On The Semantics Of Classical First Order Logic With Constructive Double Negation
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Author | : Ken Kaneiwa |
Publisher | : |
Total Pages | : 18 |
Release | : 2004 |
Genre | : |
ISBN | : |
Download On the Semantics of Classical First-order Logic with Constructive Double Negation Book in PDF, Epub and Kindle
Author | : Stewart Shapiro |
Publisher | : Cambridge University Press |
Total Pages | : 89 |
Release | : 2022-05-19 |
Genre | : Philosophy |
ISBN | : 1108991521 |
Download Classical First-Order Logic Book in PDF, Epub and Kindle
One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues. The first half of the Element develops a language for the system, as well as a proof theory and model theory. The authors provide theorems about the system they developed, such as unique readability and the Lindenbaum lemma. They also discuss the meta-theory for the system, and provide several results there, including proving soundness and completeness theorems. The second half of the Element compares first-order classical logic to other systems: classical higher order logic, intuitionistic logic, and several paraconsistent logics which reject the law of ex falso quodlibet.
Author | : Sergei Odintsov |
Publisher | : Springer Science & Business Media |
Total Pages | : 241 |
Release | : 2008-03-19 |
Genre | : Philosophy |
ISBN | : 1402068670 |
Download Constructive Negations and Paraconsistency Book in PDF, Epub and Kindle
Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.
Author | : John L. Bell |
Publisher | : Cambridge University Press |
Total Pages | : 88 |
Release | : 2022-03-31 |
Genre | : Philosophy |
ISBN | : 1108991955 |
Download Higher-Order Logic and Type Theory Book in PDF, Epub and Kindle
This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.
Author | : Eric Schechter |
Publisher | : Princeton University Press |
Total Pages | : 520 |
Release | : 2020-10-06 |
Genre | : Mathematics |
ISBN | : 069122014X |
Download Classical and Nonclassical Logics Book in PDF, Epub and Kindle
So-called classical logic--the logic developed in the early twentieth century by Gottlob Frege, Bertrand Russell, and others--is computationally the simplest of the major logics, and it is adequate for the needs of most mathematicians. But it is just one of the many kinds of reasoning in everyday thought. Consequently, when presented by itself--as in most introductory texts on logic--it seems arbitrary and unnatural to students new to the subject. In Classical and Nonclassical Logics, Eric Schechter introduces classical logic alongside constructive, relevant, comparative, and other nonclassical logics. Such logics have been investigated for decades in research journals and advanced books, but this is the first textbook to make this subject accessible to beginners. While presenting an assortment of logics separately, it also conveys the deeper ideas (such as derivations and soundness) that apply to all logics. The book leads up to proofs of the Disjunction Property of constructive logic and completeness for several logics. The book begins with brief introductions to informal set theory and general topology, and avoids advanced algebra; thus it is self-contained and suitable for readers with little background in mathematics. It is intended primarily for undergraduate students with no previous experience of formal logic, but advanced students as well as researchers will also profit from this book.
Author | : Andreas Kapsner |
Publisher | : Springer |
Total Pages | : 216 |
Release | : 2015-01-07 |
Genre | : Philosophy |
ISBN | : 3319052063 |
Download Logics and Falsifications Book in PDF, Epub and Kindle
This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne
Author | : Sergei Artemov |
Publisher | : Springer Nature |
Total Pages | : 297 |
Release | : 2019-12-13 |
Genre | : Mathematics |
ISBN | : 303036755X |
Download Logical Foundations of Computer Science Book in PDF, Epub and Kindle
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
Author | : Stephan Scheele |
Publisher | : University of Bamberg Press |
Total Pages | : 348 |
Release | : 2015-07-02 |
Genre | : |
ISBN | : 3863093208 |
Download Model and Proof Theory of Constructive ALC Book in PDF, Epub and Kindle
Author | : Ian Rumfitt |
Publisher | : |
Total Pages | : 369 |
Release | : 2015 |
Genre | : Language Arts & Disciplines |
ISBN | : 0198733631 |
Download The Boundary Stones of Thought Book in PDF, Epub and Kindle
Classical logic has been attacked by adherents of rival, anti-realist logical systems: Ian Rumfitt comes to its defence. He considers the nature of logic, and how to arbitrate between different logics. He argues that classical logic may dispense with the principle of bivalence, and may thus be liberated from the dead hand of classical semantics.
Author | : Roy T. Cook |
Publisher | : Edinburgh University Press |
Total Pages | : 328 |
Release | : 2009-03-20 |
Genre | : Reference |
ISBN | : 0748631976 |
Download Dictionary of Philosophical Logic Book in PDF, Epub and Kindle
This dictionary introduces undergraduate and post-graduate students in philosophy, mathematics, and computer science to the main problems and positions in philosophical logic. Coverage includes not only key figures, positions, terminology, and debates within philosophical logic itself, but issues in related, overlapping disciplines such as set theory and the philosophy of mathematics as well. Entries are extensively cross-referenced, so that each entry can be easily located within the context of wider debates, thereby providing a valuable reference both for tracking the connections between concepts within logic and for examining the manner in which these concepts are applied in other philosophical disciplines.