1,721,058 research outputs found
Editorial Introduction
No full textAfter providing an overview of the algebraic investigations into substructural logics in a historical perspective, with a special focus on their relationships with quantum logics, we summarise the contents of the subsequent chapters of this volume
The generalized orthomodularity property: configurations and pastings
No full textIn this paper, we consider a generalization of the notion of orthomodularity for posets to the concept of the generalized orthomodularity property (GO-property) by considering the
-operators. This seemingly mild generalization of orthomodular posets and its order theoretical analysis yield rather strong application to effect algebras and orthomodular structures. Also, for several classes of orthoalgebras, the GO-property yields a completely order-theoretical characterization of the coherence law, and, in turn, of proper orthoalgebras
On the structure theory of Łukasiewicz near semirings
No full textIn a previous article by two of the present authors and S. Bonzio, Lukasiewicz near semirings were introduced and it was proven that basic algebras can be represented (precisely, are term equivalent to) as near semirings. In the same work it has been shown that the variety of Lukasiewicz near semirings is congruence regular. In other words, every congruence is uniquely determined by its 0-coset. Thus, it seems natural to wonder whether it could be possible to provide a set-theoretical characterization of these cosets. This article addresses this question and shows that kernels can be neatly described in terms of two simple conditions. As an application, we obtain a concise characterization of ideals in Lukasiewicz semirings. Finally, we close this article with a rather general Cantor-Bernstein type theorem for the variety of involutive idempotent integral near semirings
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Editorial Introduction
No full textAfter providing an overview of the algebraic investigations into substructural logics in a historical perspective, with a special focus on their relationships with quantum logics, we summarise the contents of the subsequent chapters of this volume
Algebraic Perspectives on Substructural Logics
No full textThis volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics.
Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments.
This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics
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