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Inclusion Relationship between Pseudo-Euclidean Logics

Hashimoto Y., Maruyama A.

Reports on Mathematical Logic

2011

Vol. 46

133-142

We describe properties of simply axiomatized modal logics, which are called pseudo-Euclidean modal logics. For fixed non-negative integers m and n, let Em,n k be the logic which is obtained from the smallest normal propositional modal logic K by adding the pseudo-Euclidean axiom lozenge k fi rightarrow box m lozenge n fi, where k greater-than or equal to 0. We will then give a complete description of the inclusion relationship among these logics by showing inclusion relationships for pairs of their logics with fixed m and n.

Deformations of the semicircle law derived from random walks on free groups

Hashimoto Y.

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 2

399--410

New 1-parameter families of central limit distributions are investigated by means of random walks on trees associated with free groups under two kinds of states: one is Haagerup’s function and the other is a spherical function associated with unitary representations of the principal series. Those families give rise to deformations of Wigner’s semicircle distribution by non-symmetric probability measures.