Knowledge base
Generator settings
Used for the “Generate” button and for random knowledge bases on the Postulates and Compare tabs.
Syntax
!a¬anegation
a && ba ∧ bconjunction
a || ba ∨ bdisjunction
a ^^ ba ⊕ bexclusive or
a => ba → bimplication
a <=> ba ↔ bequivalence
+⊤tautology
-⊥contradiction
One formula per line. Binding: ! > && > || > ^^ > => > <=>. Lines starting with % or # are comments. Identical formulas are merged.
| Measure | Value | Time | Details |
|---|
The Shapley inconsistency value of a formula distributes I(K) fairly among the formulas, by averaging its marginal contribution I(S ∪ {φ}) − I(S) over all sub-bases S. All 2n sub-bases are evaluated, so at most 14 formulas are supported. Removal impact is I(K) − I(K ∖ {φ}).
Each postulate is tested on every instance that can be derived from the knowledge base (for example, every free formula for free-formula independence) rather than on a single sampled instance as in TweetyProject's ImPostulate classes. A ✓ only means that no counterexample was found.
Measures (0) and postulates (0)
Adds the formulas one at a time in the order of the editor and plots each measure on K₁ ⊆ K₂ ⊆ … ⊆ K. Each panel has its own vertical scale; the dot marks the value for the full base.
Kendall's τb between the values two measures assign to the same random knowledge bases: +1 means both measures order the bases identically, 0 means no agreement, −1 means opposite orders. Infinite values rank highest; bases where a measure is undefined are skipped.
All interpretations over the signature (at most 12 atoms). For each world: which formulas it satisfies, and its Dalal distance to the models of each formula. Rows with the most satisfied formulas are highlighted; they correspond to maximal consistent subsets of maximal size.