April 13, 2021

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Residuated Lattices: An Algebraic Glimpse at Substructural Logics

Residuated Lattices: An Algebraic Glimpse at Substructural Logics
Author : Nikolaos Galatos,Peter Jipsen,Tomasz Kowalski,Hiroakira Ono
Publisher : Elsevier
Release Date : 2007-04-25
Category : Mathematics
Total pages :532
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The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.

ECAI 2020

ECAI 2020
Author : G. De Giacomo,A. Catala,B. Dilkina
Publisher : IOS Press
Release Date : 2020-09-11
Category : Computers
Total pages :3122
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This book presents the proceedings of the 24th European Conference on Artificial Intelligence (ECAI 2020), held in Santiago de Compostela, Spain, from 29 August to 8 September 2020. The conference was postponed from June, and much of it conducted online due to the COVID-19 restrictions. The conference is one of the principal occasions for researchers and practitioners of AI to meet and discuss the latest trends and challenges in all fields of AI and to demonstrate innovative applications and uses of advanced AI technology. The book also includes the proceedings of the 10th Conference on Prestigious Applications of Artificial Intelligence (PAIS 2020) held at the same time. A record number of more than 1,700 submissions was received for ECAI 2020, of which 1,443 were reviewed. Of these, 361 full-papers and 36 highlight papers were accepted (an acceptance rate of 25% for full-papers and 45% for highlight papers). The book is divided into three sections: ECAI full papers; ECAI highlight papers; and PAIS papers. The topics of these papers cover all aspects of AI, including Agent-based and Multi-agent Systems; Computational Intelligence; Constraints and Satisfiability; Games and Virtual Environments; Heuristic Search; Human Aspects in AI; Information Retrieval and Filtering; Knowledge Representation and Reasoning; Machine Learning; Multidisciplinary Topics and Applications; Natural Language Processing; Planning and Scheduling; Robotics; Safe, Explainable, and Trustworthy AI; Semantic Technologies; Uncertainty in AI; and Vision. The book will be of interest to all those whose work involves the use of AI technology.

Manuscrito

Manuscrito
Author : Anonim
Publisher : Unknown
Release Date : 2011
Category : Philosophy
Total pages :129
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Algebraic Perspectives on Substructural Logics

Algebraic Perspectives on Substructural Logics
Author : Davide Fazio
Publisher : Springer Nature
Release Date : 2021
Category :
Total pages :129
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Mathematics, Logic, and their Philosophies

Mathematics, Logic, and their Philosophies
Author : Mojtaba Mojtahedi
Publisher : Springer Nature
Release Date : 2021
Category :
Total pages :129
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Trends in Logic

Trends in Logic
Author : Vincent F. Hendricks,Jacek Malinowski
Publisher : Springer Science & Business Media
Release Date : 2013-03-09
Category : Philosophy
Total pages :384
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In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

Actas

Actas
Author : Anonim
Publisher : Unknown
Release Date : 2007
Category : Algebra
Total pages :129
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The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic
Author : Anonim
Publisher : Unknown
Release Date : 2008
Category : Logic, Symbolic and mathematical
Total pages :129
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Analele Universității Din Craiova

Analele Universității Din Craiova
Author : Anonim
Publisher : Unknown
Release Date : 2006
Category : Information science
Total pages :129
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Reports on Mathematical Logic

Reports on Mathematical Logic
Author : Anonim
Publisher : Unknown
Release Date : 2006
Category : Logic, Symbolic and mathematical
Total pages :129
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LogKCA-07

LogKCA-07
Author : Anonim
Publisher : Universidad del Pais Basco Servicio Editorial
Release Date : 2007
Category : Philosophy
Total pages :455
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Handbook of the History of Logic

Handbook of the History of Logic
Author : Dov M. Gabbay,John Woods
Publisher : Unknown
Release Date : 2004
Category : Logic
Total pages :129
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