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Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Jagiellonian University)
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  1. added 2016-06-23
    Guram Bezhanishvili, Nick Bezhanishvili & Julia Ilin (forthcoming). Cofinal Stable Logics. Studia Logica:1-31.
    We generalize the \}\)-canonical formulas to \}\)-canonical rules, and prove that each intuitionistic multi-conclusion consequence relation is axiomatizable by \}\)-canonical rules. This yields a convenient characterization of stable superintuitionistic logics. The \}\)-canonical formulas are analogues of the \}\)-canonical formulas, which are the algebraic counterpart of Zakharyaschev’s canonical formulas for superintuitionistic logics. Consequently, stable si-logics are analogues of subframe si-logics. We introduce cofinal stable intuitionistic multi-conclusion consequence relations and cofinal stable si-logics, thus answering the question of what the analogues of cofinal (...)
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  2. added 2016-06-23
    Lloyd Humberstone (2016). Philosophical Applications of Modal Logic. College Publications.
  3. added 2016-06-22
    Nicholas Asher, Soumya Paul & Antoine Venant (forthcoming). Message Exchange Games in Strategic Contexts. Journal of Philosophical Logic:1-50.
    When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call such (...)
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  4. added 2016-06-22
    Guram Bezhanishvili & Wesley H. Holliday (forthcoming). Locales, Nuclei, and Dragalin Frames. In Lev Beklemishev & Stéphane Demri (eds.), Advances in Modal Logic, Vol. 11. College Publications
    It is a classic result in lattice theory that a poset is a complete lattice iff it can be realized as fixpoints of a closure operator on a powerset. Dragalin [9,10] observed that a poset is a locale (complete Heyting algebra) iff it can be realized as fixpoints of a nucleus on the locale of upsets of a poset. He also showed how to generate a nucleus on upsets by adding a structure of “paths” to a poset, forming what we (...)
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  5. added 2016-06-22
    Gilbert Plumer (2016). Argumentatively Evil Storytelling. In D. Mohammend & M. Lewinski (eds.), Argumentation and Reasoned Action: Proceedings of the 1st European Conference on Argumentation, Lisbon 2015, Vol. 1. College Publications 615-630.
    What can make storytelling “evil” in the sense that the storytelling leads to accepting a view for no good reason, thus allowing ill-reasoned action? I mean the storytelling can be argumentatively evil, not trivially that (e.g.) the overt speeches of characters can include bad arguments. The storytelling can be argumentatively evil in that it purveys false premises, or purveys reasoning that is formally or informally fallacious. My main thesis is that as a rule, the shorter the fictional narrative, the greater (...)
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  6. added 2016-06-21
    Christoph Benzmüller (forthcoming). Cut-Elimination for Quantified Conditional Logic. Journal of Philosophical Logic:1-21.
    A semantic embedding of quantified conditional logic in classical higher-order logic is utilized for reducing cut-elimination in the former logic to existing results for the latter logic. The presented embedding approach is adaptable to a wide range of other logics, for many of which cut-elimination is still open. However, special attention has to be payed to cut-simulation, which may render cut-elimination as a pointless criterion.
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  7. added 2016-06-19
    Robert K. Meyer & Edwin D. Mares (1993). Semantics of Entailment 0. In Peter Schroeder-Heister & Kosta Dosen (eds.), Substructural Logics. Oxford Science Publications 239-258.
  8. added 2016-06-17
    Chrysafis Hartonas (forthcoming). First-Order Frames for Orthomodular Quantum Logic. Journal of Applied Non-Classical Logics:1-12.
    One of the main problems of the orthoframe approach to quantum logic was that orthomodularity could not be captured by any first-order condition. This paper studies an elementary and natural class of orthomodular frames that can work around this limitation. Set-theoretically, the frames we propose form a natural subclass of the orthoframes, where is an irreflexive and symmetric relation on X. More specifically, they are partially-ordered orthoframes with a designated subset. Our frame class contains the canonical orthomodular frame of the (...)
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  9. added 2016-06-16
    Alessandro Giordani & Ilaria Canavotto (forthcoming). Basic Action Deontic Logic. In DEON Proceedings 2016.
    The aim of this paper is to introduce a system of dynamic deontic logic in which the main problems related to the de finition of deontic concepts, especially those emerging from a standard analysis of permission in terms of possibility of doing an action without incurring in a violation of the law, are solved. The basic idea is to introduce two crucial distinctions allowing us to differentiate (i) what is ideal with respect to a given code, which fixes the types (...)
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  10. added 2016-06-16
    Alessandro Giordani (forthcoming). Perspectival Logic of Acceptance and Rejection. Logique and Analyse.
    This paper aims at developing a logical theory of perspectival epistemic attitudes. After presenting a standard framework for modeling acceptance, where the epistemic space of an agent coincides with a unique epistemic cell, more complex systems are introduced, which are characterized by the existence of many connected epistemic cells, and different possible attitudes towards a proposition, both positive and negative, are discussed. In doing that, we also propose some interesting ways in which the systems can be interpreted on well known (...)
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  11. added 2016-06-16
    George Englebretsen (forthcoming). Fred Sommers’ Contributions to Formal Logic. History and Philosophy of Logic:1-23.
    Fred Sommers passed away in October of 2014 in his 92nd year. Having begun his teaching at Columbia University, he eventually became the Harry A. Wolfson Chair in Philosophy at Brandeis University, where he taught from 1963 to 1993. During his long and productive career, Sommers authored or co-authored over 50 books, articles, reviews, etc., presenting his ideas on numerous occasions throughout North America and Europe. His work was characterized by a commitment to the preservation and application of historical insights (...)
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  12. added 2016-06-14
    Neil Tennant (forthcoming). Normalizability, Cut Eliminability and Paradox. Synthese:1-20.
    This is a reply to the considerations advanced by Schroeder-Heister and Tranchini as prima facie problematic for the proof-theoretic criterion of paradoxicality, as originally presented in Tennant and subsequently amended in Tennant. Countering these considerations lends new importance to the parallelized forms of elimination rules in natural deduction.
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  13. added 2016-06-13
    Michael Starks, What Do Paraconsistent, Undecidable, Random, Computable and Incomplete Mean? A Review of Godel's Way: Exploits Into an Undecidable World by Gregory Chaitin, Francisco A Doria , Newton C.A. Da Costa 160p (2012).
    In ‘Godel’s Way’ three eminent scientists discuss issues such as undecidability, incompleteness, randomness, computability and paraconsistency. I approach these issues from the Wittgensteinian viewpoint that there are two basic issues which have completely different solutions. There are the scientific or empirical issues, which are facts about the world that need to be investigated observationally and philosophical issues as to how language can be used intelligibly (which include certain questions in mathematics and logic), which need to be decided by looking at (...)
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  14. added 2016-06-13
    Diego Castaño & Juan Manuel Cornejo (forthcoming). Gentzen-Style Sequent Calculus for Semi-Intuitionistic Logic. Studia Logica:1-21.
    The variety \ of semi-Heyting algebras was introduced by H. P. Sankappanavar [13] as an abstraction of the variety of Heyting algebras. Semi-Heyting algebras are the algebraic models for a logic HsH, known as semi-intuitionistic logic, which is equivalent to the one defined by a Hilbert style calculus in Cornejo :9–25, 2011) [6]. In this article we introduce a Gentzen style sequent calculus GsH for the semi-intuitionistic logic whose associated logic GsH is the same as HsH. The advantage of this (...)
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  15. added 2016-06-12
    Alex Davies (2016). Entailments Are Cancellable. Ratio 29 (2).
    Several philosophers have recently claimed that if a proposition is cancellable from an uttered sentence then that proposition is not entailed by that uttered sentence. The claim should be a familiar one. It has become a standard device in the philosopher's tool-kit. I argue that this claim is false. There is a kind of entailment—which I call “modal entailment”—that is context-sensitive and, because of this, cancellable. So cancellability does not show that a proposition is not entailed by an uttered sentence. (...)
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  16. added 2016-06-12
    Serge Robert & Janie Brisson (2016). The Klein Group, Squares of Opposition and the Explanation of Fallacies in Reasoning. Logica Universalis 10 (2-3):377-392.
    During the last decades, the psychology of reasoning has identified experimentally many fallacies committed by spontaneous reasoners. Given these experimental results, some theories have been developed about this phenomenon, mainly algorithmic theories. This paper develops instead a computational modelling of these current fallacies which appear as simplifications in the treatment of information that do not respect the formal rules of classical propositional logic. These fallacies are explained as crushes in the Klein group structure and so, in squares of opposition. These (...)
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  17. added 2016-06-11
    Alexander P. Kreuzer & Keita Yokoyama (forthcoming). On Principles Between Σ1- and Σ2-Induction, and Monotone Enumerations. Journal of Mathematical Logic.
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  18. added 2016-06-11
    Natasha Dobrinen (forthcoming). Infinite-Dimensional Ellentuck Spaces and Ramsey-Classification Theorems. Journal of Mathematical Logic.
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  19. added 2016-06-10
    Takuro Onishi (forthcoming). Understanding Negation Implicationally in the Relevant Logic R. Studia Logica:1-19.
    A star-free relational semantics for relevant logic is presented together with a sound and complete sequent proof theory. It is an extension of the dualist approach to negation regarded as modality, according to which de Morgan negation in relevant logic is better understood as the confusion of two negative modalities. The present work shows a way to define them in terms of implication and a new connective, co-implication, which is modeled by respective ternary relations. The defined negations are confused by (...)
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  20. added 2016-06-10
    Marco Panza (forthcoming). Infini, Logique, Geométrie. History and Philosophy of Logic:1-4.
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  21. added 2016-06-09
    Larry Wright (2012). Critical Thinking: An Introoduction to Analytical Reading and Reasoning. Oxford University Press Usa.
    Critical Thinking: An Introduction to Analytical Reading and Reasoning, Second Edition, provides a nontechnical vocabulary and analytic apparatus that guide students in identifying and articulating the central patterns found in reasoning and in expository writing more generally. Understanding these patterns of reasoning helps students to better analyze, evaluate, and construct arguments and to more easily comprehend the full range of everyday arguments found in ordinary journalism. Critical Thinking, Second Edition, distinguishes itself from other texts in the field by emphasizing analytical (...)
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  22. added 2016-06-06
    Jean-Yves Beziau (2016). Disentangling Contradiction From Contrariety Via Incompatibility. Logica Universalis 10 (2-3):157-170.
    Contradiction is often confused with contrariety. We propose to disentangle contrariety from contradiction using the hexagon of opposition, providing a clear and distinct characterization of three notions: contrariety, contradiction, incompatibility. At the same time, this hexagonal structure describes and explains the relations between them.
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  23. added 2016-06-06
    Jean-Yves Beziau & Raffaela Giovagnoli (2016). The Vatican Square. Logica Universalis 10 (2-3):135-141.
    After explaining the interdisciplinary aspect of the series of events organized around the square of opposition since 2007, we discuss papers related to the 4th World Congress on the Square of Opposition which was organized in the Vatican at the Pontifical Lateran University in 2014. We distinguish three categories of work: those dealing with the evolution and development of the theory of opposition, those using the square as a metalogical tool to give a better understanding of various systems of logic (...)
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  24. added 2016-06-05
    Apoloniusz Tyszka, A Conjecture on Rational Arithmetic Which Implies That There is an Algorithm Which Takes as Input a Diophantine Equation, Returns an Integer, and This Integer is Greater Than the Heights of Rational Solutions If the Solution Set is Finite.
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  25. added 2016-06-05
    Wesley H. Holliday (forthcoming). Knowledge, Time, and Paradox: Introducing Sequential Epistemic Logic. In Hans van Ditmarsch & Gabriel Sandu (eds.), Outstanding Contributions to Logic: Jaakko Hintikka. Springer
    Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...)
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  26. added 2016-06-03
    Douglas S. Bridges (2016). Apartness Spaces and Uniform Neighbourhood Structures. Annals of Pure and Applied Logic 167 (9):850-864.
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  27. added 2016-06-03
    Thierry Coquand, Maria Emilia Maietti, Giovanni Sambin & Peter Schuster (2016). Preface. Annals of Pure and Applied Logic 167 (9):725.
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  28. added 2016-06-03
    Martín Escardó & Chuangjie Xu (2016). A Constructive Manifestation of the Kleene–Kreisel Continuous Functionals. Annals of Pure and Applied Logic 167 (9):770-793.
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  29. added 2016-06-03
    Olivia Caramello (2016). Priestley-Type Dualities for Partially Ordered Structures. Annals of Pure and Applied Logic 167 (9):820-849.
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  30. added 2016-06-03
    Martín Hötzel Escardó & Thomas Streicher (2016). The Intrinsic Topology of Martin-Löf Universes. Annals of Pure and Applied Logic 167 (9):794-805.
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  31. added 2016-06-03
    Francesco Ciraulo & Steven Vickers (2016). Positivity Relations on a Locale. Annals of Pure and Applied Logic 167 (9):806-819.
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  32. added 2016-06-03
    Iosif Petrakis (2016). Limit Spaces with Approximations. Annals of Pure and Applied Logic 167 (9):737-752.
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  33. added 2016-06-03
    Dănuţ Rusu & Gabriel Ciobanu (2016). Essential and Density Topologies of Continuous Domains. Annals of Pure and Applied Logic 167 (9):726-736.
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  34. added 2016-06-03
    Basil A. Karádais (2016). Atomicity, Coherence of Information, and Point-Free Structures. Annals of Pure and Applied Logic 167 (9):753-769.
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  35. added 2016-06-02
    Dorota Leszczyńska-Jasion & Szymon Chlebowski (2015). Dual Erotetic Calculi and the Minimal $${\Mathsf{LFI}}$$ LFI. Studia Logica 103 (6):1245-1278.
    An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic. In this paper, a new erotetic calculus for Classical Propositional Logic, dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic $${\mathsf{CLuN}}$$ CLuN and its extensions $${\mathsf{CLuNs}}$$ CLuNs and $${\mathsf{mbC}}$$ mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to (...)
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  36. added 2016-06-01
    Maurice Finocchiaro (2013). Meta-Argumentation. College Publications.
  37. added 2016-06-01
    Leo Groarke, Informal Logic. Stanford Encyclopedia of Philosophy.
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  38. added 2016-06-01
    Ralph Johnson (2000). Manifest Rationality. Lawrence Earlbaum Associates.
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  39. added 2016-05-31
    Johan van Benthem (2015). Logic and Philosophy, a Sea of Stories. Tsinghua Studies in Western Philosophy 1 (1):124-153.
    The interface of logic and philosophy is diverse, and has always been so. Understanding the interplay raises issues on which some philosophers have strong a priori views. My own preference as a working logician is to proceed by actual history of ideas, something still largely to be written for modern logic. I shall present a few lines connecting logic and philosophy around the theme of implication and consequence, and show how rich the agenda is as it keeps evolving with contributions (...)
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  40. added 2016-05-29
    Fraser MacBride (2015). "On The Origins of Order: Non-Symmetric or Only Symmetric Relations?". In M. J. Loux & G. Galuzzo (eds.), The Problem of Universals in Contemporary Philosophy. Cambridge University Press 173-94.
    In this paper I contribute a further element to the case for admitting non-symmetric relations by dismantling the case against them. Armstrong and Dorr have both argued (1) that asymmetric relations give rise to ‘brute necessities’, whilst Dorr further argues (2) that admitting non-symmetric relations generates spurious possibilities and (3) that exploiting work of Goodman and Hazen, we can do without non-symmetric relations anyway. Against (1) I argue that neither Armstrong nor Dorr succeed in avoiding brute necessities themselves. Against (2) (...)
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  41. added 2016-05-24
    Joost J. Joosten (forthcoming). Turing–Taylor Expansions for Arithmetic Theories. Studia Logica:1-19.
    Turing progressions have been often used to measure the proof-theoretic strength of mathematical theories: iterate adding consistency of some weak base theory until you “hit” the target theory. Turing progressions based on n-consistency give rise to a \ proof-theoretic ordinal \ also denoted \. As such, to each theory U we can assign the sequence of corresponding \ ordinals \. We call this sequence a Turing-Taylor expansion or spectrum of a theory. In this paper, we relate Turing-Taylor expansions of sub-theories (...)
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  42. added 2016-05-22
    Koji Nakazawa & Ken-Etsu Fujita (forthcoming). Compositional Z: Confluence Proofs for Permutative Conversion. Studia Logica:1-20.
    This paper gives new confluence proofs for several lambda calculi with permutation-like reduction, including lambda calculi corresponding to intuitionistic and classical natural deduction with disjunction and permutative conversions, and a lambda calculus with explicit substitutions. For lambda calculi with permutative conversion, naïve parallel reduction technique does not work, and traditional notion of residuals is required as Ando pointed out. This paper shows that the difficulties can be avoided by extending the technique proposed by Dehornoy and van Oostrom, called the Z (...)
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  43. added 2016-05-21
    Inge Bal & Peter Verdée (2015). A New Approach to Classical Relevance. Studia Logica 103 (5):919-954.
    In this paper we present a logic that determines when implications in a classical logic context express a relevant connection between antecedent and consequent. In contrast with logics in the relevance logic literature, we leave classical negation intact—in the sense that the law of non-contradiction can be used to obtain relevant implications, as long as there is a connection between antecedent and consequent. On the other hand, we give up the requirement that our theory of relevance should be able to (...)
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  44. added 2016-05-19
    Valérie Lynn Therrien (2012). INVENTING LOGIC: THE LÖWENHEIM-SKOLEM THEOREM AND FIRST- AND SECOND-ORDER LOGIC. Pensées Canadiennes 10.
  45. added 2016-05-17
    Paul D. Thorn & Gerhard Schurz (forthcoming). Qualitative Probabilistic Inference Under Varied Entropy Levels. Journal of Applied Logic.
    In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield (...)
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  46. added 2016-05-17
    Martin L. Jönsson (forthcoming). Interpersonal Sameness of Meaning for Inferential Role Semantics. Journal of Philosophical Logic:1-29.
    Inferential Role Semantics is often criticized for being incompatible with the platitude that words of different speakers can mean the same thing. While many assume that this platitude can be accommodated by understanding sameness of meaning in terms of similarity of meaning, no worked out proposal has ever been produced for Inferential Role Semantics. I rectify this important omission by giving a detailed structural account of meaning similarity in terms of graph theory. I go on to argue that this account (...)
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  47. added 2016-05-17
    Tore Fjetland Øgaard (2016). Paths to Triviality. Journal of Philosophical Logic 45 (3):237-276.
    This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → ⊩B → trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ∧) → and → ¬A, the fusion connective and the Ackermann constant. An overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs (...)
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  48. added 2016-05-17
    Sean Walsh (2016). Predicativity, the Russell-Myhill Paradox, and Church’s Intensional Logic. Journal of Philosophical Logic 45 (3):277-326.
    This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...)
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  49. added 2016-05-17
    Tabea Hirzel (2015). Principles of Liberty: A Design-Based Research on Liberty as A Priori Constitutive Principle of the Social in the Swiss Nation Story. Dissertation, SCM University, Zug, Switzerland
    One of the still unsolved problems in liberal anarchism is a definition of social constituency in positive terms. Partially, this had been solved by the advancements of liberal discourse ethics. These approaches, built on praxeology as a universal framework for social formation, are detached from the need of any previous or external authority or rule for the discursive partners. However, the relationship between action, personal identity, and liberty within the process of a community becoming solely generated from the praxeological a (...)
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  50. added 2016-05-16
    Frode Bjørdal (2016). Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability. Logica Universalis 10 (2-3):373-376.
    We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for the Square (...)
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