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.score: 120.0
    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. Jean-Baptiste Van der Henst (2002). Mental Model Theory Versus the Inference Rule Approach in Relational Reasoning. Thinking and Reasoning 8 (3):193 – 203.score: 120.0
    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.score: 120.0
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  4. 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.score: 102.0
    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. Vladimir V. Rybakov (1993). Intermediate Logics Preserving Admissible Inference Rules of Heyting Calculus. Mathematical Logic Quarterly 39 (1):403-415.score: 102.0
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  6. J. A. Kalman (1983). Condensed Detachment as a Rule of Inference. Studia Logica 42 (4):443 - 451.score: 96.0
    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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  7. Ned Markosian (1988). On Ockham's Supposition Theory and Karger's Rule of Inference. Franciscan Studies 48 (1):40-52.score: 96.0
    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. Ivo Pezlar (2014). Towards a More General Concept of Inference. Logica Universalis 8 (1):61-81.score: 92.0
    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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  9. Valentin Goranko (1998). Axiomatizations with Context Rules of Inference in Modal Logic. Studia Logica 61 (2):179-197.score: 90.0
    A certain type of inference rules in (multi-) 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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  10. Athanassios Tzouvaras (1996). Aspects of Analytic Deduction. Journal of Philosophical Logic 25 (6):581 - 596.score: 90.0
    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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  11. David Makinson (2012). Logical Questions Behind the Lottery and Preface Paradoxes: Lossy Rules for Uncertain Inference. Synthese 186 (2):511-529.score: 84.0
    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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  12. Robert C. Pinto (2006). Evaluating Inferences: The Nature and Role of Warrants. Informal Logic 26 (3):287-317.score: 80.0
    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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  13. R. Bradshaw Angell (1960). Note on a Less Restricted Type of Rule of Inference. Mind 69 (274):253-255.score: 72.0
  14. Earl Conee & Richard Feldman (1983). Stich and Nisbett on Justifying Inference Rules. Philosophy of Science 50 (2):326-331.score: 72.0
    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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  15. Henry E. Kyburg Jr (1997). The Rule of Adjunction and Reasonable Inference. Journal of Philosophy 94 (3):109-125.score: 72.0
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  16. Tor Sandqvist (2012). Acceptance, Inference, and the Multiple-Conclusion Sequent. Synthese 187 (3):913-924.score: 72.0
    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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  17. R. B. Angell (1960). The Sentential Calculus Using Rule of Inference Re. Journal of Symbolic Logic 25 (2):143 -.score: 72.0
  18. Emil Jeřábek (2009). Canonical Rules. Journal of Symbolic Logic 74 (4):1171 - 1205.score: 72.0
    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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  19. Gary Jones & Frank E. Ritter (2003). Production Systems and Rule‐Based Inference. In L. Nadel (ed.), Encyclopedia of Cognitive Science. Nature Publishing Group.score: 72.0
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  20. 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.score: 72.0
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  21. E. Henry Jr (forthcoming). Kyburg.'The Rule of Adjunction and Reasonable Inference,'. Journal of Philosophy.score: 72.0
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  22. David K. Hardman (1998). Discussion de-Focusing on the Wason Selection Task: Mental Models or Mental Inference Rules? A Commentary on Green and Larking (1995). Thinking and Reasoning 4 (1):83 – 94.score: 68.0
    Mental models theorists have proposed that reasoners tend to focus on what is explicit in their mental models, and that certain debiasing procedures can induce them to direct their attention to other relevant information. For instance, Green and Larking 1995; also Green, 1995a facilitated performance on the Wason selection task by inducing participants to consider counterexamples to the conditional rule. However, these authors acknowledged that one aspect of their data might require some modification to the mental models theory. This (...)
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  23. V. V. Rybakov, M. Terziler & C. Gencer (2000). On Self-Admissible Quasi-Characterizing Inference Rules. Studia Logica 65 (3):417-428.score: 68.0
    We study quasi-characterizing inference rules (this notion was introduced into consideration by A. Citkin (1977). The main result of our paper is a complete description of all self-admissible quasi-characterizing inference rules. It is shown that a quasi-characterizing rule is self-admissible iff the frame of the algebra generating this rule is not rigid. We also prove that self-admissible rules are always admissible in canonical, in a sense, logics S4 or IPC regarding the type of algebra generating rules.
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  24. James B. Freeman (2001). Argument Structure and Disciplinary Perspective. Argumentation 15 (4):397-423.score: 66.0
    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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  25. 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.score: 66.0
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  26. Vladimir V. Rybakov, Vladimir R. Kiyatkin & Tahsin Oner (1999). On Finite Model Property for Admissible Rules. Mathematical Logic Quarterly 45 (4):505-520.score: 66.0
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  27. Vladimir V. Rybakov (1992). Rules of Inference with Parameters for Intuitionistic Logic. Journal of Symbolic Logic 57 (3):912-923.score: 66.0
    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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  28. Mathieu Marion (2001). Qu'est-ce que l'inférence ? Une relecture du Tractatus logico-philosophicus. Archives de Philosophie 3:545-567.score: 66.0
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  29. V. V. Rybakov (2001). Construction of an Explicit Basis for Rules Admissible in Modal System S4. Mathematical Logic Quarterly 47 (4):441-446.score: 66.0
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  30. Ran Spiegler (2001). Inferring a Linear Ordering Over a Power Set. Theory and Decision 51 (1):31-49.score: 64.0
    An observer attempts to infer the unobserved ranking of two ideal objects, A and B, from observed rankings in which these objects are `accompanied' by `noise' components, C and D. In the first ranking, A is accompanied by C and B is accompanied by D, while in the second ranking, A is accompanied by D and B is accompanied by C. In both rankings, noisy-A is ranked above noisy-B. The observer infers that ideal-A is ranked above ideal-B. This commonly used (...)
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  31. Herbert Feigl (ed.) (1958). Concepts, Theories, And The Mind-Body Problem. University of Minnesota Press.score: 60.0
    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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  32. Robert May, Notes on Frege on Rules of Inference.score: 60.0
    1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. (But cf. note regarding the latter.) 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 (bracketing), introduction of definitions, conventions for the use and replacement of the various letters(variables), and certain structural reorganizations, (e.g. amalgamation (...)
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  33. Alexej P. Pynko (2009). Distributive-Lattice Semantics of Sequent Calculi with Structural Rules. Logica Universalis 3 (1):59-94.score: 60.0
    The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables (viz., metavariables for finite sets of formulas), upon the basis of the conception of model introduced in (Fuzzy Sets Syst 121(3):27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such (...)
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  34. Alexander Citkin (2008). A Mind of a Non-Countable Set of Ideas. Logic and Logical Philosophy 17 (1-2):23-39.score: 60.0
    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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  35. W. Degen & J. Johannsen (2000). Cumulative Higher-Order Logic as a Foundation for Set Theory. Mathematical Logic Quarterly 46 (2):147-170.score: 60.0
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  36. Klemens Szaniawski (1962). On the Justification of Inductive Rules of Inference. Studia Logica 13 (1):225-225.score: 60.0
    Rules of inference can be interpreted as rules of (purposive) behavior; in such a case the behaptor consists in accepting a certain statement, called conclusion. The justification of a rule of inference with respect to a given end consists in showing that it is the most efficient method of realizing that end; the meaning of the word “efficient”, and the character of the end, should, of course, be made clear.The article is an attempt at reconstructing a part (...)
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  37. Vladimir V. Rybakov (1997). Admissibility of Logical Inference Rules. Elsevier.score: 56.0
    The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is (...)
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  38. Timothy Day & Harold Kincaid (1994). Putting Inference to the Best Explanation in its Place. Synthese 98 (2):271-295.score: 48.0
    This paper discusses the nature and the status of inference to the best explanation (IBE). We (1) outline the foundational role given IBE by its defenders and the arguments of critics who deny it any place at all; (2) argue that, on the two main conceptions of explanation, IBE cannot be a foundational inference rule; (3) sketch an account of IBE that makes it contextual and dependent on substantive empirical assumptions, much as simplicity seems to be; (4) (...)
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  39. Samuel Rathmanner & Marcus Hutter (2011). A Philosophical Treatise of Universal Induction. Entropy 13 (6):1076-1136.score: 48.0
    Understanding inductive reasoning is a problem that has engaged mankind for thousands of years. This problem is relevant to a wide range of fields and is integral to the philosophy of science. It has been tackled by many great minds ranging from philosophers to scientists to mathematicians, and more recently computer scientists. In this article we argue the case for Solomonoff Induction, a formal inductive framework which combines algorithmic information theory with the Bayesian framework. Although it achieves excellent theoretical results (...)
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  40. John Woods & Jillian Isenberg (2010). Psychologizing the Semantics of Fiction. Methodos 10.score: 48.0
    Les théoriciens sémantistes de la fiction cherchent typiquement à expliquer nos relations sémantiques au fictionnel dans le contexte plus général des théories de la référence, privilégiant une explication de la sémantique sur le psychologique. Dans cet article, nous défendons une dépendance inverse. Par l’éclaircissement de nos relations psychologiques au fictionnel, nous trouverons un guide pour savoir comment développer une sémantique de la fiction. S’ensuivra une esquisse de la sémantique.
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  41. Donald Bamber (2000). Entailment with Near Surety of Scaled Assertions of High Conditional Probability. Journal of Philosophical Logic 29 (1):1-74.score: 48.0
    An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal (...)
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  42. Niki Pfeifer & G. D. Kleiter (2006). Inference in Conditional Probability Logic. Kybernetika 42 (2):391--404.score: 48.0
    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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  43. Jesús P. Zamora Bonilla (2002). Scientific Inference and the Pursuit of Fame: A Contractarian Approach. Philosophy of Science 69 (2):300-323.score: 48.0
    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. Vladimir V. Rybakov (1994). Criteria for Admissibility of Inference Rules. Modal and Intermediate Logics with the Branching Property. Studia Logica 53 (2):203 - 225.score: 48.0
    The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable (...)
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  45. John Woods (1992). Apocalyptic Relevance. Argumentation 6 (2):189-202.score: 48.0
    In their book, Relevance, Sperber and Wilson make an important contribution towards constructing a credible theory of this unforthcoming notion. All is not clear sailing, however. If it is accepted as a condition on the adequacy of any account of relevance that it not be derivable either that nothing is relevant to anything or that everything is relevant to everything, it can be shown that Sperber and Wilson come close to violating the condition.
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  46. Alexander Citkin (2012). A Note on Admissible Rules and the Disjunction Property in Intermediate Logics. Archive for Mathematical Logic 51 (1-2):1-14.score: 48.0
    With any structural inference rule A/B, we associate the rule ${(A \lor p)/(B \lor p)}$ , providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( ${\lor}$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a ${\lor}$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the ${\lor}$ -extension of each admissible (...)
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  47. Jesús P. Zamora Bonilla (2002). Scientific Inference and the Pursuit of Fame: A Contractarian Approach. Philosophy of Science 69 (2):300-323.score: 48.0
    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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  48. Michael Miller & Donald Perlis (1996). Automated Inference in Active Logics. Journal of Applied Non-Classical Logics 6 (1):9-27.score: 48.0
    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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  49. V. V. Rybakov, M. Terziler & C. Gencer (2000). Unification and Passive Inference Rules for Modal Logics. Journal of Applied Non-Classical Logics 10 (3-4):369-377.score: 48.0
    ABSTRACT We1 study unification of formulas in modal logics and consider logics which are equivalent w.r.t. unification of formulas. A criteria is given for equivalence w.r.t. unification via existence or persistent formulas. A complete syntactic description of all formulas which are non-unifiable in wide classes of modal logics is given. Passive inference rules are considered, it is shown that in any modal logic over D4 there is a finite basis for passive rules.
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  50. David A. Plaisted (1979). Inference Rules for Unsatisfiability. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.score: 44.0
     
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