Theory Of Logical Calculi Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Theory Of Logical Calculi book. This book definitely worth reading, it is an incredibly well-written.
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.
Before his death in March, 1976, A. H. Lightstone delivered the manu script for this book to Plenum Press. Because he died before the editorial work on the manuscript was completed, I agreed (in the fall of 1976) to serve as a surrogate author and to see the project through to completion. I have changed the manuscript as little as possible, altering certain passages to correct oversights. But the alterations are minor; this is Lightstone's book. H. B. Enderton vii Preface This is a treatment of the predicate calculus in a form that serves as a foundation for nonstandard analysis. Classically, the predicates and variables of the predicate calculus are kept distinct, inasmuch as no variable is also a predicate; moreover, each predicate is assigned an order, a unique natural number that indicates the length of each tuple to which the predicate can be prefixed. These restrictions are dropped here, in order to develop a flexible, expressive language capable of exploiting the potential of nonstandard analysis. To assist the reader in grasping the basic ideas of logic, we begin in Part I by presenting the propositional calculus and statement systems. This provides a relatively simple setting in which to grapple with the some times foreign ideas of mathematical logic. These ideas are repeated in Part II, where the predicate calculus and semantical systems are studied.
Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, linear logic, and modal logic. In the first chapters, the author emphasizes classical logic and a variety of different sequent calculi for classical and intuitionistic logics. She then presents other non-classical logics and meta-logical results, including decidability results obtained specifically using sequent calculus formalizations of logics. The book is suitable for a wide audience and can be used in advanced undergraduate or graduate courses. Computer scientists will discover intriguing connections between sequent calculi and resolution as well as between sequent calculi and typed systems. Those interested in the constructive approach will find formalizations of intuitionistic logic and two calculi for linear logic. Mathematicians and philosophers will welcome the treatment of a range of variations on calculi for classical logic. Philosophical logicians will be interested in the calculi for relevance logics while linguists will appreciate the detailed presentation of Lambek calculi and their extensions.
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.
Propositional and Predicate Calculus: A Model of Argument by Derek Goldrei Pdf
Designed specifically for guided independent study. Features a wealth of worked examples and exercises, many with full teaching solutions, that encourage active participation in the development of the material. It focuses on core material and provides a solid foundation for further study.
The Functional Interpretation of Logical Deduction by Anjolina G. de Oliveira Pdf
This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an OCyenrichedOCO system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing OCylabelsOCO is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.
Russell's Hidden Substitutional Theory by Gregory Landini Pdf
This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism.
A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf
Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
This book is concerned with the mathematical analysis of the concept of formal proof in classical logic, and records - in substance - a longer exercise in applied λ-calculus. Following colloquialisms going back to L. E. J. Brouwer, the objects of study in this enterprise are called witnesses. A witness is meant to represent the logical proof of a classically valid formula, in a given proof-context. The formalisms used to express witnesses and their equational behaviour are extensions of the pure `typed' λ-calculus, considered as equational theories. Formally, a witness is generated from decorated - or `typed' - witness variables, representing assumptions, and witness operators, representing logical rules of inference. The equational specifications serve to define the witness operators. In general, this can be done by ignoring the `typing', i.e., the logic formulas themselves. Model-theoretically, the witnesses are objects of an extensional Scott λ-model. The approach - called, generically, `witness theory' - is inspired from work of N. G. de Bruijn, on a mathematical theory of proving, done during the late 1960s and the early 1970s, at the University of Eindhoven (The Netherlands), and is similar to the approach behind the Curry-Howard Correspondence, familiar from intuitionistic logic. For the classical case, the decorations - oft called `types' - are classical logic formulas. At quantifier-free level, the equational theory of concern is the λ-calculus with `surjective pairing' and some subsystens thereof, appropriately decorated. The extension to propositional, first- and second-order quantifiers is straightforward. The book consists of a collection of notes and papers written and circulated during the last ten years, as a continuation of previous research done by the author during the nineteen eighties. Among other things, it includes a survey of the origins of modern proof theory - Frege to Gentzen - from a witness-theoretical point of view, as well as a characteristic application of witness theory to a practical logic problem concerning axiomatisability.
A Concise Introduction to Mathematical Logic by Wolfgang Rautenberg Pdf
While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.
