Download or read book Natural Deduction Hybrid Systems and Modal Logics written by Andrzej Indrzejczak and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
Download or read book Hybrid Logic and its Proof Theory written by Torben Braüner and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).
Download or read book A Natural Deduction System for Modal Logic written by John Thomas Canty and published by . This book was released on 1963 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Kripke s Worlds written by Olivier Gasquet and published by Springer Science & Business Media. This book was released on 2013-11-20 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language.
Download or read book Labelled Deduction written by David Basin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Labelled deduction is an approach to providing frameworks for presenting and using different logics in a uniform and natural way by enriching the language of a logic with additional information of a semantic proof-theoretical nature. Labelled deduction systems often possess attractive properties, such as modularity in the way that families of related logics are presented, parameterised proofs of metatheoretic properties, and ease of mechanisability. It is thus not surprising that labelled deduction has been applied to problems in computer science, AI, mathematical logic, cognitive science, philosophy and computational linguistics - for example, formalizing and reasoning about dynamic `state oriented' properties such as knowledge, belief, time, space, and resources.
Download or read book Modal Logic for Philosophers written by James W. Garson and published by Cambridge University Press. This book was released on 2006-08-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book provides an accessible, yet technically sound treatment of modal logic and its philosophical applications.
Download or read book Sequents and Trees written by Andrzej Indrzejczak and published by Springer Nature. This book was released on 2020-12-16 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus. After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics. Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.
Download or read book The Lvov Warsaw School Past and Present written by Ángel Garrido and published by Birkhäuser. This book was released on 2018-06-12 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
Download or read book The Reconstruction of A N Prior s Ontology written by Zuzana Rybaříková and published by Vydavatelství Filozofické fakulty Univerzity Palackého v Olomouci. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the first analytic philosophers were primarily focused on the logical analysis of language, some of their initial works also contained ontological discussions. One of the most distinct ontological positions of the twentieth century was defended by Arthur Norman Prior. The unusual nature of the position could be demonstrated by the fact that he was ascribed to such divergent positions as nominalism and platonism. This might have been caused by his atypical combination of ontological views. He was, on the one hand, a nominalist in his mature works. On the other hand, he advocated intensional logic and presentism. The aim of this study is to reconstruct the ideas which influenced him as he formulated his ontological positions. Not only are Prior’s ideas introduced, but also the ideas of his precursors and contemporaries who influenced him. In contrast, the ideas of logicians and philosophers who Prior opposed are also presented. The dissertation consists of four parts which deal with Prior’s concepts of possible worlds, theories of quantifications, propositions and individuals. It is a historical study and therefore the polemics which arose after Prior’s death are not discussed.
Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This development in turn, directly pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded. At the same time, it socially provided employment for generations of logicians residing in computer science, linguistics and electrical engineering departments which of course helped keep the logic community to thrive. The many contributors to this Handbook are active in these application areas and are among the most famous leading figures of applied philosophical logic of our times.
Download or read book Frontiers of Combining Systems written by Andreas Herzig and published by Springer Nature. This book was released on 2019-08-22 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 12th International Symposium on Frontiers of Combining Systems, FroCoS 2019, held in London, UK, in September 2019, colocated with the 28th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2019. The 20 papers presented were carefully reviewed and selected from 30 submissions. They present research on the development of techniques and methods for the combination and integration of formal systems, their modularization and analysis. The papers are organized in the following topical sections: automated theorem proving and model building, combinations of systems, constraint solving, description logics, interactive theorem proving, modal and epistemic logics, and rewriting and unification.
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Hans De Nivelle and published by Springer. This book was released on 2015-09-10 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 24th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2015, held in Wroclaw, Poland, in September 2015. The 19 full papers and 2 papers presented in this volume were carefully reviewed and selected from 34 submissions. They are organized in topical sections named: tableaux calculi; sequent calculus; resolution; other calculi; and applications.
Download or read book Logic Rationality and Interaction written by Natasha Alechina and published by Springer Nature. This book was released on 2023-10-23 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This LNCS book is part of the FOLLI book series and constitutes the proceedings of the 9th International Workshop on Logic, Rationality, and Interaction, LORI 2023, held in Jinan, China, in October 2023. The 15 full papers presented together with 7 short papers in this book were carefully reviewed and selected from 40 submissions. The workshop covers a wide range on the following topics such as agency; argumentation and agreement; belief representation; probability and uncertainty; belief revision and belief merging; knowledge and action; dynamics of informational attitudes; intentions, plans, and goals; decision making and planning; preference and utility; cooperation; strategic reasoning and game theory; epistemology; social choice; social interaction; speech acts; knowledge representation; norms and normative systems; natural language; rationality; philosophical logic.
Download or read book Logical Methods written by Greg Restall and published by MIT Press. This book was released on 2023-01-03 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to philosophical logic, suitable for undergraduate courses and above. Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof construction on equal footing with model building and emphasizes connections to other areas of philosophy as the tools are developed. Throughout, the material draws on a broad range of examples to show readers how to develop and master tools of proofs and models for propositional, modal, and predicate logic; to construct and analyze arguments and to find their structure; to build counterexamples; to understand the broad sweep of formal logic’s development in the twentieth and twenty-first centuries; and to grasp key concepts used again and again in philosophy. This text is essential to philosophy curricula, regardless of specialization, and will also find wide use in mathematics and computer science programs. Features: An accessible introduction to proof theory for readers with no background in logic Covers proofs, models, modal logics, meta-theory, two-dimensional logics, quantification, and many other topics Provides tools and techniques of particular interest to philosophers and philosophical logicians Features short summaries of key concepts and skills at the end of each chapter Offers chapter-by-chapter exercises in two categories: basic, designed to reinforce important ideas; and challenge, designed to push students’ understanding and developing skills in new directions
Download or read book Deductive Systems in Traditional and Modern Logic written by Alex Citkin and published by MDPI. This book was released on 2020-11-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.
Download or read book Automated Reasoning written by Christoph Benzmüller and published by Springer Nature. This book was released on with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asking and Answering written by Moritz Cordes and published by Narr Francke Attempto Verlag. This book was released on 2021-12-10 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: Questions are everywhere and the ubiquitous activities of asking and answering, as most human activities, are susceptible to failure - at least from time to time. This volume offers several current approaches to the systematic study of questions and the surrounding activities and works toward supporting and improving these activities. The contributors formulate general problems for a formal treatment of questions, investigate specific kinds of questions, compare different frameworks with regard to how they regulate the activities of asking and answering of questions, and situate these activities in a wider framework of cognitive/epistemic discourse. From the perspectives of logic, linguistics, epistemology, and philosophy of language emerges a report on the state of the art of the theory of questions.
