Scalable Algorithms for Abduction via Enumerative Syntax-Guided Synthesis

Automated Completion of Statements and Proofs in Synthetic Geometry: an Approach based on Constraint Solving

“…Some approaches are based on Robinson's resolution algorithm, extended such that when no more clauses can be produced, the atomic clauses are considered as a potential abduct and consistency if checked [17]. There are also approaches developed for the context of SMT solving, dealing with decidable theories like linear arithmetic [10,23] In the context of geometry, some algebraic algorithms can generate additional assumptions for the statement to be true. For example, Wu's method [28] can produce non-degeneracy conditions.…”

An Interactive SMT Tactic in Coq using Abductive Reasoning

“…We found that eliminating these operators did yield more successful abducts. Second, we tested the ability of cvc5's abduction solver to generate conjunctive solutions quickly through unsat-core learning [33]. We found that, although the solver was much faster in generating solutions with this configuration, in almost all cases, at least one of the conjuncts was too specific, rendering the entire solution useless as it was not entailed by the Coq context.…”

“…Contribution We describe a new capability of SMTCoq, encapsulated in the new tactic abduce, for those cases where the SMT solver finds the goal to be invalid under the given hypotheses H. The new tactic exploits the ability of the cvc5 [5] SMT solver to produce abducts for a goal G invalid under H, i.e., formulas that are consistent with H and entail G [33] when added to H. With this tactic, we envision a more interactive session between the Coq user and the SMT solver, where the solver might help answer the question of what information is missing, if any, to prove the goal. The tactic returns one or more abducts as suggestions for the user on how to strengthen the hypotheses for that invalid goal.…”