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In pattern logic, a syllogism is a *transitive arrangement* of *two logical statements* with *mediation copulas* (premises) sharing a commonly quantified logical term that permits elimination of that term to conclude with a new premise.

A premise is a *logical statement* with a **mediation copula**. There are two varieties of the mediation copula:

**Predication**: the first logical term*transitively limits*the second logical term.**Counter-Predication**: the first logical term is*transitively limited by*the second logical term.

These two forms of mediation are thus only distinguishable by the *directional arrangement of their logical terms in relation to the copula*. This arrangement is **individually arbitrary** but becomes significant when a premise shares a common logical term with another premise.

Premises are the building blocks of the term logic found in Aristotle's system of syllogism found in the *Prior Analytics*.

Pattern Logic will require a premise to follow the general form of a logical statement which means that it will have:

**Terms**as*modal concepts*.**Quantifiers**for*both*the subject and the predicate of any premise.**Premises**as*modal concepts*.

The ten quantifiers of pattern logic expand the definition of premise well beyond the Aristotelian and Medieval Scholastic system of syllogism which recognized four types of premises.

- A-premise: "all S is P"
- E-premise: "no S is P"
- I-premise: "some S is P"
- O-premise: "some S is not P"

Setting the role of modality aside for the moment, Patten Logic will establish inference rules that allow for reasoning over 100 types of fully-quantified premises.

The entire list of expanded premises can be found in the download below but the subset of premises pertinent to the Aristotelian system is shown here.

Premises with two general quantifications of its subject and predicate terms. The corresponding Scholastic A, E, I and O premises are highlighted blue.

Pattern Logic establishes its rules of inference for syllogisms upon the transitivity of limitation in three ways:

**Substitution Rules**(two): pattern logic quantifiers allows for select "substituting" of one quantification of a term for another quantification within either the subject or predicate position of a premise depending on specific transitive arrangements. Substitution explains the traditional idea of "premise subalternation".**Involution Rules**(two): for select premises having specific logical terms with existential import, an involution transformation of the entire premise may be inferred due to its cyclic pattern of transitivity. Involution explains the traditional idea of "premise conversion".**Elimination Rules**(several modal versions): in the strongest (deductive) form of this rule, two premises are combined via transitive elimination of a middle term to infer a shortened pattern which is the concluding premise of a syllogism. Elimination explains the traditional idea of "syllogistic conclusion".

A pattern logic syllogism will be said to be **perfect** when both terms and copulas are of a necessary or contingent modality *and* the pattern spanning the common term permits an elimination of that term on a quantifier having existential import.

A pattern logic syllogism will be said to be **imperfect **when any of the terms or copulas are *not *of a necessary or contingent modality *or* the pattern spanning the common term permits an elimination of that term on a quantifier *lacking* existential import.

- Catalog the perfect syllogisms having aligned mediation copulas that permit an
**elimination**of the middle term on a quantifier with existential import. These are the*aligned perfect syllogisms*. - Apply the valid premise transformations in reverse to the major and minor premises of the aligned perfect syllogisms via the remaining four rules of inference to arrive at the
*upstream perfect syllogisms*. - Apply the valid premise transformations in a forward direction from the concluding premises of the aligned and upstream perfect syllogisms. These additional downstream perfect syllogisms will
**complete the full set of**.**perfect syllogisms**

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