Search results for 'Inference Rule' (try it on Scholar)

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  1. Ronald Fagin, Joseph Y. Halpern & Moshe Y. Vardi (1992). What is an Inference Rule? Journal of Symbolic Logic 57 (3):1018-1045.
    What is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference $(\sigma \vdash_\mathrm{v} \varphi$ if for every substitution $\tau$, the validity of $\tau \lbrack\sigma\rbrack$ entails the validity of $\tau\lbrack\varphi\rbrack)$, and truth inference $(\sigma \vdash_\mathrm{t} \varphi$ if for every substitution $\tau$, the truth of $\tau\lbrack\sigma\rbrack$ entails the truth of $\tau\lbrack\varphi\rbrack)$. In this paper we introduce a general semantic framework that allows us to investigate (...)
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  2.  33
    Jean-Baptiste Van der Henst (2002). Mental Model Theory Versus the Inference Rule Approach in Relational Reasoning. Thinking and Reasoning 8 (3):193 – 203.
    Researchers currently working on relational reasoning typically argue that mental model theory (MMT) is a better account than the inference rule approach (IRA). They predict and observe that determinate (or one-model) problems are easier than indeterminate (or two-model) problems, whereas according to them, IRA should lead to the opposite prediction. However, the predictions attributed to IRA are based on a mistaken argument. The IRA is generally presented in such a way that inference rules only deal with determinate (...)
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  3. Manuel Leon & Norman H. Anderson (1974). A Ratio Rule From Integration Theory Applied to Inference Judgments. Journal of Experimental Psychology 102 (1):27.
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  4.  67
    M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction. Studia Logica 92 (3):281 - 364.
    We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i , j =?. The method allows us to decide whether to declare a i , j = 0 or a i , j = (...)
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  5.  16
    Igor Douven & Sylvia Wenmackers (forthcoming). Inference to the Best Explanation Versus Bayes’s Rule in a Social Setting. British Journal for the Philosophy of Science:axv025.
    This article compares inference to the best explanation with Bayes’s rule in a social setting, specifically, in the context of a variant of the Hegselmann–Krause model in which agents not only update their belief states on the basis of evidence they receive directly from the world, but also take into account the belief states of their fellow agents. So far, the update rules mentioned have been studied only in an individualistic setting, and it is known that in such (...)
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  6. M. Abraham, Dov M. Gabbay & U. Schild (2009). Analysis of the Talmudic Argumentum A Fortiori Inference Rule Using Matrix Abduction. Studia Logica 92 (3):281-364.
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  7.  16
    Ned Markosian (1988). On Ockham's Supposition Theory and Karger's Rule of Inference. Franciscan Studies 48 (1):40-52.
    Elizabeth Karger has suggested an interpretation of Ockham's theory of the modes of common personal supposition ("TM") according to which the purpose of TM is to provide certain distinctions that Ockham will use in formulating a unified theory of immediate inference among certain kinds of sentences. Karger presents a single, powerful rule of inference that incorporates TM distinctions and that is meant to codify Ockham's theory of immediate inference. I raise an objection to Karger's rule, (...)
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  8.  15
    J. A. Kalman (1983). Condensed Detachment as a Rule of Inference. Studia Logica 42 (4):443 - 451.
    Condensed detachment is usually regarded as a notation, and defined by example. In this paper it is regarded as a rule of inference, and rigorously defined with the help of the Unification Theorem of J. A. Robinson. Historically, however, the invention of condensed detachment by C. A. Meredith preceded Robinson's studies of unification. It is argued that Meredith's ideas deserve recognition in the history of unification, and the possibility that Meredith was influenced, through ukasiewicz, by ideas of Tarski (...)
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  9.  26
    Henry E. Kyburg Jr (1997). The Rule of Adjunction and Reasonable Inference. Journal of Philosophy 94 (3):109-125.
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  10.  43
    Gary Jones & Frank E. Ritter (2003). Production Systems and Rule‐Based Inference. In L. Nadel (ed.), Encyclopedia of Cognitive Science. Nature Publishing Group
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  11. R. B. Angell (1960). The Sentential Calculus Using Rule of Inference Re. Journal of Symbolic Logic 25 (2):143 -.
  12.  72
    R. Bradshaw Angell (1960). Note on a Less Restricted Type of Rule of Inference. Mind 69 (274):253-255.
  13. Alonzo Church (1975). Review: R. Bradshaw Angell, Note on a Less Restricted Type of Rule of Inference; R. B. Angell, The Sentential Calculus Using Rule of Inference $R_e$. [REVIEW] Journal of Symbolic Logic 40 (4):602-603.
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  14. E. Henry Jr (forthcoming). Kyburg.'The Rule of Adjunction and Reasonable Inference,'. Journal of Philosophy.
  15.  20
    Ivo Pezlar (2014). Towards a More General Concept of Inference. Logica Universalis 8 (1):61-81.
    The main objective of this paper is to sketch unifying conceptual and formal framework for inference that is able to explain various proof techniques without implicitly changing the underlying notion of inference rules. We base this framework upon the so-called two-dimensional, i.e., deduction to deduction, account of inference introduced by Tichý in his seminal work The Foundation’s of Frege’s Logic (1988). Consequently, it will be argued that sequent calculus provides suitable basis for such general concept of (...) and therefore should not be seen just as technical tool, but philosophically well-founded system that can rival natural deduction in terms of its “naturalness”. (shrink)
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  16.  2
    Vladimir V. Rybakov (1993). Intermediate Logics Preserving Admissible Inference Rules of Heyting Calculus. Mathematical Logic Quarterly 39 (1):403-415.
    The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe (...)
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  17.  10
    Athanassios Tzouvaras (1996). Aspects of Analytic Deduction. Journal of Philosophical Logic 25 (6):581 - 596.
    Let ⊢ be the ordinary deduction relation of classical first-order logic. We provide an "analytic" subrelation ⊢a of ⊢ which for propositional logic is defined by the usual "containment" criterion Γ ⊢a φ iff Γ⊢φ and Atom(φ) ⊆ Atom(Γ), whereas for predicate logic, ⊢a is defined by the extended criterion Γ⊢aφ iff Γ⊢aφ and Atom(φ) ⊆' Atom(Γ), where Atom(φ) ⊆' Atom(Γ) means that every atomic formula occurring in φ "essentially occurs" also in Γ. If Γ, φ are quantifier-free, then the (...)
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  18.  8
    W. Degen & J. Johannsen (2000). Cumulative Higher-Order Logic as a Foundation for Set Theory. Mathematical Logic Quarterly 46 (2):147-170.
    The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable (...)
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  19.  6
    Mathieu Marion (2001). Qu'est-ce que l'inférence ? Une relecture du Tractatus logico-philosophicus. Archives de Philosophie 3:545-567.
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  20.  4
    J. A. Judge (forthcoming). Does the ‘Missing Fundamental’ Require an Inferentialist Explanation? Topoi:1-11.
    In arbitrating between representational and relational theories of perception, perceptual illusions—cases in which a subject’s perceptual experience diverges from the way the world really is—constitute an important battleground. The debate has, however, been dominated by discussions of visual perception. In attempting to extend the debate to audition, it is appropriate to start by considering what is thought to be a key case of auditory illusion. I consider the phenomenon of the ‘missing fundamental’, as well as examining a notion that is (...)
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  21.  19
    Tor Sandqvist (2012). Acceptance, Inference, and the Multiple-Conclusion Sequent. Synthese 187 (3):913-924.
    This paper offers an interpretation of multiple-conclusion sequents as a kind of meta-inference rule: just as single-conclusion sequents represent inferences from sentences to sentences, so multiple-conclusion sequents represent a certain kind of inference from single-conclusion sequents to single-conclusion sequents. The semantics renders sound and complete the standard structural rules of reflexivity, monotonicity (or thinning), and transitivity (or cut). The paper is not the first one to attempt to account for multiple-conclusion sequents without invoking notions of truth or (...)
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  22. Alex Citkin (2015). Characteristic Inference Rules. Logica Universalis 9 (1):27-46.
    The goal of this paper is to generalize a notion of quasi-characteristic inference rule in the following way: with every finite partial algebra we associate a rule, and study the properties of these rules. We prove that any equivalential logic can be axiomatized by such rules. We further discuss the correlations between characteristic rules of the finite partial algebras and canonical rules. Then, with every algebra we associate a set of characteristic rules that correspond to each finite (...)
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  23.  3
    Emil Jeřábek (2009). Canonical Rules. Journal of Symbolic Logic 74 (4):1171 - 1205.
    We develop canonical rules capable of axiomatizing all systems of multiple-conclusion rules over K4 or IPC, by extension of the method of canonical formulas by Zakharyaschev [37]. We use the framework to give an alternative proof of the known analysis of admissible rules in basic transitive logics, which additionally yields the following dichotomy: any canonical rule is either admissible in the logic, or it is equivalent to an assumption-free rule. Other applications of canonical rules include a generalization of (...)
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  24.  9
    Robert C. Pinto (2006). Evaluating Inferences: The Nature and Role of Warrants. Informal Logic 26 (3):287-317.
    Following David Hitchcock and Stephen Toulmin, this paper takes warrants to be material inference rules. It offers an account of the form such rules should take that is designed (a) to implement the idea that an argument/inference is valid only if it is entitlement preserving and (b) to support a qualitative version of evidence proportionalism. It attempts to capture what gives warrants their normative force by elaborating a concept of reliability tailored to its account of the form (...)
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  25.  53
    David Makinson (2012). Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference. Synthese 186 (2):511-529.
    We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A (...)
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  26. Markos Valaris (forthcoming). What Reasoning Might Be. Synthese:1-18.
    The philosophical literature on reasoning is dominated by the assumption that reasoning is essentially a matter of following rules. This paper challenges this view, by arguing that it misrepresents the nature of reasoning as a personal level activity. Reasoning must reflect the reasoner’s take on her evidence. The rule-following model seems ill-suited to accommodate this fact. Accordingly, this paper suggests replacing the rule-following model with a different, semantic approach to reasoning.
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  27.  13
    Valentin Goranko (1998). Axiomatizations with Context Rules of Inference in Modal Logic. Studia Logica 61 (2):179-197.
    A certain type of inference rules in modal logics, generalizing Gabbay's Irreflexivity rule, is introduced and some general completeness results about modal logics axiomatized with such rules are proved.
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  28.  23
    James B. Freeman (2001). Argument Structure and Disciplinary Perspective. Argumentation 15 (4):397-423.
    Many in the informal logic tradition distinguish convergent from linked argument structure. The pragma-dialectical tradition distinguishes multiple from co-ordinatively compound argumentation. Although these two distinctions may appear to coincide, constituting only a terminological difference, we argue that they are distinct, indeed expressing different disciplinary perspectives on argumentation. From a logical point of view, where the primary evaluative issue concerns sufficient strength of support, the unit of analysis is the individual argument, the particular premises put forward to support a given conclusion. (...)
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  29.  7
    P. Roger Turner (2015). Kearns on Rule A. Philosophia 43 (1):205-215.
    The so-called Direct Argument for the incompatibility of moral responsibility and causal determinism depends on a rule of inference called Rule A, a rule that says no one is even partly morally responsible for a necessary truth. While most philosophers think that Rule A is valid, Stephen Kearns has recently offered several alleged counterexamples to the rule. In the paper, I show that Kearns’ counterexamples are unsuccessful.
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  30.  1
    Sergei Odintsov & Vladimir Rybakov (2015). Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility. Logica Universalis 9 (1):93-120.
    Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak (...)
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  31. Timothy Day & Harold Kincaid (1994). Putting Inference to the Best Explanation in its Place. Synthese 98 (2):271-295.
    This paper discusses the nature and the status of inference to the best explanation. We outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all ; argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule ; sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be ; show how (...)
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  32. Vladimir V. Rybakov (1992). Rules of Inference with Parameters for Intuitionistic Logic. Journal of Symbolic Logic 57 (3):912-923.
    An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the (...)
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  33.  10
    Marc Champagne (2015). Sound Reasoning : Prospects and Challenges of Current Acoustic Logics. Logica Universalis 9 (3):331-343.
    Building on the notational principles of C. S. Peirce’s graphical logic, Pietarinen has tried to develop a propositional logic unfolding in the medium of sound. Apart from its intrinsic interest, this project serves as a concrete test of logic’s range. However, I argue that Pietarinen’s inaugural proposal, while promising, has an important shortcoming, since it cannot portray double-negation without thereby portraying a contradiction.
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  34.  32
    Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.
    An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily equal to (...)
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  35. Jesús P. Zamora Bonilla (2002). Scientific Inference and the Pursuit of Fame: A Contractarian Approach. Philosophy of Science 69 (2):300-323.
    Methodological norms are seen as rules defining a competitive game, and it is argued that rational recognition‐seeking scientists can reach a collective agreement about which specific norms serve better their individual interests, especially if the choice is made 'under a veil of ignorance', i.e. , before knowing what theory will be proposed by each scientist. Norms for theory assessment are distinguished from norms for theory choice (or inference rules), and it is argued that pursuit of recognition only affects this (...)
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  36.  6
    Jesús P. Zamora Bonilla (2002). Scientific Inference and the Pursuit of Fame: A Contractarian Approach. Philosophy of Science 69 (2):300-323.
    Methodological norms are seen as rules defining a competitive game, and it is argued that rational recognition-seeking scientists can reach a collective agreement about which specific norms serve better their individual interests, especially if the choice is made `under a veil of ignorance', i.e. , before knowing what theory will be proposed by each scientist. Norms for theory assessment are distinguished from norms for theory choice (or inference rules), and it is argued that pursuit of recognition only affects this (...)
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  37.  1
    V. V. Rybakov (2001). Construction of an Explicit Basis for Rules Admissible in Modal System S4. Mathematical Logic Quarterly 47 (4):441-446.
    We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.
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  38.  29
    Herbert Feigl (ed.) (1958). Concepts, Theories, And The Mind-Body Problem. University of Minnesota Press.
    PAUL OPPENHEIM and HILARY PUTNAM Unity of Science as a Working Hypothesis 1. Introduction 1.1. The expression "Unity of Science" is often encountered, ...
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  39.  1
    Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner (1999). On Finite Model Property for Admissible Rules. Mathematical Logic Quarterly 45 (4):505-520.
    Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...)
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  40.  12
    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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  41.  20
    Earl Conee & Richard Feldman (1983). Stich and Nisbett on Justifying Inference Rules. Philosophy of Science 50 (2):326-331.
    Stich and Nisbett offer an analysis of the concept of a justified inference rule, building upon the efforts of Goodman. They fault Goodman's view on the grounds that it is incompatible with some recent psychological research on reasoning. We criticize their proposal by arguing that it is subject to much the same objections as those they raise against other accounts.
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  42.  4
    V. V. Rybakov, M. Terziler & V. Remazki (2000). A Basis in Semi-Reduced Form for the Admissible Rules of the Intuitionistic Logic IPC. Mathematical Logic Quarterly 46 (2):207-218.
    We study the problem of finding a basis for all rules admissible in the intuitionistic propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all rules in semi-reduced form satisfying certain specific additional requirements. Using developed technique we also find a basis for rules admissible in the logic of excluded middle law KC.
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  43.  1
    Michael Miller & Donald Perlis (1996). Automated Inference in Active Logics. Journal of Applied Non-Classical Logics 6 (1):9-27.
    ABSTRACT Certain problems in commonsense reasoning lend themselves to the use of non-standard formalisms which we call active logics. Among these are problems of objects misidentification. In this paper we describe some technical issues connected with automated inference in active logics, using particular object misidentification problems as illustrations. Control of exponential growth of inferences is a key issue. To control this growth attention is paid to a limited version of an inference rule for negative introspection. We also (...)
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  44.  1
    Alexander Citkin (2008). A Mind of a Non-Countable Set of Ideas. Logic and Logical Philosophy 17 (1-2):23-39.
    The paper is dedicated to the 80th birthday of the outstanding Russian logician A.V. Kuznetsov. It is addressing a history of the ideas and research conducted by him in non-classical and intermediate logics.
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  45.  30
    Igor Douven (2013). Inference to the Best Explanation, Dutch Books, and Inaccuracy Minimisation. Philosophical Quarterly 63 (252):428-444.
    Bayesians have traditionally taken a dim view of the Inference to the Best Explanation, arguing that, if IBE is at variance with Bayes ' rule, then it runs afoul of the dynamic Dutch book argument. More recently, Bayes ' rule has been claimed to be superior on grounds of conduciveness to our epistemic goal. The present paper aims to show that neither of these arguments succeeds in undermining IBE.
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  46.  9
    Michael Robinson (forthcoming). Truthmakers, Moral Responsibility, and an Alleged Counterexample to Rule A. Erkenntnis:1-7.
    Charles Hermes argues that the Direct Argument for the incompatibility of determinism and moral responsibility fails because one of the inference rules on which it relies, Rule A, is invalid. Rule A states that if a proposition p is broadly logically necessary, then p is true and no one is, or ever has been, even partly morally responsible for the fact that p. Hermes purports to offer a counterexample to Rule A which focuses on agents’ (...)
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  47. 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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  48. Igor Douven (1999). Inference to the Best Explanation Made Coherent. Philosophy of Science 66 (Supplement):S424-S435.
    Van Fraassen (1989) argues that Inference to the Best Explanation is incoherent in the sense that adopting it as a rule for belief change will make one susceptible to a dynamic Dutch book. The present paper argues against this. A strategy is described that allows us to infer to the best explanation free of charge.
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  49. Igor Douven (2002). Testing Inference to the Best Explanation. Synthese 130 (3):355-377.
    Inference to the Best Explanation has become the subject of a livelydebate in the philosophy of science. Scientific realists maintain, while scientificantirealists deny, that it is a compelling rule of inference. It seems that anyattempt to settle this debate empirically must beg the question against theantirealist. The present paper argues that this impression is misleading. A methodis described that, by combining Glymour '' s theory of bootstrapping and Hacking '' sarguments from microscopy, allows us to test IBE (...)
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  50.  7
    Neil Tennant (2016). Rule-Irredundancy and the Sequent Calculus for Core Logic. Notre Dame Journal of Formal Logic 57 (1):105-125.
    We explore the consequences, for logical system-building, of taking seriously the aim of having irredundant rules of inference, and a preference for proofs of stronger results over proofs of weaker ones. This leads one to reconsider the structural rules of REFLEXIVITY, THINNING, and CUT. REFLEXIVITY survives in the minimally necessary form $\varphi:\varphi$. Proofs have to get started. CUT is subject to a CUT-elimination theorem, to the effect that one can always make do without applications of CUT. So CUT is (...)
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