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This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia spaces. The main theorems include a duality between...
This book constitutes the refereed proceedings of the 9th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2011, held in Kutaisi, Georgia, in September 2011. The book consists of summaries of 3 tutorials presented at the symposium together with 13 full papers that were carefully reviewed and selected from the submissions. The papers are organized in two sections, one on Language and one on Logic and Computation. The range of topics covered in the Language section includes natural language syntax, semantics, and pragmatics, frames in natural language semantics, linguistic typology, and discourse phenomena. The papers in the Logic and Computation section cover such topics as constructive, modal, algebraic, and philosophical logic, as well as logics for computer science applications.
This book constitutes the refereed proceedings of the 12th International Tbilisi Symposium on Logic, Language and Computation, TbiLLC 2017, held in Lagodekhi, Georgia, in September 2017. The volume contains 17 full revised papers presented at the conference from 22 submissions. The aim of this conference series is to bring together researchers from a wide variety of fields in Natural language syntax, Linguistic typology, Language evolution, Logics for artificial intelligence and much more.
This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.
This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.Key Features:- Complete state of the art of the importance of triangular norms in various mathematical fields- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications- Chapter authors are leading authorities in their fields- Triangular ...
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 23rd Workshop on Logic, Language, Information and Communication, WoLLIC 2016, held in Puebla, Mexico, in August 2016.The 23 contributed papers, presented together with 9 invited lectures and tutorials, were carefully reviewed and selected from 33 submissions. The focus of the workshop is to provide a forum on inter-disciplinary research involving formal logic, computing and programming theory, and natural language and reasoning.
In Potential Questions at the Semantics-Pragmatics Interface Edgar Onea proposes a novel component for question under discussion based discourse pragmatic theories thereby combining such theories with new ideas from inquisitive semantics. He shows how potential questions account for an entire range of grammatical phenomena. These phenomena include the semantics of indefinite determiners, the meaning contribution of nominal appositives, specificational constructions and non restrictive relative clauses. This book delivers a comprehensive and empirically rich investigation into the role of questions in natural language interpretation. Drawing on data from German, English, Hungarian and Russian...
Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.
This book constitutes the proceedings of the 14th European Conference on Logics in Artificial Intelligence, JELIA 2014, held in Funchal, Madeira, Portugal, in September 2014. The 35 full papers and 14 short papers included in this volume were carefully reviewed and selected from 121 submissions. They are organized in topical sections named: description logics; automated reasoning; logics for uncertain reasoning; non-classical logics; answer-set programming; belief revision; dealing with inconsistency in ASP and DL; reason about actions and causality; system descriptions; short system descriptions; and short papers. The book also contains 4 full paper invited talks.