosen (set inclusion, cardinality, weighted cost); multiple minimal models can exist; computational complexity can be high (e.g., co‑NP/NP‑hard problems), and minimality may be meaningless if no natural ordering is available.

Semantic Tension

Between parsimony (minimality) and explanatory richness: minimal models favor brevity and avoidance of assumptions, while richer models may better explain observed data or support robustness to noise.

Synthesis

Minimal model computation isolates the smallest models under a specified ordering to provide compact, canonical solutions for reasoning and repair tasks; its utility depends on the match between minimality and the domain's notion of intendedness and on handling multiplicity and complexity in practice.