Search results for 'introduction rules' (try it on Scholar)

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  1. Haydee Poubel & Luiz Pereira (1994). A Categorical Approach To Higher-Level Introduction And Elimination Rules. Reports on Mathematical Logic:3-19.
    A natural extension of Natural Deduction was defined by Schroder-Heister where not only formulas but also rules could be used as hypotheses and hence discharged. It was shown that this extension allows the definition of higher-level introduction and elimination schemes and that the set $\{ \vee, \wedge, \rightarrow, \bot \}$ of intuitionist sentential operators forms a {\it complete} set of operators modulo the higher level introduction and elimination schemes, i.e., that any operator whose introduction and elimination (...)
     
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  2.  24
    Deborah C. Smith (2001). Introduction and Elimination Rules Vs. Equivalence Rules in Systems of Formal Logic. Teaching Philosophy 24 (4):379-390.
    This paper argues that Lemmon-style proof systems have several pedagogical benefits over Copi-style systems . It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason (...)
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  3. Peter Achinstein (ed.) (2004). Science Rules: A Historical Introduction to Scientific Methods. Johns Hopkins University Press.
    Is there a universal set of rules for discovering and testing scientific hypotheses? Since the birth of modern science, philosophers, scientists, and other thinkers have wrestled with this fundamental question of scientific practice. Efforts to devise rigorous methods for obtaining scientific knowledge include the twenty-one rules Descartes proposed in his Rules for the Direction of the Mind and the four rules of reasoning that begin the third book of Newton's Principia , and continue today in debates (...)
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  4.  5
    Deborah C. Smith (2001). Introduction and Elimination Rules Vs. Equivalence Rules in Systems of Formal Logic: A Pedagogical Comparison. Teaching Philosophy 24 (4):379-390.
    This paper argues that Lemmon-style proof systems have several pedagogical benefits over Copi-style systems . It is argued that Lemmon-style systems are easier to learn as they do not require memorizing as many rules, they do not require learning the subtle distinction between a rule of inference and a rule of replacement, and deriving material conditionals is more straightforward. Finally, it is argued that the need for learning provisional assumptions in Lemmon-style rules is not a significant enough reason (...)
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  5.  10
    Giuseppina Mecchia (2007). Introduction to Christian Marazzi's "Rules for The Incommensurable". Substance 36 (1):10-11.
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  6.  11
    Richard Stoneman (1978). The Rules of Epinician Mary R Lefkowitz: The Victory Ode: An Introduction. Pp. 186. Park Ridge, N.J.: Noyes Press, 1976. Cloth, $18. [REVIEW] The Classical Review 28 (02):211-213.
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  7.  6
    Niels Öffenberger (1977). Logical Rules of Language. An Introduction to Logic. Philosophy and History 10 (2):165-166.
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  8.  1
    Alonzo Church (1968). Parkinson G. H. R.. Introduction. Leibniz, Logical Papers, A Selection Translated and Edited with an Introduction by Parkinson G. H. R., Clarendon Press, Oxford 1966, Pp. Ix–Ixv.Leibniz Gottfried Wilhelm. From Of the Art of Combination . English Translation of a Portion of 11 by Parkinson G. H. R.. Clarendon Press, Oxford 1966, Pp. 1–11.Leibniz Gottfried Wilhelm. Elements of a Calculus . English Translation of 114 by Parkinson G. H. R.. Clarendon Press, Oxford 1966, Pp. 17–24.Leibniz Gottfried Wilhelm. Rules From Which a Decision Can Be Made, by Means of Numbers, About the Validity of Inferences and About the Forms and Moods of Categorical Syllogisms . English Translation of 118 by Parkinson G. H. R.. Clarendon Press, Oxford 1966, Pp. 25–32.Leibniz Gottfried Wilhelm. A Specimen of the Universal Calculus . English Translation of 111 by Parkinson G. H. R.. Clarendon Press, Oxford 1966, Pp. 33–39.Leibniz Gottfried Wilhelm. Addenda to the Specimen of the Universal Calculus . English Transl. [REVIEW] Journal of Symbolic Logic 33 (1):139-140.
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  9.  1
    Andrew Hampton Gleeson, Introduction: Language Without Fantasy: Essays on Conversation, Rules and Use.
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  10. James M. DuBois (1993). An Introduction to Adolf Reinach's 'The Supreme Rules of Rational Inference According to Kant'. Aletheia 6:94.
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  11. Nissim Francez & Roy Dyckhoff (2012). A Note on Harmony. Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known (...)
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  12. Stephen Barker (2012). Expressivism About Making and Truth-Making. In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical Grounding: Understanding the Structure of Reality. Cambridge University Press 272-293.
    My goal is to illuminate truth-making by way of illuminating the relation of making. My strategy is not to ask what making is, in the hope of a metaphysical theory about is nature. It's rather to look first to the language of making. The metaphor behind making refers to agency. It would be absurd to suggest that claims about making are claims about agency. It is not absurd, however, to propose that the concept of making somehow emerges from some feature (...)
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  13.  12
    Peter Schroeder-Heister (2014). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica 102 (6):1185-1216.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational account of proof-theoretic harmony. With every set of (...)
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  14.  62
    L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. Mind 120 (480):1035-1051.
    The interplay of introduction and elimination rules for propositional connectives is often seen as suggesting a distinguished role for intuitionistic logic. We prove three formal results concerning intuitionistic propositional logic that bear on that perspective, and discuss their significance. First, for a range of connectives including both negation and the falsum, there are no classically or intuitionistically correct introduction rules. Second, irrespective of the choice of negation or the falsum as a primitive connective, classical and intuitionistic (...)
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  15.  19
    Wagner de Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.
    The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister (1990, 1991) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister (2007). Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the (...)
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  16.  42
    Ruy J. G. B. de Queiroz (2008). On Reduction Rules, Meaning-as-Use, and Proof-Theoretic Semantics. Studia Logica 90 (2):211-247.
    The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that (...)
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  17.  19
    Wagner Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.
    The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister . Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left (...) rules are admissible when the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. (shrink)
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  18. Robert May, Notes on Frege on Rules of Inference.
    1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. There are other ways of making transitions between propositions in proofs, but these are never labeled by Frege “rules of inference.” These pertain to scope of quantification, parsing of formulas, introduction of definitions, conventions for the use and replacement of the various letters, and certain structural reorganizations, ; cf. the list in Gg §48.
     
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  19.  13
    Bartosz Więckowski (2011). Rules for Subatomic Derivation. Review of Symbolic Logic 4 (2):219-236.
    In proof-theoretic semantics the meaning of an atomic sentence is usually determined by a set of derivations in an atomic system which contain that sentence as a conclusion (see, in particular, Prawitz, 1971, 1973). The paper critically discusses this standard approach and suggests an alternative account which proceeds in terms of subatomic introduction and elimination rules for atomic sentences. A simple subatomic normal form theorem by which this account of the semantics of atomic sentences and the terms from (...)
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  20. Amos Witztum (2008). Corporate Rules, Distributive Justice, and Efficiency. Business Ethics Quarterly 18 (1):85-116.
    The question whether corporations should be used as a means for administering distributive justice is crucial. There are two fundamental issues associated with this. Firstly, would the introduction of rules have any distributional effect? Secondly, what would be the efficiency cost? In this paper, we explore both questions with reference to a job-security corporate rule. We show that the job-security rule will always produce distributional consequences which are consistent with its objectives. However, whether or not it is a (...)
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  21. Barry Gower (2012). Scientific Method: A Historical and Philosophical Introduction. Routledge.
    The central theme running throughout this outstanding new survey is the nature of the philosophical debate created by modern science's foundation in experimental and mathematical method. More recently, recognition that reasoning in science is probabilistic generated intense debate about whether and how it should be constrained so as to ensure the practical certainty of the conclusions drawn. These debates brought to light issues of a philosophical nature which form the core of many scientific controversies today. _Scientific Method: A Historical and (...)
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  22.  30
    William P. Bechtel (1988). Connectionism and Rules and Representation Systems: Are They Compatible? Philosophical Psychology 1 (1):5-16.
    The introduction of connectionist or parallel distributed processing (PDP) systems to model cognitive functions has raised the question of the possible relations between these models and traditional information processing models which employ rules to manipulate representations. After presenting a brief account of PDP models and two ways in which they are commonly interpreted by those seeking to use them to explain cognitive functions, I present two ways one might relate these models to traditional information processing models and so (...)
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  23. Peter Milne (1994). Classical Harmony: Rules of Inference and the Meaning of the Logical Constants. Synthese 100 (1):49 - 94.
    The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they (...)
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  24. Helen Frowe (2011). The Ethics of War and Peace: An Introduction. Routledge.
    When is it right to go to war? When is a war illegal? What are the rules of engagement? What should happen when a war is over? How should we view terrorism? _The Ethics of War and Peace_ is a fresh and contemporary introduction to one of the oldest but still most relevant ethical debates. It introduces students to contemporary Just War Theory in a stimulating and engaging way, perfect for those approaching the topic for the first time. (...)
     
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  25.  37
    Gordon P. Baker (2010). Wittgenstein-- Rules, Grammar, and Necessity: Essays and Exegesis of 185-242. Wiley-Blackwell.
    Analytical commentary -- Fruits upon one tree -- The continuation of the early draft into philosophy of mathematics -- Hidden isomorphism -- A common methodology -- The flatness of philosophical grammar -- Following a rule 185-242 -- Introduction to the exegesis -- Rules and grammar -- The tractatus and rules of logical syntax -- From logical syntax to philosophical grammar -- Rules and rule-formulations -- Philosophy and grammar -- The scope of grammar -- Some morals -- (...)
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  26.  14
    Peter Schroeder-Heister (2011). Implications-as-Rules Vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW] Journal of Philosophical Logic 40 (1):95 - 101.
    The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form.
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  27.  14
    Richard Bornat (2005). Proof and Disproof in Formal Logic: An Introduction for Programmers. New Yorkoxford University Press.
    Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. (...)
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  28.  28
    Julien Murzi & Massimiliano Carrara (2015). Paradox and Logical Revision. A Short Introduction. Topoi 34 (1):7-14.
    Logical orthodoxy has it that classical first-order logic, or some extension thereof, provides the right extension of the logical consequence relation. However, together with naïve but intuitive principles about semantic notions such as truth, denotation, satisfaction, and possibly validity and other naïve logical properties, classical logic quickly leads to inconsistency, and indeed triviality. At least since the publication of Kripke’s Outline of a theory of truth , an increasingly popular diagnosis has been to restore consistency, or at least non-triviality, by (...)
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  29.  24
    Marie Duží & Bjørn Jespersen (2015). Introduction. Synthese 192 (3):525-534.
    The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any (...)
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  30.  3
    G. M. Prosperi (2016). Introduction of a Classical Level in Quantum Theory. Foundations of Physics 46 (11):1426-1460.
    In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to quantum mechanics. The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. In fact the main aim (...)
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  31. Kazuo Tanaka (1997). An Introduction to Fuzzy Logic for Practical Applications. Springer.
    Fuzzy logic has become an important tool for a number of different applications ranging from the control of engineering systems to artificial intelligence. In this concise introduction, the author presents a succinct guide to the basic ideas of fuzzy logic, fuzzy sets, fuzzy relations, and fuzzy reasoning, and shows how they may be applied. The book culminates in a chapter which describes fuzzy logic control: the design of intelligent control systems using fuzzy if-then rules which make use of (...)
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  32.  35
    Frederic B. Fitch (1973). Natural Deduction Rules for English. Philosophical Studies 24 (2):89 - 104.
    A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, (...)
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  33.  16
    David Botting (2014). Do Syllogisms Commit the Petitio Principii? The Role of Inference-Rules in Mill's Logic of Truth. History and Philosophy of Logic 35 (3):237-247.
    It is a common complaint that the syllogism commits a petitio principii. This is discussed extensively by John Stuart Mill in ‘A System of Logic’ [1882. Eighth Edition, New York: Harper and Brothers] but is much older, being reported in Sextus Empiricus in chapter 17 of the ‘Outlines of Pyrrhonism’ [1933. in R. G. Bury, Works, London and New York: Loeb Classical Library]. Current wisdom has it that Mill gives an account of the syllogism that avoids being a petitio by (...)
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  34.  7
    Fabrice Pataut, Logical Revisionism: Logical Rules Vs. Structural Rules.
    As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. Intuitionistic logic (...)
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  35.  7
    David C. Makinson, Intelim Rules for Classical Connectives.
    We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also (...)
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  36.  5
    Fabrice Pataut, Antirealism, Strict Finitism and Structural Rules.
    According to semantic antirealism, intuitionistic logic satisfies the requirement that truth should be constrained by provability in principle. Some philosophers have argued that semantic antirealism must be committed to effective provability and that the commitment leads to a stronger kind of logical revisionism exemplified by substructural logics. I shall take into account two different kinds of reply. The first is concerned with meaning per se and grasp or fixing of meaning. It rests on the idea that if we have a (...)
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  37.  14
    Tomasz Furmanowski (1983). The Logic of Algebraic Rules as a Generalization of Equational Logic. Studia Logica 42 (2-3):251 - 257.
    In this paper we start an investigation of a logic called the logic of algebraic rules. The relation of derivability of this logic is defined on universal closures of special disjunctions of equations extending the relation of derivability of the usual equational logic. The paper contains some simple theorems and examples given in justification for the introduction of our logic. A number of open questions is posed.
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  38.  10
    Pablo E. Navarro (1993). Promulgation and Derogation of Legal Rules. Law and Philosophy 12 (4):385 - 394.
    In this paper, I consider some problems concerning the structure of legal systems. In order to do this, I basically analyze the promulgation and derogation of legal rules. Frequently, promulgation has been referred to as the introduction of a rule into, and derogation as the removal of a rule from, a normative system. I try to show that there is more to it than that. One of the main ideas of the paper is that the enactment or derogation (...)
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  39.  1
    John Vickers (2002). Reflection Without Rules: Economic Methodology and Contemporary Science Theory. [REVIEW] Isis: A Journal of the History of Science 93:350-350.
    This fine book is a comprehensive and careful survey of the current situation in the methodology of economics. It is directed primarily at economists and students of economics. Indeed, the economist who reads it with the care it deserves will have a better grip on matters of methodology in economics than most philosophers of science, but philosophers and historians of science will also find the work rewarding and interesting. Though a few examples may be beyond the economically untutored reader, they (...)
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  40.  3
    Östen Dahl (1988). The Role of Deduction Rules in Semantics. Journal of Semantics 6 (1):1-18.
    The distinction between ‘partial’ and ‘total’ interpretations (models) is discussed and related to the distinction between proof-theoretical and model-theoretical treatments of logic. It is claimed that there is a parallel between the construction of a proof based on a set of premises and e.g. the production of a natural-language text which is based on information in some kind of data-base. The main part of the paper is devoted to a discussion of the relations between the deduction rules traditionally associated (...)
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  41. Mark Alfano (2016). Moral Psychology: An Introduction. Polity.
    This book provides a rich, systematic, and accessible introduction to moral psychology, aimed at undergraduate philosophy and psychology majors. There are eight chapters, in addition to a short introduction, prospective conclusion, and extensive bibliography. The recipe for each chapter will be: a) to introduce a philosophical topic (e.g., altruism, virtue, preferences, rules) and some prominent positions on it, without assuming prior acquaintance on the part of the reader b) to canvass and explain the relevance of a particular (...)
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  42. Helen Frowe (2013). The Ethics of War and Peace: An Introduction. Routledge.
    When is it right to go to war? When is a war illegal? What are the rules of engagement? What should happen when a war is over? How should we view terrorism? _The Ethics of War and Peace_ is a fresh and contemporary introduction to one of the oldest but still most relevant ethical debates. It introduces students to contemporary Just War Theory in a stimulating and engaging way, perfect for those approaching the topic for the first time. (...)
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  43. Jordi Galí (2008). Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework. Princeton University Press.
    The New Keynesian framework has emerged as the workhorse for the analysis of monetary policy and its implications for inflation, economic fluctuations, and welfare. It is the backbone of the new generation of medium-scale models under development at major central banks and international policy institutions, and provides the theoretical underpinnings of the inflation stability-oriented strategies adopted by most central banks throughout the industrialized world. This graduate-level textbook provides an introduction to the New Keynesian framework and its applications to monetary (...)
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  44.  61
    Barry Gower (1996). Scientific Method: A Historical and Philosophical Introduction. Routledge.
    The central theme running throughout this outstanding new survey is the nature of the philosophical debate created by modern science's foundation in experimental and mathematical method. More recently, recognition that reasoning in science is probabilistic generated intense debate about whether and how it should be constrained so as to ensure the practical certainty of the conclusions drawn. These debates brought to light issues of a philosophical nature which form the core of many scientific controversies today. _Scientific Method: A Historical and (...)
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  45. Robert Nola & Howard Sankey (2007). Theories of Scientific Method: An Introduction. Routledge.
    What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit about what this (...)
     
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  46. Robert Nola & Howard Sankey (2014). Theories of Scientific Method: An Introduction. Routledge.
    What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit about what this (...)
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  47. J. Philip Wogaman (2009). Moral Dilemmas: An Introduction to Christian Ethics. Westminster John Knox Press.
    Introduction -- Part I: Starting points -- Some decisions are easier than others -- Easy decisions -- More difficult decisions -- Moral dilemmas -- The deep basis of the moral life -- Practical decision making -- Why ethics is ultimately religious -- Acceptable and unacceptable forms of revelation -- The useful incomplete ness of religious tradition -- Moral virtue and character -- Intuition and deliberation in moral decision-making -- The absolute and the relative in moral life -- Have we (...)
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  48.  16
    Douglas Walton (2016). Some Artificial Intelligence Tools for Argument Evaluation: An Introduction. Argumentation 30 (3):317-340.
    Even though tools for identifying and analyzing arguments are now in wide use in the field of argumentation studies, so far there is a paucity of resources for evaluating real arguments, aside from using deductive logic or Bayesian rules that apply to inductive arguments. In this paper it is shown that recent developments in artificial intelligence in the area of computational systems for modeling defeasible argumentation reveal a different approach that is currently making interesting progress. It is shown how (...)
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  49.  21
    Nissim Francez (2014). Harmony in Multiple-Conclusion Natural-Deduction. Logica Universalis 8 (2):215-259.
    The paper studies the extension of harmony and stability, major themes in proof-theoretic semantics, from single-conclusion natural-deduction systems to multiple -conclusions natural-deduction, independently of classical logic. An extension of the method of obtaining harmoniously-induced general elimination rules from given introduction rules is suggested, taking into account sub-structurality. Finally, the reductions and expansions of the multiple -conclusions natural-deduction representation of classical logic are formulated.
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  50.  20
    Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
    A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that (...)
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