SemantEq
A bidirectional equivalence relation for judging the equivalence of formal mathematical statements, based on Lean proof terms rather than tactic scripts. It requires statements to be mutually transformable through permitted steps such as logical rearrangement and in-library equality rewriting, thereby more strictly verifying whether a formalized statement faithfully corresponds to its natural language original.
Timeline (last 90 days)
SemantEq is a bidirectional equivalence relation for judging the equivalence of formal mathematical statements, aimed at solving the problem that existing logical equivalence tests are too permissive.
SemantEq judges equivalence by checking proof terms rather than tactic scripts, to avoid bias introduced by differences in tactic style.
SemantEq requires each statement to be transformed into the other only through a series of allowed steps (such as logical rearrangement and rewriting using the library's own equalities), and these steps form a transformation chain verifiable by the Lean kernel.
SemantEq's design separates the generation of equivalence proofs from their acceptance, so that a stronger prover can raise recall without changing what acceptance means.
The research team has open-sourced the code and data of SemantEq at https://github.com/hlxr89/SemantEq.
All Facts (5)
SemantEq is a bidirectional equivalence relation for judging the equivalence of formal mathematical statements, aimed at solving the problem that existing logical equivalence tests are too permissive.
50%UnverifiedSemantEq judges equivalence by checking proof terms rather than tactic scripts, to avoid bias introduced by differences in tactic style.
50%UnverifiedSemantEq requires each statement to be transformed into the other only through a series of allowed steps (such as logical rearrangement and rewriting using the library's own equalities), and these steps form a transformation chain verifiable by the Lean kernel.
50%UnverifiedSemantEq's design separates the generation of equivalence proofs from their acceptance, so that a stronger prover can raise recall without changing what acceptance means.
50%UnverifiedThe research team has open-sourced the code and data of SemantEq at https://github.com/hlxr89/SemantEq.
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