Results for 'Melvin C. Fitting'

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  1.  75
    Many-Valued Modal Logics.Melvin C. Fitting - unknown
    Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.
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  2.  30
    Well-Founded Semantics, Generalized.Melvin C. Fitting - unknown
    Classical fixpoint semantics for logic programs is based on the TP immediate consequence operator. The Kripke/Kleene, three-valued, semantics uses ΦP, which extends TP to Kleene’s strong three-valued logic. Both these approaches generalize to cover logic programming systems based on a wide class of logics, provided only that the underlying structure be that of a bilattice. This was presented in earlier papers. Recently well-founded semantics has become influential for classical logic programs. We show how the well-founded approach also extends naturally to (...)
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  3.  22
    An Axiomatic Approach to Computers.Melvin C. Fitting - 1979 - Theoria 45 (3):97-113.
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  4.  13
    Computability Theory, Semantics, and Logic Programming.J. C. Shepherdson & Melvin Fitting - 1988 - Journal of Symbolic Logic 53 (4):1257.
  5.  9
    Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics.Melvin Fitting - 2021 - Australasian Journal of Logic 18 (2).
    This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides (...)
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  6.  20
    Fitting Melvin. Computability Theory, Semantics, and Logic Programming. Oxford Logic Guides, No. 13. Clarendon Press, Oxford University Press, Oxford and New York 1987, Xi + 198 Pp. [REVIEW]J. C. Shepherdson - 1988 - Journal of Symbolic Logic 53 (4):1257-1257.
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  7.  28
    Realizations and LP.Melvin Fitting - 2010 - Annals of Pure and Applied Logic 161 (3):368-387.
    LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...)
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  8.  65
    Possible World Semantics for First Order Lp.Melvin Fitting - unknown
    First we have individual variables, as usual in first-order logics. (We do not have individual constants, but this is a minor point.) The propositional logic LP has justification constants, but in FOLP these are generalized to allow individual variables as arguments. Thus we have as justification constants c, c(x), c(x, y), . . . . Similarly LP has justification variables, but in FOLP these can be parametrized with individual variables p, p(x), p(x, y), . . . . To keep terminology (...)
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  9.  23
    A Program to Compute G¨Odel-L¨Ob Fixpoints.Melvin Fitting - unknown
    odel-L¨ ob computability logic. In order to make things relatively self-contained, I sketch the essential ideas of GL, and discuss the significance of its fixpoint theorem. Then I give the algorithm embodied in the program in a little more detail. It should be emphasized that nothing new is presented here — all the theory and methodology are due to others. The main interest is, in a sense, psychological. The approach taken here has been declared in the literature, more than once, (...)
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  10.  12
    Troublemaker: The Life and History of A. J. P. Taylor.Melvin C. Shefftz - 2003 - International Studies in Philosophy 35 (4):182-184.
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  11.  7
    Political Ideas in Modern Britain.Melvin C. Shefftz - 1981 - International Studies in Philosophy 13 (2):81-82.
  12.  1
    Voltages Induced in Superconductors in the Absence of Transport Currents.Melvin C. Ohmer & W. C. H. Joiner - 1972 - Philosophical Magazine 26 (1):15-32.
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  13.  3
    Review: Melvin Chris Fitting, Intuitionistic Logic Model Theory and Forcing. [REVIEW]F. R. Drake - 1971 - Journal of Symbolic Logic 36 (1):166-167.
  14.  16
    First-Order Modal Logic.Melvin Chris Fitting & Richard L. Mendelsohn - 1998 - Dordrecht, Netherland: Kluwer Academic Publishers.
    This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.
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  15.  6
    Logic and Structure.Melvin Fitting - 1986 - Journal of Symbolic Logic 51 (3):826-827.
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  16. Essays for Raymond Smullyan.Melvin Fitting (ed.) - forthcoming
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  17.  33
    The Stable Model Semantics for Logic Programming.Melvin Fitting - 1992 - Journal of Symbolic Logic 57 (1):274-277.
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  18.  25
    Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
  19.  24
    Intuitionistic Logic, Model Theory and Forcing.Melvin Chris Fitting - 1969 - Amsterdam: North-Holland Pub. Co..
  20.  16
    First Order Modal Logic.Melvin Fitting & Richard Mendelsohn - 1998 - Studia Logica 68 (2):287-289.
  21.  58
    Bilattices and the Semantics of Logic Programming.Melvin Fitting - unknown
    Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap’s four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides (...)
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  22.  75
    The Logic of Proofs, Semantically.Melvin Fitting - 2005 - Annals of Pure and Applied Logic 132 (1):1-25.
    A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.
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  23.  21
    Tableau Methods of Proof for Modal Logics.Melvin Fitting - 1972 - Notre Dame Journal of Formal Logic 13 (2):237-247.
  24.  73
    Kleene's Three Valued Logics and Their Children.Melvin Fitting - unknown
    Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.
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  25.  30
    Notes on the Mathematical Aspects of Kripke’s Theory of Truth.Melvin Fitting - 1986 - Notre Dame Journal of Formal Logic 27 (1):75-88.
  26.  27
    Paraconsistent Logic, Evidence, and Justification.Melvin Fitting - 2017 - Studia Logica 105 (6):1149-1166.
    In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as asserting (...)
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  27.  22
    A Family of Strict/Tolerant Logics.Melvin Fitting - 2021 - Journal of Philosophical Logic 50 (2):363-394.
    Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been extended to meta, metameta, … (...)
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  28. Many-Valued Modal Logics II.Melvin Fitting - unknown
    Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal (...)
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  29.  78
    Kleene's Logic, Generalized.Melvin Fitting - unknown
    Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.
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  30.  57
    Bilattices Are Nice Things.Melvin Fitting - 2006 - In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. CSLI Publications.
    One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artificial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while making (...)
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  31.  40
    Bilattices In Logic Programming.Melvin Fitting - unknown
    Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiple-valued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to logic programming languages that can, at least in principle, be implemented. Appropriate bilattice background information is presented, so the paper is relatively self-contained.
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  32.  30
    First-Order Modal Logic.Melvin Fitting, R. Mendelsohn & Roderic A. Girle - 2002 - Bulletin of Symbolic Logic 8 (3):429-430.
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  33.  72
    Prefixed Tableaus and Nested Sequents.Melvin Fitting - 2012 - Annals of Pure and Applied Logic 163 (3):291 - 313.
    Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants (...)
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  34.  35
    Bilattices and the Theory of Truth.Melvin Fitting - 1989 - Journal of Philosophical Logic 18 (3):225 - 256.
    While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. Thus, with (...)
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  35.  40
    Modal Logics, Justification Logics, and Realization.Melvin Fitting - 2016 - Annals of Pure and Applied Logic 167 (8):615-648.
  36.  86
    First-Order Intensional Logic.Melvin Fitting - 2004 - Annals of Pure and Applied Logic 127 (1-3):171-193.
    First - order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently, several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been involved with this line of development for some time. In the present paper, I briefly sketch several (...)
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  37.  31
    Possible World Semantics for First-Order Logic of Proofs.Melvin Fitting - 2014 - Annals of Pure and Applied Logic 165 (1):225-240.
    In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and (...)
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  38.  45
    Intensional Logic.Melvin Fitting - 2008 - Stanford Encyclopedia of Philosophy.
    There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.
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  39. First-Order Logic and Automated Theorem Proving.Melvin Fitting - 1998 - Studia Logica 61 (2):300-302.
  40.  96
    Tableaus for Many-Valued Modal Logic.Melvin Fitting - 1995 - Studia Logica 55 (1):63 - 87.
    We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cut-free tableau formulation is presented, and its completeness is proved.
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  41.  69
    A Quantified Logic of Evidence.Melvin Fitting - 2008 - Annals of Pure and Applied Logic 152 (1):67-83.
    A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. (...)
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  42.  38
    Fixpoint Semantics for Logic Programming A Survey.Melvin Fitting - unknown
    The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact (...)
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  43.  85
    Justification Logics, Logics of Knowledge, and Conservativity.Melvin Fitting - unknown
    Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...)
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  44.  8
    Types Tableaus and Gödel's God.Melvin Fitting - 2005 - Studia Logica 81 (3):425-427.
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  45.  37
    Reasoning with Justifications.Melvin Fitting - unknown
    This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a (...)
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  46.  55
    First-Order Modal Logic.Roderic A. Girle, Melvin Fitting & Richard L. Mendelsohn - 2002 - Bulletin of Symbolic Logic 8 (3):429.
  47.  39
    Negation As Refutation.Melvin Fitting - unknown
    A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilattice notion. An efficient implementation based on semantic tableaux is sketched; it reduces to SLD resolution when negations are not involved. The resulting system (...)
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  48.  52
    A Logic of Explicit Knowledge.Melvin Fitting - unknown
    A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. One kind of reason is (...)
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  49.  5
    Raymond Smullyan on Self Reference.Brian Rayman & Melvin Fitting (eds.) - 2017 - Cham, Switzerland: Springer Verlag.
    This book collects, for the first time in one volume, contributions honoring Professor Raymond Smullyan’s work on self-reference. It serves not only as a tribute to one of the great thinkers in logic, but also as a celebration of self-reference in general, to be enjoyed by all lovers of this field. Raymond Smullyan, mathematician, philosopher, musician and inventor of logic puzzles, made a lasting impact on the study of mathematical logic; accordingly, this book spans the many personalities through which Professor (...)
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  50.  24
    Fitting Melvin Chris. Intuitionistic Logic Model Theory and Forcing. Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Company, Amsterdam and London 1969, 191 Pp. [REVIEW]F. R. Drake - 1971 - Journal of Symbolic Logic 36 (1):166-167.
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