6: The Logical Language

Let's talk more about {du'u}. For many folks, {du'u} is the core of what makes Lojban logical; it is how we talk about propositions. What we can internalize under {du'u} are the one-way conclusions that can be drawn using classical logic. It is crucially important to understand that, while the relational and classical parts of Lojban do interact, the relational logic is the outer layer which hosts the classical logic inside.

Contradiction:

Relational logic is infamously squishy and gooey, with genuine witnesses to contradiction being rare. Nonetheless, there's at least one, based on the characteristic functions: a selbri cannot simultaneously relate given terbri and also not relate them.

ro da poi ke'a broda ro de poi broda ke'a zo'u:

pa du'u da broda de kei natfe pa du'u da na broda de (natfe-na)

natfe3 will be left blank as part of a convention of not specifying which logical system we are working under; it's still accessible, but we won't insist on it being any particular value.

List of {du'u} logic gismu

• {nibli}: x1 implies x2; poset (reflexive, antisymmetric, transitive)
• {natfe}: x1 contradicts x2; not clear whether symmetric
• {kanxe}: x1 is the conjunction of x2 and x3
• {vlina}: x1 is the disjunction of x2 or x3
• {sigda} [exp]: x1 is the material implication x2 => x3
• {tsida} [exp]: x1 is the material biimplication x2 <=> x3