Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram

Neutrality and Many-Valued Logics

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.Comment: 119 page

Fuzzy Logic

Fuzzy Logic is becoming an essential method of solving problems in all domains. It gives tremendous impact on the design of autonomous intelligent systems. The purpose of this book is to introduce Hybrid Algorithms, Techniques, and Implementations of Fuzzy Logic. The book consists of thirteen chapters highlighting models and principles of fuzzy logic and issues on its techniques and implementations. The intended readers of this book are engineers, researchers, and graduate students interested in fuzzy logic systems

Institutional complementarities and gender diversity on boards: a configurational approach

Manuscript Type: Empirical Research Question/Issue: To address the lack of a complementarities-based approach in studies of board diversity, this paper seeks to understandwhether and howcertain country-level factors are causally and jointly related towomen on boards and the nature of their complementarities (are they synergic or substitutes?). Moreover, we intend to learn more about the adoption/diffusion of board gender quotas, by taking into account their role in the existing national configurations (whether they are necessary and/or sufficient conditions). Research Findings/Insights: Using fs/QCA, our findings reveal a particular configuration of country-level conditions that supports the existence of a joint causal relation between given institutional arrangements. Furthermore, we find that board gender quota legislation is not a sufficient condition on its own to achieve a higher number of women on boards. Such evidence suggests that its diffusion across countries could be the result of institutional isomorphismor social legitimacy more than to rational reasons. Theoretical/Academic Implications: For scholars, our paper refines and expands insights from the extant comparative corporate governance literature. By finding support for the “bundled” or jointly causal nature of given institutional factors,we open a window for further research that investigates board-level phenomena in a complementarities-based perspective. Practitioner/Policy Implications: For policymakers, this study provides some insights that could better drive their choice about which mix of policies is necessary to improve female representation on boards, and especially in which institutional areas they should be implemented. It is particularly relevant, because once gender quotas are endorsed at board level, they could have ambiguous effects on firm performance and corporate governance

Toward a probability theory for product logic: states, integral representation and reasoning

The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique regular Borel probability measure. Furthermore, the relation between states and measures is shown to be one-one. In addition, we study geometrical properties of the convex set of states and show that extremal states, i.e., the extremal points of the state space, are the same as the truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur