Thereforeoptimaalsete

Thereforeoptimaalsete is a theoretical construct used in discussions that blend logical deduction with optimization. It describes a class of decision problems where the quality of a decision is evaluated by the number or weight of conclusions that can be entailed from a given theory after the decision is made. The term is not widely attested in established literature and is mainly used in speculative or pedagogical contexts.

Etymology and scope. The name combines elements related to consequence and optimality, with the form echoing Estonian roots for therefore (seetõttu) and optimal (optimaalne). The concept signals a focus on derivability and logical entailment as a driver of optimality, rather than purely numerical or penalized objectives.

Formal idea. Let P be a set of premises, R a set of inference rules, and D a set of decisions. Each decision d induces a theory T(d) = closure of P under R plus d. Each outcome o in a set O has a provability weight w(o) if o is entailed by T(d). The Therefore-optimal objective is to choose a decision d that maximizes the sum of weights of entailed outcomes: maximize sum over o of w(o) for which o is entailed by T(d). Practical formulations may include constraints on resources or feasibility, as in standard optimization problems.

Example. Suppose P = {A, B}, R contains A → C and B → D, and O = {C, D, E}. If a decision d corresponds to asserting A and B, then C and D become entailed, increasing the objective score relative to decisions that do not entail these conclusions. This illustrates how entailment drives the notion of optimality in this framework.

Applications and relation. Thereforeoptimaalsete intersects with areas such as max-satisfiability, logic programming, and argumentation theory, offering a lens where verification of conclusions contributes to optimal choice. It remains primarily theoretical, with debates about definitional precision and computational tractability.

See also: entailment, logic programming, optimization, max-SAT, decision theory.