Elements Of The Theory Of Completeness In Propositional Logic
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Elements Of The Theory Of Completeness In Propositional Logic
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Author : Witold A. Pogorzelski
language : en
Publisher:
Release Date : 1982
Elements Of The Theory Of Completeness In Propositional Logic written by Witold A. Pogorzelski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Completeness theorem categories.
Theory Of Logical Calculi
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Author : Ryszard Wójcicki
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Theory Of Logical Calculi written by Ryszard Wójcicki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t'Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz's seminar on mathematicallogi.
The History And Philosophy Of Polish Logic
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Author : K. Mulligan
language : en
Publisher: Springer
Release Date : 2016-01-26
The History And Philosophy Of Polish Logic written by K. Mulligan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-26 with Philosophy categories.
The book presents the state of the art of research into the legacy of interwar Polish analytic philosophy and exemplifies different approaches to the history of philosophy. It contains discussions and reconstructions of aspects of Polish philosophy and logic as well as reactions to and developments of this tradition.
An Introduction To Proof Theory
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2021
An Introduction To Proof Theory written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
"Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail"--
Ordered Sets And Lattices Ii
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Ordered Sets And Lattices Ii written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
Mathematical Logic Through Python
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Author : Yannai A. Gonczarowski
language : en
Publisher: Cambridge University Press
Release Date : 2022-09-15
Mathematical Logic Through Python written by Yannai A. Gonczarowski and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-15 with Computers categories.
A unique approach to mathematical logic where students implement the underlying concepts and proofs in the Python programming language.
Elements Of Logical Reasoning
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Author : Jan von Plato
language : en
Publisher: Cambridge University Press
Release Date : 2013
Elements Of Logical Reasoning written by Jan von Plato and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
This book provides an accessible and at the same time scientifically rigorous introduction to the principles of logical reasoning.
Theorem Proving In Higher Order Logics
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Author : Mark Aagaard
language : en
Publisher: Springer
Release Date : 2007-07-23
Theorem Proving In Higher Order Logics written by Mark Aagaard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-23 with Computers categories.
This volume is the proceedings of the 13th International Conference on Theo rem Proving in Higher Order Logics (TPHOLs 2000) held 14-18 August 2000 in Portland, Oregon, USA. Each of the 55 papers submitted in the full rese arch category was refereed by at least three reviewers who were selected by the program committee. Because of the limited space available in the program and proceedings, only 29 papers were accepted for presentation and publication in this volume. In keeping with tradition, TPHOLs 2000 also offered a venue for the presen tation of work in progress, where researchers invite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplemen tary proceedings containing associated papers for work in progress was published by the Oregon Graduate Institute (OGI) as technical report CSE-00-009. The organizers are grateful to Bob Colwell, Robin Milner and Larry Wos for agreeing to give invited talks. Bob Colwell was the lead architect on the Intel P6 microarchitecture, which introduced a number of innovative techniques and achieved enormous commercial success. As such, he is ideally placed to offer an industrial perspective on the challenges for formal verification. Robin Milner contributed many key ideas to computer theorem proving, and to functional programming, through his leadership of the influential Edinburgh LCF project.
Logica Universalis
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Author : Jean-Yves Beziau
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-08
Logica Universalis written by Jean-Yves Beziau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-08 with Mathematics categories.
Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic. It was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. The present book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. It will help those who are lost in the jungle of heterogeneous logical systems to find a way. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.
The Internal Structure Of Predicates And Names
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Author : Richard L Epstein
language : en
Publisher: Advanced Reasoning Forum
Release Date : 2018-10-31
The Internal Structure Of Predicates And Names written by Richard L Epstein and has been published by Advanced Reasoning Forum this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-31 with Philosophy categories.
This series of volumes is meant to extend the scope of what we can formalize in classical predicate logic, and in doing so see the limitations of what can be done. The first section of this volume presents classical predicate logic with equality. In the second section, that logic is extended to formalize reasoning that involves adverbs and relative adjectives by viewing those as modifiers of simpler predicates. What is normally taken to be an atomic predicate, such as "barking loudly", can then have internal structure. Reasoning that involves conjunctions of terms, as in "Tom and Dick lifted the table", conjunctions of modifiers, conjunctions of predicates, and disjunctions of predicates can also be formalized by viewing them as part of the internal structure of atomic predicates. Many questions about the nature of formalizing arise in doing this. The internal structure of names is the topic of the third and last section. Names for functions are used in classical predicate logic to form complex names. In our ordinary reasoning we also use descriptions to form functions, such as "the wife of", and descriptions to form names, such as "the cat that scratched Zoe". To reason with those we can take account of their internal structure by dropping the assumption that every name must refer to a specific thing. The formal systems that are developed here are meant to help us understand how to reason well. Many worked examples show how to use them. Those examples also uncover limitations of the formal work. Throughout this series of volumes, the work proceeds by abstracting and creating formal models to formalize reasoning. By paying attention to the process of abstracting we gain insight into why we consider some reasoning to be good and some reasoning bad, and insight also into the deeper assumptions we make about the world on which our judgments rely.