The authors investigate the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine prover9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. prover9, however, discovered a simpler valid argument for ...

An N -angulation is a finite simple plane graph such that each face is bounded by a cycle of length N , where N ≥ 3 is an integer. We consider diagonal transformations in N -angulations which consist of ⌊ 2 ⌋ kinds of operations. In the literature, Wagner proved that any two 3angulations (which are often called triangulations) with the same number of vertices can be transformed into each other ...

Abstract We develop a tropical intersection formalism of forms and currents that extends classical theory in two ways. First, it allows to work with arbitrary polyhedra, also non-rational ones. Second, for smooth differential as coefficients. The product our can be defined through the diagonal method Allermann–Rau or fan displacement rule. prove limiting argument both definitions agree.

Let T n denote the set of triangulations of a convex polygon K with n sides. We study the random walk on T n whose transitions are \\ips" of one of the n ? 3 internal diagonals of the current triangulation, the choice of diagonal being random. By bounding the conductance of this graph we show that the walk mixes rapidly, namely in time O(n). A direct argument is given for the fact that the mixi...

For one qubit systems, we present a short, elementary argument characterizing unital quantum operators in terms of their action on Bloch vectors. We then show how our approach generalizes to multi-qubit systems, obtaining inequalities that govern when a “diagonal” superoperator on the Bloch region is a quantum operator. These inequalities are the n-qubit analogue of the Algoet-Fujiwara conditio...

We give bijective proofs that, when combined with one of the combinatorial proofs of the general ballot formula, constitute a combinatorial argument yielding the number of lattice paths from (0, 0) to (n, rn) that touch or cross the diagonal y = rx at exactly k lattice points. This enumeration partitions all lattice paths from (0, 0) to (n, rn). While the resulting formula can be derived using ...

Cantor’s proof of this result [2, §2] makes use of nested intervals, but today a proof based on another ingenious idea of Cantor is more popular, namely the diagonal method, which he introduced in 1891 to prove the uncountability of 2 [3]. However, Cantor himself did not employ diagonalization directly in the proof of uncountability of R, but gave a rather intricate derivation of ∣ ∣2 ∣ ∣ = |R|...

How can one justify the secession of a territory from a liberal-democratic state of the kind currently prevalent in North America and Western Europe? The question does not primarily concern a mutually agreed secession, such as that of Norway from the United Kingdoms of Norway and Sweden in 1905. If the government and legislature of the ‘parent state’ freely agree to a secession of a part of its...

We study the mutual consistency of twisted boundary conditions in the coset conformal field theory G/H. We calculate the overlap of the twisted boundary states of G/H with the untwisted ones, and show that the twisted boundary states are consistently defined in the diagonal modular invariant. The overlap of the twisted boundary states is expressed by the branching functions of a twisted affine ...