axiomsor

Axiomsor is a theoretical framework in mathematical logic and theoretical computer science that describes a system for selecting and revising axioms in response to goals or constraints. The term combines the notion of axioms with a revision mechanism, often interpreted as a system of revision or selection, though exact formulations vary among authors. Axiomsor is typically discussed as a way to formalize how axioms might adapt when pursuing properties such as consistency, explanatory power, or computational efficiency.

Formal structure and core ideas. In a typical axiomsor formulation, a theory T is a set of sentences in a formal language L, and A is a pool of candidate axioms available for augmentation, modification, or replacement. A revision operator S maps (T, A) to a revised theory T′ by applying a specified set of rules R. These rules encode objectives such as preserving existing consequences, minimizing changes, and achieving desired theoretical features. The process yields a family of theories generated by varying criteria, thresholds, or selection strategies, often denoted {T_i}.

Variants. Several variants of axiomsor appear in the literature. Static axiomsor fixes both T and A and performs a one-shot revision. Dynamic axiomsor allows the candidate pool to evolve, incorporating new axioms over time. Probabilistic or heuristic axiomsor uses probabilistic selection criteria or scoring functions to guide revision, producing theories that optimize expected outcomes under uncertainty.

Relation to other topics. Axiomsor relates to belief revision, nonmonotonic reasoning, and dynamic logic, offering a framework for understanding how axiom sets might adapt without sacrificing formal coherence. It is primarily a topic of theoretical exploration and has potential implications for automated theorem proving and formal verification.

See also: axiomatic system, belief revision, nonmonotonic logic, automated theorem proving, model theory.