This article shows a Boolean Multivalued logical model of varying confirmation by observation of events in human inference and, as an introductory example, applies the model to solve Hempel's paradox of the ravens.

This paper proposes () an algorithm that dynamically constructs an asymptotically-balanced binary tree to store successively-given keys without knowledge of the distribution of key occurence, and () another algorithm for quick key search over the constructed tree such that: If the tree has in memory at least a key that is inside the Δ-neighbor (in a Hamming space) of a reference key, then the algorithm can find one of such Δ-neighbor keys almost with probability 1. The memory capacity required to describe a tree in the tree construction algorithm is of order being proportional to the number l of keys already processed. For an independently and idenically distributed binary source of generating keys, the mean computation time required to update a tree for every key input can be of an order being a little higher than (log2l)2log2(log2l), and that required to search a Δ-neighbor key can be of an order being a little higher than (log2l)3.

Let U denote a set comprising elements called "keys." The goal of the nearest point problem is to search quickly for a key among some keys x1 , xn that is the nearest to a reference key x under a partial order relation defined as (x, y) (x, z) for x, y, zU if d(x, y)d(x, z) given a wide-sense distance measure d. This article proposes a method of rearranging x1 , xn into a binary perfectly-balanced tree for solving quickly the nearest point problems. Further, computational performances of the proposed method are evaluated experimentally.

This article proposes, given an independently-and-identically distributed binary source, an arithmetic code-like variable-to-variable length source code whose compression efficiency achieves nearly the rate function in a range of small distortion. Inheriting advantages of arithmetic codes, the proposed code requires neither large memory capacity nor large computation time for management of messages and codewords. The Elias code, which can be regarded as an antecedent of arithmetic codes, is defined originally in terms of the first-in-first-out (FIFO) coding form. The proposed code corresponds to an extension from the Elias code refined in terms of the last-in-first-out (LIFO) coding form into one considered a fidelity criterion.

The paper proposes a method of variable-to-fixed length binary data encryption in the class of conventional cryptosystems. An encryption algorithm reduces an interval of the integers that mean candidates of cryptograph according to a key and messages. A decryption algorithm traces the trajectory of reduction of interval according to the key and cryptographs to reproduce the messages. These algorithms are executable with simple arithmetics on several registers. However, wiretappers without knowledge on the key cannot correctly reproduce messages since they cannot trace the trajectory of reduction. The exhaustive cryptanalysis identifies the correct decryption procedure only from cryptographs. The comparing cryptanalysis identifies the correct decryption procedure from some pairs of message and cryptograph. Asymptotic evaluations for the computational complexity of cryptanalysis show a satisfactory endurance against wiretapping.

This article shows construction of an asymptotically optimal source code for transmitting sentences together with truth values on a [0,1]-valued logic system.

This article shows that a multivalued logic defined as juxtaposition of Boolean binary logics can use all of inference chain, induction and deduction that are important in realization of intelligent inference systems.