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Books on the topic 'First-order modal logic'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Fitting, Melvin. First-order modal logic. Kluwer Academic, 1998.

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2

Fitting, Melvin, and Richard L. Mendelsohn. First-Order Modal Logic. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5292-1.

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3

Weaver, George. Henkin-Keisler models. Kluwer Academic Publishers, 1997.

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4

Weaver, George. Henkin-Keisler Models {Mathematics and Its Applications (Kluwer Academic Publishers) ; V. 392}. Springer, 1997.

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5

Simple theories and hyperimaginaries. Cambridge University Press, 2011.

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6

Fitting, Melvin. First-Order Modal Logic. Springer, 2011.

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7

Corfield, David. Modal Homotopy Type Theory. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198853404.001.0001.

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In[KF1] 1914, in an essay entitled ‘Logic as the Essence of Philosophy’, Bertrand Russell promised to revolutionize philosophy by introducing there the ‘new logic’ of Frege and Peano: “The old logic put thought in fetters, while the new logic gives it wings.” A century later, this book proposes a comparable revolution with a newly emerging logic, modal homotopy type theory. Russell’s prediction turned out to be accurate. Frege’s first-order logic, along with its extension to modal logic, is to be found throughout anglophone analytic philosophy. This book provides a considerable array of eviden

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8

Bělohlávek, Radim, Joseph W. Dauben, and George J. Klir. Fuzzy Logic in the Narrow Sense. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780190200015.003.0004.

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The chapter examines the various propositional and predicate many-valued logics that were studied prior to the emergence of the concept of a fuzzy set in the mid-1960s, which led to the genesis of fuzzy logic in broad and narrow senses. Early ideas regarding formal systems of fuzzy logic allowed for deduction from partially true premises to partially true consequences, as suggested first by Goguen in the 1960s and further developed by Pavelka in the 1970s, and these ideas were developed from the 1990s onward. The systematic development of fuzzy logics based on t-norms and their residua, pursue

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9

Kishida, Kohei. Categories and Modalities. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0009.

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Category theory provides various guiding principles for modal logic and its semantic modeling. In particular, Stone duality, or “syntax-semantics duality”, has been a prominent theme in semantics of modal logic since the early days of modern modal logic. This chapter focuses on duality and a few other categorical principles, and brings to light how they underlie a variety of concepts, constructions, and facts in philosophical applications as well as the model theory of modal logic. In the first half of the chapter, I review the syntax-semantics duality and illustrate some of its functions in K

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10

Bell, John L. Categorical Logic and Model Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198748991.003.0007.

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The chapter begins with an introduction describing the development of categorical logic from the 1960s. The next section, `Categories and Deductive Systems’, describes the relationship between categories and propositional logic, while the ensuing section, `Functorial Semantics’, is devoted to Lawvere’s provision of the first-order theory of models with a categorical formulation. In the section `Local Set Theories and Toposes’ the categorical counterparts—toposes—to higher-order logic are introduced, along with their associated theories—local set theories. In the section `Models of First-Order

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11

Shapiro, Stewart. Higher‐order Logic. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0025.

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The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.

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12

Hellman, Geoffrey. Structuralism. Edited by Stewart Shapiro. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780195325928.003.0017.

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The main types of mathematical structuralism that have been proposed and developed to the point of permitting systematic and instructive comparison are four: structuralism based on model theory, carried out formally in set theory (e.g., first- or second-order Zermelo–Fraenkel set theory), referred to as STS (for set-theoretic structuralism); the approach of philosophers such as Shapiro and Resnik of taking structures to be sui generis universals, patterns, or structures in an ante rem sense (explained in this article), referred to as SGS (for sui generis structuralism); an approach based on ca

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13

Hedman, Shawn. A First Course in Logic. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198529804.001.0001.

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The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is

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14

Button, Tim, and Sean Walsh. Categoricity and the natural numbers. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0007.

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This chapter focuses on modelists who want to pin down the isomorphism type of the natural numbers. This aim immediately runs into two technical barriers: the Compactness Theorem and the Löwenheim-Skolem Theorem (the latter is proven in the appendix to this chapter). These results show that no first-order theory with an infinite model can be categorical; all such theories have non-standard models. Other logics, such as second-order logic with its full semantics, are not so expressively limited. Indeed, Dedekind's Categoricity Theorem tells us that all full models of the Peano axioms are isomor

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15

Button, Tim, and Sean Walsh. Boolean-valued structures. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198790396.003.0013.

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Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or

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16

Mackay, Ellen. Indecorum. Edited by Henry S. Turner. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199641352.013.16.

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This chapter examines the ways in which the traffic between life and stage is always governed by a set of social, ethical, and interpretive norms, the violation of which threatens to humiliate (at best) or physically harm (at worst) the spectator. More specifically, it considers the problem of epistemological decorum in early modern theatre and describes the figure of the female playgoer as a model for indecorous participation, one that knowingly exploits the tensions between actuality and theatricality in order to sustain the play while also revealing its dependence upon the absorption and ju

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17

Li, Quan. Using R for Data Analysis in Social Sciences. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190656218.001.0001.

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This book seeks to teach undergraduate and graduate students in social sciences how to use R to manage, visualize, and analyze data in order to answer substantive questions and replicate published findings. This book distinguishes itself from other introductory R or statistics books in three ways. First, targeting an audience rarely exposed to statistical programming, it adopts a minimalist approach and covers only the most important functions and skills in R that one will need for conducting reproducible research projects. Second, it emphasizes meeting the practical needs of students using R

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