Results for 'Inference Rule'

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  1. What is an Inference Rule?Ronald Fagin, Joseph Y. Halpern & Moshe Y. Vardi - 1992 - 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.  63
    Mental Model Theory Versus the Inference Rule Approach in Relational Reasoning.Jean-Baptiste Van der Henst - 2002 - 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.  2
    A Ratio Rule From Integration Theory Applied to Inference Judgments.Manuel Leon & Norman H. Anderson - 1974 - Journal of Experimental Psychology 102 (1):27.
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  4.  87
    Analysis of the Talmudic Argumentum a Fortiori Inference Rule (Kal Vachomer) Using Matrix Abduction.M. Abraham, Dov M. Gabbay & U. Schild - 2009 - 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.  3
    Analysis of the Talmudic Argumentum A Fortiori Inference Rule Using Matrix Abduction.M. Abraham, Dov M. Gabbay & U. Schild - 2009 - 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 $a_{i,j} = 1$ or $a_{i,j} =?$ undecided. This algorithmic method is then (...)
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  6.  1
    An Examination of the SEP Candidate Analogical Inference Rule Within Pure Inductive Logic.E. Howarth, J. B. Paris & A. Vencovská - 2016 - Journal of Applied Logic 14:22-45.
  7.  25
    Inference to the Best Explanation Versus Bayes’s Rule in a Social Setting.Igor Douven & Sylvia Wenmackers - 2017 - British Journal for the Philosophy of Science 68 (2).
    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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  8.  53
    On Ockham's Supposition Theory and Karger's Rule of Inference.Ned Markosian - 1988 - 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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  9.  21
    Condensed Detachment as a Rule of Inference.J. A. Kalman - 1983 - 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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  10.  38
    The Rule of Adjunction and Reasonable Inference.Henry E. Kyburg Jr - 1997 - Journal of Philosophy 94 (3):109-125.
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  11. The Sentential Calculus Using Rule of Inference Re.R. B. Angell - 1960 - Journal of Symbolic Logic 25 (2):143 -.
  12.  86
    Note on a Less Restricted Type of Rule of Inference.R. Bradshaw Angell - 1960 - Mind 69 (274):253-255.
  13.  46
    Production Systems and Rule‐Based Inference.Gary Jones & Frank E. Ritter - 2003 - In L. Nadel (ed.), Encyclopedia of Cognitive Science. Nature Publishing Group.
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  14. The Rule of Adjunction and Reasonable Inference.Henry E. Kyburg - 1997 - Journal of Philosophy 94 (3):109.
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  15. Angell R. Bradshaw. Note on a Less Restricted Type of Rule of Inference. Mind, N.S. Vol. 69 , Pp. 253–255.Angell R. B.. The Sentential Calculus Using Rule of Inference Re. [REVIEW]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):602-603.
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  16. 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]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):602-603.
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  17. Kyburg.'The Rule of Adjunction and Reasonable Inference,'.E. Henry Jr - forthcoming - Journal of Philosophy.
  18. The Rule of Adjunction and Reasonable Inference. Kyburg - 1997 - Journal of Philosophy 94 (3):109-125.
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  19.  28
    Towards a More General Concept of Inference.Ivo Pezlar - 2014 - 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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  20.  2
    Intermediate Logics Preserving Admissible Inference Rules of Heyting Calculus.Vladimir V. Rybakov - 1993 - 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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  21.  18
    Aspects of Analytic Deduction.Athanassios Tzouvaras - 1996 - 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 ⊆ Atom, whereas for predicate logic, ⊢a is defined by the extended criterion Γ⊢aφ iff Γ⊢aφ and Atom ⊆' Atom, where Atom ⊆' Atom 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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  22.  11
    Cumulative Higher-Order Logic as a Foundation for Set Theory.W. Degen & J. Johannsen - 2000 - 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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  23.  60
    Logical Inference and Its Dynamics.Carlotta Pavese - June 2016 - In Tamminga Allard, Willer Malte & Roy Olivier (eds.), Deontic Logic and Normative Systems The 13th International Conference. DEON 2016, Bayreuth, Germany. College Publications. pp. 203-219.
    This essay advances and develops a dynamic conception of inference rules and uses it to reexamine a long-standing problem about logical inference raised by Lewis Carroll’s regress.
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  24.  6
    Deductive Inference and Aspect Perception.Arif Ahmed - 2010 - In Wittgenstein's Philosophical Investigations: A Critical Guide. Cambridge University Press.
    Deductive inference seems to reveal semantic connections between their premise(s) and conclusion that were there all along. This looks inconsistent with Wittgenstein's later views on meaning. The paper argues that W's treatment of aspects suggests a Wittgensteinian treatment of deduction that accommodates the troublesome phenomenon without conceding its force.
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  25.  98
    Inference to the Best Explanation Made Incoherent.Nevin Climenhaga - 2017 - Journal of Philosophy 114 (5):251-273.
    Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of (...)
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  26.  7
    Qu'est-ce que l'inférence ? Une relecture du Tractatus logico-philosophicus.Mathieu Marion - 2001 - Archives de Philosophie 3:545-567.
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  27.  12
    Inferential Transitions.Jake Quilty-Dunn & Eric Mandelbaum - forthcoming - Australasian Journal of Philosophy:1-16.
    This paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit (...)
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  28.  26
    Does the ‘Missing Fundamental’ Require an Inferentialist Explanation?J. A. Judge - 2017 - Topoi 36 (2):319-329.
    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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  29.  1
    Characteristic Inference Rules.Alex Citkin - 2015 - 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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  30.  38
    Acceptance, Inference, and the Multiple-Conclusion Sequent.Tor Sandqvist - 2012 - 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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  31.  84
    What Reasoning Might Be.Markos Valaris - 2017 - Synthese 194 (6).
    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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  32.  6
    Canonical Rules.Emil Jeřábek - 2009 - 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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  33.  17
    Evaluating Inferences: The Nature and Role of Warrants.Robert C. Pinto - 2006 - 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 such (...)
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  34.  90
    Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference.David Makinson - 2012 - 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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  35.  24
    Axiomatizations with Context Rules of Inference in Modal Logic.Valentin Goranko - 1998 - 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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  36.  26
    Argument Structure and Disciplinary Perspective.James B. Freeman - 2001 - 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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  37.  7
    Algebraic Logic Perspective on Prucnal’s Substitution.Alex Citkin - 2016 - Notre Dame Journal of Formal Logic 57 (4):503-521.
    A term $\mathit{td}$ is called a ternary deductive term for a variety of algebras $\mathcal{V}$ if the identity $\mathit{td}\approxr$ holds in $\mathcal{V}$ and $\in\theta$ yields $\mathit{td}\approx\mathit{td}$ for any $\mathscr{A}\in\mathcal{V}$ and any principal congruence $\theta$ on $\mathscr{A}$. A connective $f$ is called $\mathit{td}$-distributive if $\mathit{td})\approx$ $f,\dots,\mathit{td})$. If $\mathsf{L}$ is a propositional logic and $\mathcal{V}$ is a corresponding variety that has a TD term $\mathit{td}$, then any admissible in $\mathsf{L}$ rule, the premises of which contain only $\mathit{td}$-distributive operations, is derivable, and (...)
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  38.  10
    Kearns on Rule A.P. Roger Turner - 2015 - 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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  39.  1
    Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility.Sergei Odintsov & Vladimir Rybakov - 2015 - 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 admissibility and (...)
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  40. Putting Inference to the Best Explanation in its Place.Timothy Day & Harold Kincaid - 1994 - 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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  41. Inference in Conditional Probability Logic.Niki Pfeifer & G. D. Kleiter - 2006 - 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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  42. Rules of Inference with Parameters for Intuitionistic Logic.Vladimir V. Rybakov - 1992 - 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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  43. Scientific Inference and the Pursuit of Fame: A Contractarian Approach.P. Zamora Bonilla Jesús - 2002 - 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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  44.  30
    Sound Reasoning : Prospects and Challenges of Current Acoustic Logics.Marc Champagne - 2015 - 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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  45.  3
    On Finite Model Property for Admissible Rules.Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner - 1999 - 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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  46.  32
    Concepts, Theories, And The Mind-Body Problem.Herbert Feigl (ed.) - 1958 - 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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  47.  1
    Construction of an Explicit Basis for Rules Admissible in Modal System S4.V. V. Rybakov - 2001 - 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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  48.  26
    Stich and Nisbett on Justifying Inference Rules.Earl Conee & Richard Feldman - 1983 - 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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  49.  21
    Do Syllogisms Commit the Petitio Principii? The Role of Inference-Rules in Mill's Logic of Truth.David Botting - 2014 - 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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    Inference Networks : Bayes and Wigmore.Philip Dawid, David Schum & Amanda Hepler - 2011 - In Philip Dawid, William Twining & Mimi Vasilaki (eds.), Evidence, Inference and Enquiry. Oup/British Academy. pp. 119.
    Methods for performing complex probabilistic reasoning tasks, often based on masses of different forms of evidence obtained from a variety of different sources, are being sought by, and developed for, persons in many important contexts including law, medical diagnosis, and intelligence analysis. The complexity of these tasks can often be captured and represented by graphical structures now called inference networks. These networks are directed acyclic graphs, consisting of nodes, representing relevant hypotheses, items of evidence, and unobserved variables, and arcs (...)
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