In essence, a set of classification rules can be regarded as a logical disjunction of rules, so that each rule can be regarded as a disjunct.
Finally, the tag of the policy is calculated applying Definition 5 to every rule disjunction resulting from the expansion of the EXIST quantifiers (lines 12 25).
Transforming a set of trees (e.g., see Figure 3), each of which encodes a disjunction of conjunctive rules on the conditions (gene expression levels) under which a single target gene is expressed, to a network that captures the combination of regulatory dependencies between multiple genes in a user-friendly way is not straightforward.
The many-valued rule for disjunction is to assign the whole statement the truth-value of its highest disjunct.
Then the inversion principle says that A∨B →C is admissible assuming A →C and B →C, which justifies the elimination rule for disjunction.
The specific relationship between introduction and elimination rules as formulated in an inversion principle excludes alleged inferential definitions such as that of the connective tonk, which combines an introduction rule for disjunction with an elimination rule for conjunction, and which has given rise to a still ongoing debate on the format of inferential definitions (see Humberstone, 2010).
A fact is a ground rule without disjunction and with an empty body.
Independently, in Béziau 2004, it was observed that by putting together the sequent rules for classical conjunction and the rules for classical disjunction, the resulting sequent calculus will (unexpectedly) prove the distributivity between conjunction and disjunction.
Compare with the following rules for multiplicative disjunction, known as par: The meanings of the two multiplicative particles are obviously dual to each other.
The double-line rules for conjunction and disjunction are read as implicit definitions of these constants, which by some procedure can be turned into the explicit sequent-style rules we are used to.
