A System of Formal Logic. Pt. I: The Problem of Single Implication PDF Download
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Author: Henrt Bradford Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 60
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Book Description
Author: Henrt Bradford Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 60
Get Book Here
Book Description
Author:
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 1092
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Book Description
Covers topics in philosophy, psychology, and scientific methods. Vols. 31- include "A Bibliography of philosophy," 1933-
Author: L.H. Hackstaff
Publisher: Springer Science & Business Media
ISBN: 9401035474
Category : Philosophy
Languages : en
Pages : 367
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Book Description
The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.
Author: Jacob Gould Schurman
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 634
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Book Description
An international journal of general philosophy.
Author: Henry Bradford Smith
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 144
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Book Description
Author: Richard C. Jeffrey
Publisher:
ISBN:
Category : Philosophy
Languages : en
Pages : 232
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Book Description
The first beginning logic text to employ the tree method--a complete formal system of first-order logic that is remarkably easy to understand and use--this text allows students to take control of the nuts and bolts of formal logic quickly, and to move on to more complex and abstract problems. The tree method is elaborated in manageable steps over five chapters, in each of which its adequacy is reviewed; soundness and completeness proofs are extended at each step, and the decidability proof is extended at the step from truth functions to the logic of nonoverlapping quantifiers with a single variable, after which undecidability is demonstrated by example. The first three chapters are bilingual, with arguments presented twice, in logical notation and in English. The last three chapters consider the discoveries defining the scope and limits of formal methods that marked logic¿s coming of age in the 20th century: Godel¿s completeness and incompleteness theorems for first and second-order logic, and the Church-Turing theorem on the undecidability of first-order logic. This new edition provides additional problems, solutions to selected problems, and two new Supplements: Truth-Functional Equivalence reinstates material on that topic from the second edition that was omitted in the third, and Variant Methods, in which John Burgess provides a proof regarding the possibility of modifying the tree method so that it will always find a finite model when there is one, and another, which shows that a different modification?once contemplated by Jeffrey--can result in a dramatic speed--up of certain proofs.
Author: J. Barkley Rosser
Publisher: Courier Dover Publications
ISBN: 0486468984
Category : Mathematics
Languages : en
Pages : 587
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Book Description
Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
Author: David Agler
Publisher: Rowman & Littlefield Publishers
ISBN: 144221743X
Category : Philosophy
Languages : en
Pages : 397
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Book Description
Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Symbolic Logic: Syntax, Semantics, and Proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems, propositional and predicate logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs. This text makes this often confounding topic much more accessible with step-by-step example proofs, chapter glossaries of key terms, hundreds of homework problems and solutions for practice, and suggested further readings.
Author: Gillian K. Russell
Publisher: Oxford University Press
ISBN: 0192874837
Category : Philosophy
Languages : en
Pages : 316
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Book Description
A barrier to entailment exists if you can't get conclusions of a certain kind from premises of another. One of the most famous barriers in philosophy is Hume's Law, which says that you can't get normative conclusions from descriptive premises, or in slogan form: you can't get an ought from an is. This barrier is highly controversial, and many famous counterexamples were proposed in the last century. But there are other barriers which function almost as philosophical platitudes: no Universal conclusions from Particular premises, no Future conclusions from premises about the Past, and no claims that attribute Necessity from premises that merely tell us how things happen to be in the Actual world. Barriers to Entailment proposes a unified logical account of five barriers that have played important roles in philosophy, in the process showing how to diagnose proposed counterexamples and arguing that the case for Hume's Law is as strong as that for the platitudinous barriers. The first two parts of the book employ techniques from formal logic, but present them in an accessible way, suitable for any reader with some background in first-order model theory (of the kind that might be taught in a first class in logic). Gillian Russell introduces tense, modal, indexical, and deontic formal logics, but always avoids unneeded complexity. Each barrier is connected to broader philosophical topics: universality, time, necessity, context-sensitivity, and normativity. Russell brings out under-recognised connections between the domains and lays the groundwork for further work at the intersections. The last part of the book transposes the formal work to informal barrier theses in the philosophy of language, in the process doing new work on the concept of logical consequence, and providing new responses to proposed informal counterexamples to Hume's Law which employ hard-to-formalise tools from natural language, such as speech acts and thick normative expressions.
Author: P.J. Fleming
Publisher: Elsevier
ISBN: 1483298256
Category : Technology & Engineering
Languages : en
Pages : 279
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Book Description
Computer scientists have long appreciated that the relationship between algorithms and architecture is crucial. Broadly speaking the more specialized the architecture is to a particular algorithm then the more efficient will be the computation. The penalty is that the architecture will become useless for computing anything other than that algorithm. This message holds for the algorithms used in real-time automatic control as much as any other field. These Proceedings will provide researchers in this field with a useful up-to-date reference source of recent developments.
