Logic and Implication

Logic and Implication

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  • Author: Petr Cintula
  • Publisher: Springer Nature
  • ISBN: 3030856755
  • Category : Philosophy
  • Languages : en
  • Pages : 465

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.


The Semantics and Proof Theory of the Logic of Bunched Implications

The Semantics and Proof Theory of the Logic of Bunched Implications

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  • Author: David J. Pym
  • Publisher: Springer Science & Business Media
  • ISBN: 9401700915
  • Category : Mathematics
  • Languages : en
  • Pages : 323

This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.


Foundations of Logico-Linguistics

Foundations of Logico-Linguistics

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  • Author: W.S. Cooper
  • Publisher: Springer Science & Business Media
  • ISBN: 9400998201
  • Category : Language Arts & Disciplines
  • Languages : en
  • Pages : 264

In 1962 a mimeographed sheet of paper fell into my possession. It had been prepared by Ernest Adams of the Philosophy Department at Berkeley as a handout for a colloquim. Headed 'SOME FALLACIES OF FORMAL LOGIC' it simply listed eleven little pieces of reasoning, all in ordinary English, and all absurd. I still have the sheet, and quote a couple of the arguments here to give the idea. • If you throw switch S and switch T, the motor will start. There fore, either if you throw switch S the motor will start, or, if you throw switch T the motor will start . • It is not the case that if John passes history he will graduate. Therefore, John will pass history. The disconcerting thing about these inferences is, of course, that under the customary truth-functional interpretation of and, or, not, and if-then, they are supposed to be valid. What, if anything, is wrong? At first I was not disturbed by the examples. Having at that time consider able personal commitment to rationality in general and formal logic in par ticular, I felt it my duty and found myself easily able (or so I thought) to explain away most of them. But on reflection I had to admit that my expla nations had an ad hoc character, varying suspiciously from example to example.


The Formalization of Implication in Propositional Logic

The Formalization of Implication in Propositional Logic

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  • Author: Patrick Foster Schindler
  • Publisher:
  • ISBN:
  • Category :
  • Languages : en
  • Pages :

"This thesis presents the results or an attempt to isolate and give an axiomatic basis for the pure-implication fragment or each or several logical systems. C. I. Lewis points out that exact logic may be taken as a canon or deductive inference, and that the chief business of a canon or deduction is to delineate correctly the properties of the relation of 'implication'. It seems clear, then, that criticism or any logical calculus must include consideration of just what properties are imputed to the relation of 'implication' by that calculus." --


Logic, Language, and Meaning, Volume 1

Logic, Language, and Meaning, Volume 1

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  • Author: L. T. F. Gamut
  • Publisher: University of Chicago Press
  • ISBN: 022679167X
  • Category : Philosophy
  • Languages : en
  • Pages : 297

Although the two volumes of Logic, Language, and Meaning can be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1, Introduction to Logic, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained.


The Art of Logic

The Art of Logic

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  • Author: Eugenia Cheng
  • Publisher: Profile Books
  • ISBN: 1782834427
  • Category : Mathematics
  • Languages : en
  • Pages : 336

Emotions are powerful. In newspaper headlines and on social media, they have become the primary way of understanding the world. But strong feelings make it more difficult to see the reality behind the rhetoric. In The Art of Logic, Eugenia Cheng shows how mathematical logic can help us see things more clearly - and know when politicians and companies are trying to mislead us. First Cheng explains how to use black-and-white logic to illuminate the world around us, giving us new insight into thorny political questions like public healthcare, Black Lives Matter and Brexit. Then she explains how logic and emotions, used side-by-side, can help us not only to be more rational individuals, but also to live more thoughtfully. Clear-sighted, revelatory and filled with useful real-life examples of logic and illogic at work, The Art of Logic is an essential guide to decoding modern life.


Logical Studies

Logical Studies

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  • Author: Georg Henrik Von Wright
  • Publisher: Psychology Press
  • ISBN: 9780415225472
  • Category : Logic
  • Languages : en
  • Pages : 208

First Published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.


Language and Logic

Language and Logic

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  • Author: Johan van der Auwera
  • Publisher: John Benjamins Publishing
  • ISBN: 9027279543
  • Category : Philosophy
  • Languages : en
  • Pages : 256

In this volume Van der Auwera attempts to clarify the idea that language reflects both mind and reality and to elucidate the reflection idea by turning it into the cornerstone of a linguistic theory of meaning.


Problems of the Logic of Scientific Knowledge

Problems of the Logic of Scientific Knowledge

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  • Author: P.V. Tavanec
  • Publisher: Springer Science & Business Media
  • ISBN: 9401033935
  • Category : Science
  • Languages : en
  • Pages : 442


Larisa Maksimova on Implication, Interpolation, and Definability

Larisa Maksimova on Implication, Interpolation, and Definability

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  • Author: Sergei Odintsov
  • Publisher: Springer
  • ISBN: 3319699172
  • Category : Philosophy
  • Languages : en
  • Pages : 371

This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original contributions from experts in the field of non-classical logics. Professor Larisa Maksimova's influential work involved combining methods of algebraic and relational semantics. Readers will be able to trace both influences on her work, and the ways in which her work has influenced other logicians. In the historical part of this book, it is possible to trace important milestones in Maksimova’s career. Early on, she developed an algebraic semantics for relevance logics and relational semantics for the logic of entailment. Later, Maksimova discovered that among the continuum of superintuitionisitc logics there are exactly three pretabular logics. She went on to obtain results on the decidability of tabularity and local tabularity problems for superintuitionistic logics and for extensions of S4. Further investigations by Maksimova were aimed at the study of fundamental properties of logical systems (different versions of interpolation and definability, disjunction property, etc.) in big classes of logics, and on decidability and recognizability of such properties. To this end she determined a powerful combination of algebraic and semantic methods, which essentially determine the modern state of investigations in the area, as can be seen in the later chapters of this book authored by leading experts in non-classical logics. These original contributions bring the reader up to date on the very latest work in this field.