package impl
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Type Members
- trait BinaryInferenceRule extends InferenceRule
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class
Cls extends AnyRef
Data structure for clauses derived in Escargot.
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class
EscargotState extends AnyRef
Main class of the Escargot superposition prover.
Main class of the Escargot superposition prover.
A practical introduction to superposition provers can be found in [1], Section 3.
Essentially, we start with a set of clauses and apply inferences until we either: 1. have derived the empty clause, or 2. applied all possible inferences without producing new clauses
The clauses are stored in various sets, the main two ones are: * workedOff: all inferences between clauses in this set have already been applied * usable: these clauses have not yet been used in inferences
In every iteration of the prover (see the loop method), we 1. pick a "given" clause from usable (using the choose method) 2. perform all inferences between the given clause and all clauses in workedOff 2a. add the given clause to workedOff (unless discarded by an inference) 3. now newlyDerived contains the newly derived clauses, and we perform preprocessing on them 3a. the preprocessed clauses get moved to usable
(The names are non-standard and picked from different sources with no regard for consistency, sorry.)
Inferences: an InferenceRule is an operation that looks at the given clause, and the set of worked off clauses; it returns a set of new clauses, plus a set of clauses that should be discarded.
For example, StandardInferences.BackwardSubsumption is an inference rule: it returns no new clauses, but the subsumed clauses in usable are returned as discarded.
Avatar splitting: Escargot employs the Avatar splitting regime [2]. Clauses are annotated with propositional assertions, see at.logic.gapt.proofs.resolution.ResolutionProof for the syntax. We always have a propositional model (avatarModel), and only consider clauses whose assertions are true in this model (called "active" here). Clauses whose assertions are false in the model are stored in locked. Whenever we derive an empty clause, we call the SAT solver to obtain a model in which every empty clause has a false assertion. If there is no such model, then we have found a proof!
[1] Weidenbach, Combining Superposition, Sorts and Splitting. Handbook of Automated Reasoning II, 2001 [2] Voronkov, AVATAR: The Architecture for first-order theorem provers. CAV 2014
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trait
InferenceRule extends PreprocessingRule
An operation that looks at the given clause, and the set of worked off clauses; it returns a set of new clauses, plus a set of clauses that should be discarded.
- trait PreprocessingRule extends AnyRef
- trait RedundancyRule extends InferenceRule
- trait SimplificationRule extends InferenceRule
- class StandardInferences extends AnyRef
Value Members
- object getFOPositions
This is the API documentation for GAPT.
The main package is at.logic.gapt.