Collections of Knowledge Bases in Normal Forms
Each normal form is explained briefly. For the formal definition please refer to the paper linked next to the respective normal form.
The collections over the signatures Σ={a,b} and Σ={a,b,c} can be downloaded as a whole via the respective links.
For each collection there are also a couple of examples available for online viewing via the given links.
Conditional Normal Form - CndNF
[BH 2022]A consistent knowledge base is in Conditional Normal Form (CndNF) if it:
- consists solely of normal form conditionals
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_CndNF_553651803 |
| kb_ab_CndNF_554796638 |
| kb_ab_CndNF_555135063 |
| [partial collection] |
Antecedent Normal Form - ANF
[BK 2019]A consistent knowledge base is in Antecedent Normal Form (ANF) if it:
- is in CndNF
- and every antecedent is only present once, meaning no two conditionals in the knowledge base have equivalent antecedents
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_ANF_0000001 |
| kb_ab_ANF_0694772 |
| kb_ab_ANF_1353105 |
| [complete collection] |
Reduced Antedecent Normal Form - RANF
[BH 2020]A consistent knowledge base is in Reduced Antecedent Normal Form (RANF) if it:
- is in ANF
- is in Reduced Form with respect to System P, i.e., it does not contain any conditional that can be derived from the other conditionals in the knowledge base with the rules from System P
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_RANF_0001 |
| kb_ab_RANF_1487 |
| kb_ab_RANF_4168 |
| [complete collection] |
System P Normal Form - SPNF
[BHK 2021]A consistent knowledge base is in System P Normal Form (SPNF) if it:
- is in RANF
- is smaller with respect to the linear ordering over sets of normal form conditionals than every other knowledge base in RANF that induces the same System P inference relation
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_SPNF_001 |
| kb_ab_SPNF_262 |
| kb_ab_SPNF_484 |
| [complete collection] |
Renaming Normal Form - ρNF
[BH 2020]A consistent knowledge base is in Renaming Normal Form (ρNF) if it:
- is smaller with respect to the linear ordering over sets of normal form conditionals than every other knowledge base, which is equivalent under signature renaming
Resulting combinations with ρNF:
Renaming ANF - ρANF
[BH 2022]A consistent knowledge base is in Renaming ANF (ρANF) if it:
- is in ρNF
- is in ANF
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_rhoANF_000001 |
| kb_ab_rhoANF_384902 |
| kb_ab_rhoANF_676951 |
| [complete collection] |
Renaming RANF - ρRANF
[BH 2022]A consistent knowledge base is in Renaming RANF (ρRANF) if it:
- is in ρNF
- is in RANF
Renaming SPNF - ρSPNF
[BHK 2021]A consistent knowledge base is in Renaming SPNF (ρSPNF) if it:
- is in ρNF
- is in SPNF
| For Σ={a,b}: |
|---|
| [collection README] |
| kb_ab_rhoSPNF_001 |
| kb_ab_rhoSPNF_124 |
| kb_ab_rhoSPNF_262 |
| [complete collection] |