Indicative Propositions

Two new problems of bivalent propositional logic are proposed here: firstly, to distinguish the sense of propositions, besides the logical value and secondly, to analyze the ”ponderal” difference between two parts of a proposition: subject-predicate. 1 Relational projections and extensions Let r = (A1, A2, A3, R) be a ternary relation (see [3]). Starting with this, we may define three binary relations (induced projections), namely r12 = (A1, A2, R12), r23 = (A2, A3, R23) and r13 = (A1, A3, R13) defined by (x1, x2) ∈ R12 ⇐⇒ there exists x3 ∈ A3 such that (x1, x2, x3) ∈ R and its analogs. Denote r < x1, x2 >= {x3 ∈ A3 | (x1, x2, x3) ∈ R} and analogously r < x2, x3 > and r < x1, x3 >, where (x1, x2, x3) ∈ A1×A2× A3. Proposition 1.1 xi rij xj ⇐⇒ r < xi, xj >6= ∅ , where i, j ∈ {1, 2, 3}, i < j. This proposition follows by the above definitions. To each of the binary relations rij , i, j ∈ {1, 2, 3}, i < j, we associate a ternary ponderal extension ∼ r ij = (Ai, Aj , N, ∼ Rij) defined by (x1, x2, n) ∈ ∼ R12 ⇐⇒ (x1, x2) ∈ R12 and |r < x1, x2 > | = n and its analogs. Remark. The relational projections and extensions may be generalized to the case of arbitrary n-ary relations. Received: October, 2001.