## Appendix B: Quantified Hypotheticals

### B.1 Quantified Conditional Propositions with Quantified Parts

#### B.1.1 Universal affirmative conditional

 1 (a-$$\mathbb{C}$$)aa Always, if every A is B, then every C is D (kullamā kāna kull A B fa-kull C D) 2 (a-$$\mathbb{C}$$)ai Always, if every A is B, then some C is D (kullamā kāna kull A B fa-baʿḍ C D) 3 (a-$$\mathbb{C}$$)ia Always, if some A is B, then every C is D (kullamā kāna baʿḍ A B fa-kull C D) 4 (a-$$\mathbb{C}$$)ii Always, if some A is B, then some C is D (kullamā kāna baʿḍ A B fa-baʿḍ C D) 5 (a-$$\mathbb{C}$$)ee Always, if no A is B, then no C is D (kullamā kāna lā šayʾ min A B fa-lā šayʾ min C D) 6 (a-$$\mathbb{C}$$)eo Always, if no A is B, then not every C is D (kullamā kāna lā šayʾ min A B fa-lā kull CD) 7 (a-$$\mathbb{C}$$)oe Always, if not every A is B, then no C is D 8 (a-$$\mathbb{C}$$)oo Always, if not every A is B, then not every C is D 9 (a-$$\mathbb{C}$$)ae Always, if every A is B, then no C is D 10 (a-$$\mathbb{C}$$)ao Always, if every A is B, then not every C is D 11 (a-$$\mathbb{C}$$)ie Always, if some A is B, then no C is D 12 (a-$$\mathbb{C}$$)io Always, if some A is B, then not every C is D 13 (a-$$\mathbb{C}$$)ea Always, if no A is B, then every C is D 14 (a-$$\mathbb{C}$$)ei Always, if no A is B, then some C is D 15 (a-$$\mathbb{C}$$)oi Always, if not every A is B, then some C is D 16 (a-$$\mathbb{C}$$)oa Always, if not every A is B, then every C is D

Note that the luzūmī-ittifāqī distinction is often expressed by syntactic variations on the above forms, which typically involves prefixing the verb yalzamu (or its negation) to a declarative clause (e.g., for (1) “Always, when every A is B, it necessarily follows that every C is D”).

Laysa is often used for negation instead of .

#### B.1.2 Universal negative conditional

 1 (e-$$\mathbb{C}$$)aa Never, if every A is B, then every C is D (laysa albattata in/iḏā … fa-…) 2 (e-$$\mathbb{C}$$)ai Never, if every A is B, then some C is D 3 (e-$$\mathbb{C}$$)ia Never, if some A is B, then every C is D 4 (e-$$\mathbb{C}$$)ii Never, if some A is B, then some C is D 5 (e-$$\mathbb{C}$$)ee Never, if no A is B, then no C is D 6 (e-$$\mathbb{C}$$)eo Never, if no A is B, then not every C is D 7 (e-$$\mathbb{C}$$)oe Never, if not every A is B, then no C is D 8 (e-$$\mathbb{C}$$)oo Never, if not every A is B, then not every C is D 9 (e-$$\mathbb{C}$$)ae Never, if every A is B, then no C is D 10 (e-$$\mathbb{C}$$)ao Never, if every A is B, then not every C is D 11 (e-$$\mathbb{C}$$)ie Never, if some A is B, then no C is D 12 (e-$$\mathbb{C}$$)io Never, if some A is B, then not every C is D 13 (e-$$\mathbb{C}$$)ea Never, if no A is B, then every C is D 14 (e-$$\mathbb{C}$$)ei Never, if no A is B, then some C is D 15 (e-$$\mathbb{C}$$)oi Never, if not every A is B, then some C is D 16 (e-$$\mathbb{C}$$)oa Never, if not every A is B, then every C is D

#### B.1.3 Particular affirmative conditional

 1 (i-$$\mathbb{C}$$)aa Sometimes, if every A is B, then every C is D (qad yakūnu iḏā … fa-…) 2 (i-$$\mathbb{C}$$)ai Sometimes, if every A is B, then some C is D 3 (i-$$\mathbb{C}$$)ia Sometimes, if some A is B, then every C is D 4 (i-$$\mathbb{C}$$)ii Sometimes, if some A is B, then some C is D 5 (i-$$\mathbb{C}$$)ee Sometimes, if no A is B, then no C is D 6 (i-$$\mathbb{C}$$)eo Sometimes, if no A is B, then not every C is D 7 (i-$$\mathbb{C}$$)oe Sometimes, if not every A is B, then no C is D 8 (i-$$\mathbb{C}$$)oo Sometimes, if not every A is B, then not every C is D 9 (i-$$\mathbb{C}$$)ae Sometimes, if every A is B, then no C is D 10 (i-$$\mathbb{C}$$)ie Sometimes, if some A is B, then no C is D 11 (i-$$\mathbb{C}$$)ao Sometimes, if every A is B, then not every C is D 12 (i-$$\mathbb{C}$$)io Sometimes, if some A is B, then not every C is D 13 (i-$$\mathbb{C}$$)ea Sometimes, if no A is B, then every C is D 14 (i-$$\mathbb{C}$$)oa Sometimes, if not every A is B, then every C is D 15 (i-$$\mathbb{C}$$)ei Sometimes, if no A is B, then some C is D 16 (i-$$\mathbb{C}$$)oi Sometimes, if not every A is B, then some C is D

#### B.1.4 Particular negative conditional

 1 (o-$$\mathbb{C}$$)aa Not always, if every A is B, then every C is D (laysa kullamā … fa-…) 2 (o-$$\mathbb{C}$$)ia Not always, if some A is B, then every C is D 3 (o-$$\mathbb{C}$$)ai Not always, if every A is B, then some C is D 4 (o-$$\mathbb{C}$$)ii Not always, if some A is B, then some C is D 5 (o-$$\mathbb{C}$$)ee Not always, if no A is B, then no C is D 6 (o-$$\mathbb{C}$$)oe Not always, if not every A is B, then no C is D 7 (o-$$\mathbb{C}$$)eo Not always, if no A is B, then not every C is D 8 (o-$$\mathbb{C}$$)oo Not always, if not every A is B, then not every C is D 9 (o-$$\mathbb{C}$$)ae Not always, if every A is B, then no C is D 10 (o-$$\mathbb{C}$$)ao Not always, if every A is B, then not every C is D 11 (o-$$\mathbb{C}$$)ie Not always, if some A is B, then no C is D 12 (o-$$\mathbb{C}$$)io Not always, if some A is B, then not every C is D 13 (o-$$\mathbb{C}$$)ea Not always, if no A is B, then every C is D 14 (o-$$\mathbb{C}$$)ei Not always, if no A is B, then some C is D 15 (o-$$\mathbb{C}$$)oa Not always, if not every A is B, then every C is D 16 (o-$$\mathbb{C}$$)oi Not always, if not every A is B, then some C is D

### B.2 Quantified Disjunctive Propositions with Quantified Parts

#### B.2.1 Universal affirmative disjunction

 1 (a-$$\mathbb{D}$$)aa Always, either every A is B or every C is D (dāʾiman immā an yakūna … aw …) 2 (a-$$\mathbb{D}$$)ai Always, either every A is B or some C is D 3 (a-$$\mathbb{D}$$)ia Always, either some A is B or every C is D 4 (a-$$\mathbb{D}$$)ii Always, either some A is B or some C is D 5 (a-$$\mathbb{D}$$)ee Always, either no A is B or no C is D 6 (a-$$\mathbb{D}$$)eo Always, either no A is B or not every C is D 7 (a-$$\mathbb{D}$$)oe Always, either not every A is B or no C is D 8 (a-$$\mathbb{D}$$)oo Always, either not every A is B or not every C is D 9 (a-$$\mathbb{D}$$)ae Always, either every A is B or no C is D 10 (a-$$\mathbb{D}$$)ao Always, either every A is B or not every C is D 11 (a-$$\mathbb{D}$$)ie Always, either some A is B or no C is D 12 (a-$$\mathbb{D}$$)io Always, either some A is B or not every C is D 13 (a-$$\mathbb{D}$$)ea Always, either no A is B or every C is D 14 (a-$$\mathbb{D}$$)ei Always, either no A is B or some C is D 15 (a-$$\mathbb{D}$$)oi Always, either not every A is B or some C is D 16 (a-$$\mathbb{D}$$)oa Always, either not every A is B or every C is D

#### B.2.2 Universal negative disjunction

 1 (e-$$\mathbb{D}$$)aa Never, either every A is B or every C is D (laysa al-battata immā … wa-immā …) 2 (e-$$\mathbb{D}$$)ai Never, either every A is B or some C is D 3 (e-$$\mathbb{D}$$)ia Never, either some A is B or every C is D 4 (e-$$\mathbb{D}$$)ii Never, either some A is B or some C is D 5 (e-$$\mathbb{D}$$)ee Never, either no A is B or no C is D 6 (e-$$\mathbb{D}$$)eo Never, either no A is B or not every C is D 7 (e-$$\mathbb{D}$$)oe Never, either not every A is B or no C is D 8 (e-$$\mathbb{D}$$)oo Never, either not every A is B or not every C is D 9 (e-$$\mathbb{D}$$)ae Never, either every A is B or no C is D 10 (e-$$\mathbb{D}$$)ao Never, either every A is B or not every C is D 11 (e-$$\mathbb{D}$$)ie Never, either some A is B or no C is D 12 (e-$$\mathbb{D}$$)io Never, either some A is B or not every C is D 13 (e-$$\mathbb{D}$$)ea Never, either no A is B or every C is D 14 (e-$$\mathbb{D}$$)ei Never, either no A is B or some C is D 15 (e-$$\mathbb{D}$$)oi Never, either not every A is B or some C is D 16 (e-$$\mathbb{D}$$)oa Never, either not every A is B or every C is D

#### B.2.3 Particular affirmative disjunction

 1 (i-$$\mathbb{D}$$)aa Sometimes, either every A is B or every C is D (qad yakūnu immā an yakūna … aw …) 2 (i-$$\mathbb{D}$$)ai Sometimes, either every A is B or some C is D 3 (i-$$\mathbb{D}$$)ia Sometimes, either some A is B or every C is D 4 (i-$$\mathbb{D}$$)ii Sometimes, either some A is B or some C is D 5 (i-$$\mathbb{D}$$)ee Sometimes, either no A is B or no C is D 6 (i-$$\mathbb{D}$$)eo Sometimes, either no A is B or not every C is D 7 (i-$$\mathbb{D}$$)oe Sometimes, either not every A is B or no C is D 8 (i-$$\mathbb{D}$$)oo Sometimes, either not every A is B or not every C is D 9 (i-$$\mathbb{D}$$)ae Sometimes, either every A is B or no C is D 10 (i-$$\mathbb{D}$$)ao Sometimes, either every A is B or not every C is D 11 (i-$$\mathbb{D}$$)ie Sometimes, either some A is B or no C is D 12 (i-$$\mathbb{D}$$)io Sometimes, either some A is B or not every C is D 13 (i-$$\mathbb{D}$$)ea Sometimes, either no A is B or every C is D 14 (i-$$\mathbb{D}$$)ei Sometimes, either no A is B or some C is D 15 (i-$$\mathbb{D}$$)oi Sometimes, either not every A is B or some C is D 16 (i-$$\mathbb{D}$$)oa Sometimes, either not every A is B or every C is D

#### B.2.4 Particular negative disjunction

 1 (o-$$\mathbb{D}$$)aa Not always, either every A is B or every C is D (laysa dāʾiman immā … wa-immā …) 2 (o-$$\mathbb{D}$$)ai Not always, either every A is B or some C is D 3 (o-$$\mathbb{D}$$)ia Not always, either some A is B or every C is D 4 (o-$$\mathbb{D}$$)ii Not always, either some A is B or some C is D 5 (o-$$\mathbb{D}$$)ee Not always, either no A is B or no C is D 6 (o-$$\mathbb{D}$$)eo Not always, either no A is B or not every C is D 7 (o-$$\mathbb{D}$$)oe Not always, either not every A is B or no C is D 8 (o-$$\mathbb{D}$$)oo Not always, either not every A is B or not every C is D 9 (o-$$\mathbb{D}$$)ae Not always, either every A is B or no C is D 10 (o-$$\mathbb{D}$$)ao Not always, either every A is B or not every C is D 11 (o-$$\mathbb{D}$$)ie Not always, either some A is B or no C is D 12 (o-$$\mathbb{D}$$)io Not always, either some A is B or not every C is D 13 (o-$$\mathbb{D}$$)ea Not always, either no A is B or every C is D 14 (o-$$\mathbb{D}$$)ei Not always, either no A is B or some C is D 15 (o-$$\mathbb{D}$$)oi Not always, either not every A is B or some C is D 16 (o-$$\mathbb{D}$$)oa Not always, either not every A is B or every C is D