sealed abstract class Polarity extends AnyRef
Polarity of a formula.
There are two polarities, positive/in-succedent and negative/in-antecedent. Polarities serve multiple purposes:
- They distinguish strong and weak quantifiers. A universal (∀) quantifier in positive/in-succedent polarity is strong (requires an eigenvariable/Skolem inference), and is weak in negative/in-antecedent polarity (can be instantiated with any term).
- They guide the construction of expansion trees and their deep formulas. A merge in positive polarity has a disjunction as deep formula, in negative polarity it has a conjunction.
- They specify the side/cedent of a sequent.
Our convention is based on proofs in LK:
- formulas in the succedent are positive
- formulas in the antecedent are negative
This is used consistently, except for a major exception: in resolution proofs, the polarity is reversed. A formula in the antecedent of a clause in a resolution proof has the negative/in-antecedent polarity (as it is in the antecedent of a sequent). However upon conversion to LK/ET, the polarity switches to positive/in-succedent polarity.
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- Polarity.scala
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This is the API documentation for GAPT.
The main package is at.logic.gapt.