Results for 'axiomatics'

946 found
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  1.  44
    Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
    At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the (...)
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  2.  52
    On Axiomatization of Łukasiewicz's Four-Valued Modal Logic.Marcin Tkaczyk - 2011 - Logic and Logical Philosophy 20 (3):215-232.
    Formal aspects of various ways of description of Jan Łukasiewicz’s four-valued modal logic £ are discussed. The original Łukasiewicz’s description by means of the accepted and rejected theorems, together with the four-valued matrix, is presented. Then the improved E.J. Lemmon’s description based upon three specific axioms, together with the relational semantics, is presented as well. It is proved that Lemmon’s axiomatic is not independent: one axiom is derivable on the base of the remanent two. Several axiomatizations, based on three, two (...)
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  3. Shortest Axiomatizations of Implicational S4 and S.Zachary Ernst, Branden Fitelson, Kenneth Harris & Larry Wos - 2002 - Notre Dame Journal of Formal Logic 43 (3):169-179.
    Shortest possible axiomatizations for the implicational fragments of the modal logics S4 and S5 are reported. Among these axiomatizations is included a shortest single axiom for implicational S4—which to our knowledge is the first reported single axiom for that system—and several new shortest single axioms for implicational S5. A variety of automated reasoning strategies were essential to our discoveries.
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  4. Alternative axiomatics and complexity of deliberative stit theories.Philippe Balbiani, Andreas Herzig & Nicolas Troquard - 2008 - Journal of Philosophical Logic 37 (4):387 - 406.
    We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...)
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  5. Axiomatizing Kripke’s Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
    We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...)
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  6. Axiomatic Natural Philosophy and the Emergence of Biology as a Science.Hein van den Berg & Boris Demarest - 2020 - Journal of the History of Biology 53 (3):379-422.
    Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...)
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  7.  70
    Axiomatics and progress in the light of 20th century philosophy of science and mathematics.Dirk Schlimm - 2006 - In Benedikt Löwe, Volker Peckhaus & T. Rasch (eds.), Foundations of the Formal Sciences IV. College Publications. pp. 233–253.
    This paper is a contribution to the question of how aspects of science have been perceived through history. In particular, I will discuss how the contribution of axiomatics to the development of science and mathematics was viewed in 20th century philosophy of science and philosophy of mathematics. It will turn out that in connection with scientific methodology, in particular regarding its use in the context of discovery, axiomatics has received only very little attention. This is a rather surprising (...)
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  8.  36
    Comparing Axiomatic Theories of Truth.Mateusz Łełyk - 2019 - Studia Semiotyczne 33 (2):255-286.
    The main aim of our paper was to present three formal tools for comparing various axiomatic theories of truth. In Section 2 we aimed at showing that there are indeed many different approaches to defining a set of axioms for the notion of truth. In Section 3 we introduced three different \measures of strength" of axiomatic theories of truth, i.e. three reflexive and transitive relations on the set of axiomatic theories of truth. We have explained the intuition behind each of (...)
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  9.  86
    Axiomatic Foundations of Galilean Quantum Field Theories.G. Puccini & H. Vucetich - 2004 - Foundations of Physics 34 (2):263-295.
    A realistic axiomatic formulation of Galilean Quantum Field Theories is presented, from which the most important theorems of the theory can be deduced. In comparison with others formulations, the formal aspect has been improved by the use of certain mathematical theories, such as group theory and the theory of rigged Hilbert spaces. Our approach regards the fields as real things with symmetry properties. The general structure is analyzed and contrasted with relativistic theories.
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  10.  7
    Axiomatization of XPath with general data comparison.Sergio Abriola, Santiago Figueira & Nicolás González - forthcoming - Journal of Applied Non-Classical Logics:1-20.
    In this work, we study Hilbert-style proof systems for logics based on the data-aware language CoreDataXPath(↓) where the comparison relation between nodes is not necessarily an equivalence relation. We give a sound and complete axiomatization of the class of tree-like Kripke frames endowed with a general comparison relation between nodes. Modular extensions of this axiomatization are also discussed, including cases where the comparison relation is reflexive, symmetric, transitive and an equivalence. A notable highlight that we recover an axiomatization for CoreDataXPath(↓) (...)
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  11. Axiomatic foundations of Quantum Mechanics revisited: the case for systems.S. E. Perez-Bergliaffa, Gustavo E. Romero & H. Vucetich - 1996 - International Journal of Theoretical Phyisics 35:1805-1819.
    We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is discussed in this framework. It is shown that there is no contradiction between realism and recent experimental results.
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  12.  4
    Axiomatization of XPath with general data comparison.Conicet-uba Sergio Abriola Santiago Figueira Nicolás González A. Instituto de Ciencias de la Computación, Facultad de Ciencias Exactas Y. Naturales Argentinab Departamento de Computación & Argentina Uba - forthcoming - Journal of Applied Non-Classical Logics:1-20.
    In this work, we study Hilbert-style proof systems for logics based on the data-aware language CoreDataXPath(↓) where the comparison relation between nodes is not necessarily an equivalence relation. We give a sound and complete axiomatization of the class of tree-like Kripke frames endowed with a general comparison relation between nodes. Modular extensions of this axiomatization are also discussed, including cases where the comparison relation is reflexive, symmetric, transitive and an equivalence. A notable highlight that we recover an axiomatization for CoreDataXPath(↓) (...)
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  13.  70
    Axiomatizing the Logic of Imagination.Alessandro Giordani - 2019 - Studia Logica 107 (4):639-657.
    In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed (...)
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  14.  52
    An Axiomatic Theory of Inductive Inference.Luciano Pomatto & Alvaro Sandroni - 2018 - Philosophy of Science 85 (2):293-315.
    This article develops an axiomatic theory of induction that speaks to the recent debate on Bayesian orgulity. It shows the exact principles associated with the belief that data can corroborate universal laws. We identify two types of disbelief about induction: skepticism that the existence of universal laws of nature can be determined empirically, and skepticism that the true law of nature, if it exists, can be successfully identified. We formalize and characterize these two dispositions toward induction by introducing novel axioms (...)
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  15.  95
    Axiomatic foundations of non-relativistic quantum mechanics: A realistic approach.S. E. Perez Bergliaffa, Gustavo E. Romero & H. Vucetich - 1993 - International Journal of Theoretical Physics 32 (9):1507-1522.
    A realistic axiomatic formulation of nonrelativistic quantum mechanics for a single microsystem with spin is presented, from which the most important theorems of the theory can be deduced. In comparison with previous formulations, the formal aspect has been improved by the use of certain mathematical theories, such as the theory of equipped spaces, and group theory. The standard formalism is naturally obtained from the latter, starting from a central primitive concept: the Galilei group.
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  16. On Axiomatizing Shramko-Wansing’s Logic.Sergei P. Odintsov - 2009 - Studia Logica 91 (3):407-428.
    This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f, determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.
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  17.  74
    The Case Against Axiomatization.D. Lu - manuscript
    This paper provides a philosophical proof for the case against axiomatization.
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  18.  64
    Axiomatic quantum theory.Storrs McCall - 2001 - Journal of Philosophical Logic 30 (5):465-477.
    The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra-ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its adjoint. (...)
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  19. Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
    Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...)
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  20.  74
    Axiomatic rationality and ecological rationality.Gerd Gigerenzer - 2019 - Synthese 198 (4):3547-3564.
    Axiomatic rationality is defined in terms of conformity to abstract axioms. Savage limited axiomatic rationality to small worlds, that is, situations in which the exhaustive and mutually exclusive set of future states S and their consequences C are known. Others have interpreted axiomatic rationality as a categorical norm for how human beings should reason, arguing in addition that violations would lead to real costs such as money pumps. Yet a review of the literature shows little evidence that violations are actually (...)
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  21. Axiomatizing semantic theories of truth?Martin Fischer, Volker Halbach, Jönne Kriener & Johannes Stern - 2015 - Review of Symbolic Logic 8 (2):257-278.
    We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.
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  22. Why Axiomatize?Mario Bunge - 2017 - Foundations of Science 22 (4):695-707.
    Axiomatization is uncommon outside mathematics, partly for being often viewed as embalming, partly because the best-known axiomatizations have serious shortcomings, and partly because it has had only one eminent champion, namely David Hilbert. The aims of this paper are to describe what will be called dual axiomatics, for it concerns not just the formalism, but also the meaning of the key concepts; and to suggest that every instance of dual axiomatics presupposes some philosophical view or other. To illustrate (...)
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  23. Axiomatic Method in Albert the Great’s Metaphysics and Some of its Axioms. 박규희 - 2024 - philosophia medii aevi 30:55-90.
    알베르투스는 형이상학을 모든 학문들의 원리를 제공하는 기초 학문으로, 그 연구 대상은 “가장 먼저 유출된 존재”로 이해한다. 그리고 공리적 방법으로 존재와 선의 관계를 규명한 보에티우스의 『데헵도마디부스』를 자신의 형이상학적 체계 내에서 핵심적인 요소로 수용한다. 제일원인이 만물의 단일한 근거이고 세계가 여기서 창조되었다는 사상은 공리들과 그것들로 조합된 다수의 학적 지식들의 논증 질서에 대응한다. 알베르투스는 『원인론』의 제일원인을 그 자신인 것을 산출하는 원인으로 이해하는데, 어떠한 원인도 가지지 않고 피조물과도 결합되지 않는다는 점이 제일원인의 본질적인 특성이다. 이를 알베르투스는 『원인론 주해』와 『형이상학 주해』에서 보에티우스의 네 가지 공리를 가지고 해명한다.본 (...)
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  24.  20
    Minimal Axiomatization in Modal Logic.Fabio Bellissima & Saverio Cittadini - 1997 - Mathematical Logic Quarterly 43 (1):92-102.
    We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.
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  25. Optical axiomatization of Minkowski space-time geometry.Brent Mundy - 1986 - Philosophy of Science 53 (1):1-30.
    Minkowski geometry is axiomatized in terms of the asymmetric binary relation of optical connectibility, using ten first-order axioms and the second-order continuity axiom. An axiom system in terms of the symmetric binary optical connection relation is also presented. The present development is much simpler than the corresponding work of Robb, upon which it is modeled.
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  26.  35
    An axiomatic characterization of temporalised belief revision in the law.Luciano H. Tamargo, Diego C. Martinez, Antonino Rotolo & Guido Governatori - 2019 - Artificial Intelligence and Law 27 (4):347-367.
    This paper presents a belief revision operator that considers time intervals for modelling norm change in the law. This approach relates techniques from belief revision formalisms and time intervals with temporalised rules for legal systems. Our goal is to formalise a temporalised belief base and corresponding timed derivation, together with a proper revision operator. This operator may remove rules when needed or adapt intervals of time when contradictory norms are added in the system. For the operator, both constructive definition and (...)
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  27.  42
    Axiomatic extensions of the constructive logic with strong negation and the disjunction property.Andrzej Sendlewski - 1995 - Studia Logica 55 (3):377 - 388.
    We study axiomatic extensions of the propositional constructive logic with strong negation having the disjunction property in terms of corresponding to them varieties of Nelson algebras. Any such varietyV is characterized by the property: (PQWC) ifA,B V, thenA×B is a homomorphic image of some well-connected algebra ofV.We prove:• each varietyV of Nelson algebras with PQWC lies in the fibre –1(W) for some varietyW of Heyting algebras having PQWC, • for any varietyW of Heyting algebras with PQWC the least and the (...)
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  28.  38
    An axiomatization for until and since over the reals without the IRR rule.Mark Reynolds - 1992 - Studia Logica 51 (2):165 - 193.
    We give a Hilbert style axiomatization for the set of formulas in the temporal language with Until and Since which are valid over the real number flow of time. The axiomatization, which is orthodox in the sense of only having the usual temporal rules of inference, is complete with respect to single formulas.
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  29.  29
    Axiomatizations of Peano Arithmetic: A Truth-Theoretic View.Ali Enayat & Mateusz Łełyk - 2023 - Journal of Symbolic Logic 88 (4):1526-1555.
    We employ the lens provided by formal truth theory to study axiomatizations of Peano Arithmetic ${\textsf {(PA)}}$. More specifically, let Elementary Arithmetic ${\textsf {(EA)}}$ be the fragment $\mathsf {I}\Delta _0 + \mathsf {Exp}$ of ${\textsf {PA}}$, and let ${\textsf {CT}}^-[{\textsf {EA}}]$ be the extension of ${\textsf {EA}}$ by the commonly studied axioms of compositional truth ${\textsf {CT}}^-$. We investigate both local and global properties of the family of first order theories of the form ${\textsf {CT}}^-[{\textsf {EA}}] +\alpha $, where $\alpha (...)
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  30.  58
    An Axiomatic System and a Tableau Calculus for STIT Imagination Logic.Grigory K. Olkhovikov & Heinrich Wansing - 2018 - Journal of Philosophical Logic 47 (2):259-279.
    We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.
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  31.  11
    Axiomatic Formal Ontology.Uwe Meixner - 1997 - Dordrecht, Boston, and London: Kluwer Academic Publishers.
    Axiomatic Formal Ontology is a fairly comprehensive systematic treatise on general metaphysics. The axiomatic method is applied throughout the book. Its main theme is the construction of a general non-set-theoretical theory of intensional entities. Other important matters discussed are the metaphysics of modality, the nature of actual existence, mereology and the taxonomy of entities.
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  32.  25
    Axiomatizing a Minimal Discussive Logic.Oleg Grigoriev, Marek Nasieniewski, Krystyna Mruczek-Nasieniewska, Yaroslav Petrukhin & Vasily Shangin - 2023 - Studia Logica 111 (5):855-895.
    In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as D0 {\textsf {D}}_{\textsf {0}} D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic D2 {\textsf {D}}_{\textsf {2}} D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic D2 {\textsf {D}}_{\textsf {2}} D 2 but with the help of the deontic normal logic (...)
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  33.  51
    An axiomatic approach to predictability of outcomes in an interactive setting.Sebastian Bervoets - 2010 - Theory and Decision 68 (3):311-323.
    This article is an axiomatic approach to the problem of ranking game forms in terms of the predictability they offer to individuals. Two criteria are proposed and characterized, the CardMin and the CardMax. Both compare game forms on the basis of the number of distinct outcomes that can result from the choice of a CardMin (resp. CardMax) strategy. The CardMin (resp. CardMax) strategy is defined as a strategy leading to the smallest (resp. highest) number of different outcomes. In both cases, (...)
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  34. Axiomatizing bounded rationality: the priority heuristic.Mareile Drechsler, Konstantinos Katsikopoulos & Gerd Gigerenzer - 2014 - Theory and Decision 77 (2):183-196.
    This paper presents an axiomatic framework for the priority heuristic, a model of bounded rationality in Selten’s (in: Gigerenzer and Selten (eds.) Bounded rationality: the adaptive toolbox, 2001) spirit of using empirical evidence on heuristics. The priority heuristic predicts actual human choices between risky gambles well. It implies violations of expected utility theory such as common consequence effects, common ratio effects, the fourfold pattern of risk taking and the reflection effect. We present an axiomatization of a parameterized version of the (...)
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  35. The axiomatization of classical mechanics.Herbert A. Simon - 1954 - Philosophy of Science 21 (4):340-343.
    The purpose of this note is to examine a recent axiomatization of classical particle mechanics, and its relation to an alternative axiomatization I had earlier proposed. A comparison of the two proposals casts some interesting light on the problems of operationalism in classical celestial mechanics.1. Comparison of the Two Axiomatizations. The basic differences between the two proposals arise from the nature of the undefined terms. Both systems take the set of particles, time, and position as primitive notions. Both systems assume (...)
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  36. 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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  37.  27
    Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry.Victor Pambuccian - 2001 - Mathematical Logic Quarterly 47 (1):129-136.
    In this paper we provide quantifier-free, constructive axiomatizations for 2-dimensional absolute, Euclidean, and hyperbolic geometry. The main novelty consists in the first-order languages in which the axiom systems are formulated.
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  38.  90
    Axiomatizing Changing Conceptions of the Geometric Continuum I: Euclid-Hilbert†.John T. Baldwin - 2018 - Philosophia Mathematica 26 (3):346-374.
    We give a general account of the goals of axiomatization, introducing a variant on Detlefsen’s notion of ‘complete descriptive axiomatization’. We describe how distinctions between the Greek and modern view of number, magnitude, and proportion impact the interpretation of Hilbert’s axiomatization of geometry. We argue, as did Hilbert, that Euclid’s propositions concerning polygons, area, and similar triangles are derivable from Hilbert’s first-order axioms. We argue that Hilbert’s axioms including continuity show much more than the geometrical propositions of Euclid’s theorems and (...)
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  39. Axiomatic Theories of Partial Ground I: The Base Theory.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):161-191.
    This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...)
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  40.  27
    Axiomatizing first order consequences in inclusion logic.Fan Yang - 2020 - Mathematical Logic Quarterly 66 (2):195-216.
    Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed‐point logic. Inclusion logic is not axiomatisable in full, but its first order consequences can be axiomatized. In this paper, we provide such an explicit partial axiomatization by introducing a system of natural deduction for inclusion logic that is sound and complete for first order consequences in inclusion logic.
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  41. On axiomatizations of public announcement logic.Yanjing Wang & Qinxiang Cao - 2013 - Synthese 190 (S1).
    In the literature, different axiomatizations of Public Announcement Logic (PAL) have been proposed. Most of these axiomatizations share a “core set” of the so-called “reduction axioms”. In this paper, by designing non-standard Kripke semantics for the language of PAL, we show that the proof system based on this core set of axioms does not completely axiomatize PAL without additional axioms and rules. In fact, many of the intuitive axioms and rules we took for granted could not be derived from the (...)
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  42.  39
    Axiomatizing the monodic fragment of first-order temporal logic.Frank Wolter & Michael Zakharyaschev - 2002 - Annals of Pure and Applied Logic 118 (1-2):133-145.
    It is known that even seemingly small fragments of the first-order temporal logic over the natural numbers are not recursively enumerable. In this paper we show that the monodic fragment is an exception by constructing its finite Hilbert-style axiomatization. We also show that the monodic fragment with equality is not recursively axiomatizable.
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  43.  43
    An Axiomatic Approach to the Quantified Argument Calculus.Matteo Pascucci - 2023 - Erkenntnis 88 (8):3605-3630.
    The present article employs a model-theoretic semantics to interpret a fragment of the language of the Quantified Argument Calculus (Quarc), a recently introduced logical system whose main aim is capturing the structure of natural language sentences in a closer way than does the language of classical logic. The main contribution is an axiomatization for the set of formulas that are valid in all standard interpretations within the employed semantics.
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  44. What is the axiomatic method?Jaakko Hintikka - 2011 - Synthese 183 (1):69-85.
    The modern notion of the axiomatic method developed as a part of the conceptualization of mathematics starting in the nineteenth century. The basic idea of the method is the capture of a class of structures as the models of an axiomatic system. The mathematical study of such classes of structures is not exhausted by the derivation of theorems from the axioms but includes normally the metatheory of the axiom system. This conception of axiomatization satisfies the crucial requirement that the derivation (...)
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  45.  11
    Axiomatization of a Basic Logic of Logical Bilattices.Mitio Takano - 2016 - Bulletin of the Section of Logic 45 (2).
    A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing as a candidate for the basic logic of logical bilattices.
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    Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron).Gianpiero Cattaneo & Federico Laudisa - 1994 - Foundations of Physics 24 (5):631-683.
    On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an (...)
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  47. (1 other version)An axiomatic formulation of the Montevideo interpretation of quantum mechanics.Rodolfo Gambini, Luis Pedro García-Pintos & Jorge Pullin - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (4):256-263.
    We make a first attempt to axiomatically formulate the Montevideo interpretation of quantum mechanics. In this interpretation environmental decoherence is supplemented with loss of coherence due to the use of realistic clocks to measure time to solve the measurement problem. The resulting formulation is framed entirely in terms of quantum objects without having to invoke the existence of measurable classical quantities like the time in ordinary quantum mechanics. The formulation eliminates any privileged role to the measurement process giving an objective (...)
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  48. Axiomatic truth, syntax and metatheoretic reasoning.Graham E. Leigh & Carlo Nicolai - 2013 - Review of Symbolic Logic 6 (4):613-636.
    Following recent developments in the literature on axiomatic theories of truth, we investigate an alternative to the widespread habit of formalizing the syntax of the object-language into the object-language itself. We first argue for the proposed revision, elaborating philosophical evidences in favor of it. Secondly, we present a general framework for axiomatic theories of truth with theories of syntax. Different choices of the object theory O will be considered. Moreover, some strengthenings of these theories will be introduced: we will consider (...)
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  49.  53
    Axiomatizing Jaśkowski’s Discussive Logic D2\mathbf {D_2} D 2.Hitoshi Omori & Jesse Alama - 2018 - Studia Logica 106 (6):1163-1180.
    We outline the rather complicated history of attempts at axiomatizing Jaśkowski’s discussive logic D2\mathbf {D_2} D2 and show that some clarity can be had by paying close attention to the language we work with. We then examine the problem of axiomatizing D2\mathbf {D_2} D2 in languages involving discussive conjunctions. Specifically, we show that recent attempts by Ciuciura are mistaken. Finally, we present an axiomatization of D2\mathbf {D_2} D2 in the language Jaśkowski suggested in his second paper on discussive logic, by (...)
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    Axiomatizing the Logic of Comparative Probability.John P. Burgess - 2010 - Notre Dame Journal of Formal Logic 51 (1):119-126.
    1 Choice conjecture In axiomatizing nonclassical extensions of classical sentential logic one tries to make do, if one can, with adding to classical sentential logic a finite number of axiom schemes of the simplest kind and a finite number of inference rules of the simplest kind. The simplest kind of axiom scheme in effect states of a particular formula P that for any substitution of formulas for atoms the result of its application to P is to count as an axiom. (...)
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