Results for 'partial logic'

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  1.  66
    Truth, Partial Logic and Infinitary Proof Systems.Martin Fischer & Norbert Gratzl - 2017 - Studia Logica 106 (3):1-26.
    In this paper we apply proof theoretic methods used for classical systems in order to obtain upper bounds for systems in partial logic. We focus on a truth predicate interpreted in a Kripke style way via strong Kleene; whereas the aim is to connect harmoniously the partial version of Kripke–Feferman with its intended semantics. The method we apply is based on infinitary proof systems containing an ω-rule.
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  2. Validity in Simple Partial Logic.Daisuke Kachi - 2002 - Annals of the Japan Association for Philosophy of Science 10 (4):139-153.
    Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.
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  3.  14
    Partial Logic as a Logic of Extensional Alethic Modality.Daisuke Kachi - 2007 - Journal of the Japan Association for Philosophy of Science 34 (2):61-70.
    In my paper 'Validity in Simple Partial Logic'(2002) I made comparison between several definitions of validity in Simple Partial Logic(SPL) and adopted two of them as most appropriate. In this paper, after elaborating more on these two definitions than in my previous paper and considering the characteristics of Partial Semantics, in which these definitions are given, I construct a tableau proof system and prove its soundness and completeness. Then, based on the characterization of Partial (...)
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  4.  45
    Probabilistic Canonical Models for Partial Logics.François Lepage & Charles Morgan - 2003 - Notre Dame Journal of Formal Logic 44 (3):125-138.
    The aim of the paper is to develop the notion of partial probability distributions as being more realistic models of belief systems than the standard accounts. We formulate the theory of partial probability functions independently of any classical semantic notions. We use the partial probability distributions to develop a formal semantics for partial propositional calculi, with extensions to predicate logic and higher order languages. We give a proof theory for the partial logics and obtain (...)
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  5.  39
    Honesty in Partial Logic.Wiebe van der Hoek, Jan Jaspars & Elias Thijsse - 1996 - Studia Logica 56 (3):323-360.
    We propose an epistemic logic in which knowledge is fully introspective and implies truth, although truth need not imply epistemic possibility. The logic is presented in sequential format and is interpreted in a natural class of partial models, called balloon models. We examine the notions of honesty and circumscription in this logic: What is the state of an agent that 'only knows φ' and which honest φ enable such circumscription? Redefining stable sets enables us to provide (...)
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  6.  22
    Honesty in Partial Logic.Wiebe Hoek, Jan Jaspars & Elias Thijsse - 1996 - Studia Logica 56 (3):323-360.
    We propose an epistemic logic in which knowledge is fully introspective and implies truth, although truth need not imply epistemic possibility. The logic is presented in sequential format and is interpreted in a natural class of partial models, called balloon models. We examine the notions of honesty and circumscription in this logic: What is the state of an agent that only knows and which honest enable such circumscription? Redefining stable sets enables us to provide suitable syntactic (...)
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  7. Tensed Ontology Based on Simple Partial Logic.Daisuke Kachi - 2002 - Proceedings of Ninth International Symposium on Temporal Representation and Reasoning: TIME-02:141-145.
    Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I (...)
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  8.  49
    Semantic Games with Chance Moves Revisited: From IF Logic to Partial Logic.Xuefeng Wen & Shier Ju - 2013 - Synthese 190 (9):1605-1620.
    We associate the semantic game with chance moves conceived by Blinov with Blamey’s partial logic. We give some equivalent alternatives to the semantic game, some of which are with a third player, borrowing the idea of introducing the pseudo-player called Nature in game theory. We observe that IF propositional logic proposed by Sandu and Pietarinen can be equivalently translated to partial logic, which implies that imperfect information may not be necessary for IF propositional logic. (...)
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  9.  41
    A Modal Reduction for Partial Logic.Juan Barba - 1993 - Journal of Philosophical Logic 22 (4):429 - 435.
  10.  19
    Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic.Roland Hinnion - 1994 - Notre Dame Journal of Formal Logic 35 (1):15-40.
    Two distinct and apparently "dual" traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of "easy-to-handle" versions of these logics is given, in which full naive set theory, i.e. Frege's comprehension principle + extensionality, is not absurd.
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  11. On the Logic of Theory Change: Partial Meet Contraction and Revision Functions.Carlos E. Alchourrón, Peter Gärdenfors & David Makinson - 1985 - Journal of Symbolic Logic 50 (2):510-530.
    This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...)
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  12.  59
    Partiality and Adjointness in Modal Logic.Wesley H. Holliday - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Vol. 10. College Publications. pp. 313-332.
    Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking (...)
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  13.  14
    Partiality and Games: Propositional Logic.G. Sandu & A. Pietarinen - 2001 - Logic Journal of the IGPL 9 (1):101-121.
    We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated (...)
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  14. On Partial and Paraconsistent Logics.Reinhard Muskens - 1999 - Notre Dame Journal of Formal Logic 40 (3):352-374.
    In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent (...)
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  15.  8
    Partiality and Adjointness in Modal Logic.Wesley H. Holliday - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 313-332.
    Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking (...)
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  16.  30
    Partial and Unsharp Quantum Logics.M. L. Dalla Chiara & R. Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.
    The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples (...)
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  17.  42
    Partial Confirmation of a Conjecture on the Boxdot Translation in Modal Logic.Rohan French & Lloyd Humberstone - 2009 - Australasian Journal of Logic 7:56-61.
    The purpose of the present note is to advertise an interesting conjecture concerning a well-known translation in modal logic, by confirming a (highly restricted) special case of the conjecture.
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  18.  18
    Partial Structures and the Logic of Azande.Newton da Costa & Steven French - 1995 - American Philosophical Quarterly 32 (4):325 - 339.
  19.  12
    Implicational Partial Galois Logics: Relational Semantics.Eunsuk Yang & J. Michael Dunn - 2021 - Logica Universalis 15 (4):457-476.
    Implicational tonoid logics and their relational semantics have been introduced by Yang and Dunn. This paper extends this investigation to implicational partial Galois logics. For this, we first define some implicational partial gaggle logics as special kinds of implicational tonoid logics called “implicational partial Galois logics.” Next, we provide Routley–Meyer-style relational semantics for finitary those logics.
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  20.  52
    Partial and Paraconsistent Approaches to Future Contingents in Tense Logic.Seiki Akama, Tetsuya Murai & Yasuo Kudo - 2016 - Synthese 193 (11).
    The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These approaches theoretically meet (...)
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  21.  32
    Partial Structures and the Logic of Azande.Steven French - 2011 - Principia: An International Journal of Epistemology 15 (1):77-105.
    Em Science and Partial Truth (da Costa and French 2003) argumentamos que inconsistências no raciocínio científico podem ser acomodadas pela combinação de estruturas parciais e quase-verdade, junto com uma noção de ‘crença representacional’. Neste artigo, examino se isso pode ser estendido aos raciocínios e crenças de outras culturas, focando em particular nas crenças de feitiçaria dos Azande. Argumento que tais crenças são similares às crenças teóricas da ciência ocidental, mas que o modo mais apropriado de representar esta última — (...)
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  22.  24
    Partial Semantics for Quantified Modal Logic.Eric Johannesson - 2018 - Journal of Philosophical Logic 47 (6):1049-1060.
    When it comes to Kripke-style semantics for quantified modal logic, there’s a choice to be made concerning the interpretation of the quantifiers. The simple approach is to let quantifiers range over all possible objects, not just objects existing in the world of evaluation, and use a special predicate to make claims about existence. This is the constant domain approach. The more complicated approach is to assign a domain of objects to each world. This is the varying domain approach. Assuming (...)
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  23.  23
    Partial Entailment as a Basis for Inductive Logic.Wesley C. Salmon - 1969 - In Nicholas Rescher (ed.), Essays in Honor of Carl G. Hempel. Reidel. pp. 47--82.
  24. Vagueness, Partial Belief, and Logic.Hartry Field - manuscript
    Discussion of Chapter 5 of Stephen Schiffer's "The Things We Mean' in which Stephen Schiffer advances two novel theses: 1. Vagueness (and indeterminacy more generally) is a psychological phenomenon; 2. It is indeterminate whether classical logic applies in situations where vagueness matters.
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  25. Can Logical Probability Be Viewed as a Measure of Degrees of Partial Entailment?Alberto Mario Mura - 2008 - Logic and Philosophy of Science 6 (1):25-33.
     
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  26. Partiality and nonmonotonicity in classical logic.J. Van Benthem - 1986 - Logique Et Analyse 29 (14):225.
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  27.  33
    Logics Based on Partial Boolean Σ-Algebras (1).Janusz Czelakowski - 1974 - Studia Logica 33 (4):371 - 396.
  28.  29
    The Logic of Partial Supposition.Benjamin Eva & Stephan Hartmann - 2021 - Analysis (2):215-224.
    According to orthodoxy, there are two basic moods of supposition: indicative and subjunctive. The most popular formalizations of the corresponding norms of suppositional judgement are given by Bayesian conditionalization and Lewisian imaging, respectively. It is well known that Bayesian conditionalization can be generalized to provide a model for the norms of partial indicative supposition. This raises the question of whether imaging can likewise be generalized to model the norms of ‘partial subjunctive supposition’. The present article casts doubt on (...)
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  29.  11
    Partial and Unsharp Quantum Logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.
  30.  26
    Partial-Order Boolean Games: Informational Independence in a Logic-Based Model of Strategic Interaction.Julian Bradfield, Julian Gutierrez & Michael Wooldridge - 2016 - Synthese 193 (3):781-811.
    As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a game. More precisely, dependency graphs play two roles. First, when we say that variable x depends on variable y, then (...)
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  31. Partial Wh-Movement and Logical Form an Introduction.Arnim von Stechow - unknown
    On Friday the 1st and Saturday the 2nd of December 1995, the Sonderforschungsbereich 340 held a workshop entitled Syntax and Semantics of Partial Wh-Movement. This volume contains most of the papers presented there.1 One of the leading ideas underlying the workshop was that detailed investigation of the partial wh-movement construction provides an excellent test ground for checking assumptions about the syntax/semantics interface.
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  32.  31
    Partial Algebras for Łukasiewicz Logics and its Extensions.Thomas Vetterlein - 2005 - Archive for Mathematical Logic 44 (7):913-933.
    It is a well-known fact that MV-algebras, the algebraic counterpart of Łukasiewicz logic, correspond to a certain type of partial algebras: lattice-ordered effect algebras fulfilling the Riesz decomposition property. The latter are based on a partial, but cancellative addition, and we may construct from them the representing ℓ-groups in a straightforward manner. In this paper, we consider several logics differing from Łukasiewicz logics in that they contain further connectives: the PŁ-, PŁ'-, PŁ'△-, and ŁΠ-logics. For all their (...)
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  33.  6
    Logics Based on Partial Boolean Σ-Algebras.Janusz Czelakowski - 1974 - Studia Logica 33 (4):371-396.
  34.  13
    Logic, Partial Orders and Topology.Hugo Mariano & Francisco Miraglia - 2005 - Manuscrito 28 (2):449-546.
    We give a version of L´os’ ultraproduct result for forcing in Kripke structures in a first-order language with equality and discuss ultrafilters in a topology naturally associated to a partial order. The presentation also includes background material so as to make the exposition accessible to those whose main interest is Computer Science, Artificial Intelligence and/or Philosophy.
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  35.  34
    Partial Probability Functions and Intuitionistic Logic.François Lepage - 2012 - Bulletin of the Section of Logic 41 (3/4):173-184.
  36.  23
    Partial Horn Logic and Cartesian Categories.Erik Palmgren & Steven J. Vickers - 2007 - Annals of Pure and Applied Logic 145 (3):314-353.
  37.  83
    Language, Partial Truth, and Logic[REVIEW]C. Z. Elgin - 2011 - Analysis 71 (2):313-322.
    In Hard Truths, Elijah Millgram maintains that analytic philosophy rests on a mistake. 1 It is committed to bivalence – the contention that every truth bearer is either true or false. As a result of this commitment, its views about logic and metaphysics are profoundly misguided. He believes that rather than restricting ourselves to two truth values, we should recognize a plethora of partial truths – sentences, beliefs and opinions that are partly true or true in a way. (...)
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  38. A Partial Account of Presupposition Projection.David Beaver & Emiel Krahmer - 2001 - Journal of Logic, Language and Information 10 (2):147-182.
    In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. (...)
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  39. Is the Partial Identity Account of Property Resemblance Logically Incoherent?Sophie Gibb - 2007 - Dialectica 61 (4):539-558.
    According to the partial identity account of resemblance, exact resemblance is complete identity and inexact resemblance is partial identity. In this paper, I examine Arda Denkel's (1998) argument that this account of resemblance is logically incoherent as it results in a vicious regress. I claim that although Denkel's argument does not succeed, a modified version of it leads to the conclusion that the partial identity account is plausible only if the constituents of every determinate property are ultimately (...)
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  40.  64
    Partial Isomorphisms and Intuitionistic Logic.Bernd I. Dahn - 1981 - Studia Logica 40 (4):405 - 413.
    A game for testing the equivalence of Kripke models with respect to finitary and infinitary intuitionistic predicate logic is introduced and applied to discuss a concept of categoricity for intuitionistic theories.
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  41. Partial Belief as a Solution to the Logical Problem of Holding Simultaneous, Contrary Beliefs in Self-Deception Research.Keith Gibbins - 1997 - Behavioral and Brain Sciences 20 (1):115-116.
    A major worry in self-deception research has been the implication that people can hold a belief that something is true and false at the same time: a logical as well as a psychological impossibility. However, if beliefs are held with imperfect confidence, voluntary self-deception in the sense of seeking evidence to reject an unpleasant belief becomes entirely plausible and demonstrably real.
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  42.  6
    Partial Up and Down Logic.Jan O. M. Jaspars - 1995 - Notre Dame Journal of Formal Logic 36 (1):134-157.
    This paper presents logics for reasoning about extension and reduction of partial information states. This enterprise amounts to nonpersistent variations of certain constructive logics, in particular the so-called logic of constructible falsity of Nelson. We provide simple semantics, sequential calculi, completeness and decidability proofs.
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  43.  38
    Confirmation as Partial Entailment: A Representation Theorem in Inductive Logic.Vincenzo Crupi & Katya Tentori - 2013 - Journal of Applied Logic 11 (4):364-372.
  44.  8
    Partially Independent Variables and Internal Logic in Classical Marxist Economic Analysis.Ernest Mandel - 1985 - Social Science Information 24 (3):485-505.
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  45.  35
    Logics based on partial Boolean sigma-algebras.Janusz Czelakowski - 1975 - Studia Logica 34:69.
  46.  18
    Equational Logic of Partial Functions Under Kleene Equality: A Complete and an Incomplete Set of Rules.Anthony Robinson - 1989 - Journal of Symbolic Logic 54 (2):354-362.
  47. Logics Based on Partial Boolean Σ-Algebras.Janusz Czelakowski - 1974 - Bulletin of the Section of Logic 3 (2):31-37.
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  48.  16
    Negation and Partial Axiomatizations of Dependence and Independence Logic Revisited.Fan Yang - 2019 - Annals of Pure and Applied Logic 170 (9):1128-1149.
    In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence (...) by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms. (shrink)
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  49.  11
    Triangular Logic of Partial Toposes.Adam Obtulowicz - 2000 - Journal of Applied Non-Classical Logics 10 (2):173-212.
    ABSTRACT We present a new method for proving theorems in the equational theory of partial maps over toposes introduced in the papers [C'089] and [086], The method is given by a system of rules of formation of proofs. The proofs of f is defined' and the proofs of correctness ‘φ)' formed by application of the rules of the system are such that they contain a computation of the value f, where f is a partial function valued in natural (...)
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  50.  24
    On Modal Logics of Partial Recursive Functions.Pavel Naumov - 2005 - Studia Logica 81 (3):295-309.
    The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.
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