GEC Formal Spec Part 3 - Relations

tThis is a formal specification for the relation propositions of gGated eEpistemic cCalculus (gecGEC) for those interested in jumping into the math.

rRelation oObjects

dDefinition 1. pProposition universe

lLet:

P$$ \mathcal{P} $$

be a finite set of proposition nodes.

eEvery node in $P$\mathcal{P}$$ is a proposition. tThe evaluator may distinguish fact propositions from relational propositions for parsing and uiUI, but this is a category distinction inside one proposition universe, not a separate object type.

dDefinition 2. fFact proposition

aA fact proposition is an ordinary claim whose content is not an inferential relation.

eExamples:

"sStudy aA reports a positive association."
"cCoffee is healthy."
"sStudy aA's sample population was too narrow."

dDefinition 3. rRelational proposition

aA relational proposition is a proposition whose content states that one proposition-state contributes evidence to another proposition-state.

tThe canonical form is:

contributes(A, X, z, k)

where:

𝐴,𝑋∈P,𝑧,𝑘∈{𝑇,𝐹,𝑉}.$$ A, X \in \mathcal{P}, \qquad z,k \in \{T,F,V\}. $$

A being in source state z is evidence for X being in target state k.

rRelational propositions are themselves elements of $P$\mathcal{P}$$ and may be the source or target of other relational propositions.

dDefinition 4. uUser-facing aliases

tThe following aliases compile to contributes:

aAlias	iInternal form	rReading
`evidences(A, X)`	`contributes(A, X, T, T)`	`A`'s truth supports `X`'s truth
`counters(A, X)`	`contributes(A, X, T, F)`	`A`'s truth supports `X`'s falsity
`problematizes(A, X)`	`contributes(A, X, T, V)`	`A`'s truth supports `X` being ill-posed or not evaluable as stated
`vague_of(A, X)`	`contributes(A, X, V, V)`	`A`'s vagueness supports `X`'s vagueness
`negative_evidences(A, X)`	`contributes(A, X, F, T)`	`A`'s falsity supports `X`'s truth
`negative_counters(A, X)`	`contributes(A, X, F, F)`	`A`'s falsity supports `X`'s falsity