Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics.     

The elimination of de re formulas

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme x x.     

Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.     

康德哲学与广松涉"交互主体的共同主观性"理论

广松涉认为,对近代认识论基础的问题式及其构成机制和局限进行反思,首先需要将着眼点放在康德哲学的问题式及其构成机制上。康德哲学的总的问题式就是在以先验逻辑学为基础的逻辑学、认识论和本体论“三位一体”的哲学构架中,探讨人的认识以及纯粹理性的先天综合判断及其能力何以可能。这一问题式潜含着一个意义非常重大的认识论问题——即“主体际共同主观性”问题．需要我们认真地加以研究。     

A new experimental method to identify the process of logical reasoning

Abstract: A new method to identify the process of logical reasoning is presented. In spite of its indispensability and importance, we have had few methods to identify a subject's reasoning process, except that of using verbal protocol data. In this paper, for the purpose of objective identification of the reasoning process, we propose a new method to obtain the subject's reasoning process, in terms of a resolution tree for a task of which the logical structure can be written by first-order predicate logic. The results of an experiment using this method are presented. They revealed some interesting features of human reasoning such as, large differences between subjects, remarkable parallel processes, and the existence of subgoals for each subject.     

Products of modal logics and tensor products of modal algebras

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto's results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.     

Global problems,globalization, and predictability

The term globalization is questioned in its validity and applicability to structures other than verbal. Globalization is a historical term which changes its meaning with time and culture. It is not only that its content changes but the validity of a globalization concept changes with the historical perspective. Morever, solution of global problems depends heavily on the correct analysis of the problem. Without such an analysis there is no possibility to find even an approximate solution. Hence, predictability is impossible. There is no trend which is sufficiently long to make any reliable prediction for global problems other than the most simple ones.