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Mathematical logic

New York: Springer. Edited by Jörg Flum & Wolfgang Thomas (1996)

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  1. Dialectical Contradictions and Classical Formal Logic.Inoue Kazumi - 2014 - International Studies in the Philosophy of Science 28 (2):113-132.
    A dialectical contradiction can be appropriately described within the framework of classical formal logic. It is in harmony with the law of noncontradiction. According to our definition, two theories make up a dialectical contradiction if each of them is consistent and their union is inconsistent. It can happen that each of these two theories has an intended model. Plenty of examples are to be found in the history of science.
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  • The structure of the models of decidable monadic theories of graphs.D. Seese - 1991 - Annals of Pure and Applied Logic 53 (2):169-195.
    In this article the structure of the models of decidable monadic theories of planar graphs is investigated. It is shown that if the monadic theory of a class K of planar graphs is decidable, then the tree-width in the sense of Robertson and Seymour of the elements of K is universally bounded and there is a class T of trees such that the monadic theory of K is interpretable in the monadic theory of T.
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  • A history of theoria.Sven Ove Hansson - 2009 - Theoria 75 (1):2-27.
    Theoria , the international Swedish philosophy journal, was founded in 1935. Its contributors in the first 75 years include the major Swedish philosophers from this period and in addition a long list of international philosophers, including A. J. Ayer, C. D. Broad, Ernst Cassirer, Hector Neri Castañeda, Arthur C. Danto, Donald Davidson, Nelson Goodman, R. M. Hare, Carl G. Hempel, Jaakko Hintikka, Saul Kripke, Henry E. Kyburg, Keith Lehrer, Isaac Levi, David Lewis, Gerald MacCallum, Richard Montague, Otto Neurath, Arthur N. (...)
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  • Can robots make good models of biological behaviour?Barbara Webb - 2001 - Behavioral and Brain Sciences 24 (6):1033-1050.
    How should biological behaviour be modelled? A relatively new approach is to investigate problems in neuroethology by building physical robot models of biological sensorimotor systems. The explication and justification of this approach are here placed within a framework for describing and comparing models in the behavioural and biological sciences. First, simulation models – the representation of a hypothesis about a target system – are distinguished from several other relationships also termed “modelling” in discussions of scientific explanation. Seven dimensions on which (...)
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  • (1 other version)Indiscernibles, general covariance, and other symmetries.Simon Saunders - 2002 - In Abhay Ashtekar, Jürgen Renn, Don Howard, Abner Shimony & S. Sarkar (eds.), Revisiting the Foundations of Relativistic Physics. Festschrift in Honour of John Stachel. Kluwer Academic Publishers.
    What is the meaning of general covariance? We learn something about it from the hole argument, due originally to Einstein. In his search for a theory of gravity, he noted that if the equations of motion are covariant under arbitrary coordinate transformations, then particle coordinates at a given time can be varied arbitrarily - they are underdetermined - even if their values at all earlier times are held fixed. It is the same for the values of fields. The argument can (...)
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  • On the logical foundations of compound predicate formulae for legal knowledge representation.Hajime Yoshino - 1997 - Artificial Intelligence and Law 5 (1-2):77-96.
    In order to represent legal knowledge adequately, it is vital to create a formal device that can freely construct an individual concept directly from a predicate expression. For this purpose, a Compound Predicate Formula (CPF) is formulated for use in legal expert systems. In this paper, we willattempt to explain the nature of CPFs by rigorous logical foundation, i.e., establishing their syntax and semantics precisely through the use of appropriate examples. We note the advantages of our system over other such (...)
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  • A logical expression of reasoning.Arthur Buchsbaum, Tarcisio Pequeno & Marcelino Pequeno - 2007 - Synthese 154 (3):431 - 466.
    A non-monotonic logic, the Logic of Plausible Reasoning (LPR), capable of coping with the demands of what we call complex reasoning, is introduced. It is argued that creative complex reasoning is the way of reasoning required in many instances of scientific thought, professional practice and common life decision taking. For managing the simultaneous consideration of multiple scenarios inherent in these activities, two new modalities, weak and strong plausibility, are introduced as part of the Logic of Plausible Deduction (LPD), a deductive (...)
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  • Animals, zombanimals, and the total Turing test: The essence of artificial intelligence.Selmer Bringsjord - 2000 - Journal of Logic Language and Information 9 (4):397-418.
    Alan Turing devised his famous test (TT) through a slight modificationof the parlor game in which a judge tries to ascertain the gender of twopeople who are only linguistically accessible. Stevan Harnad hasintroduced the Total TT, in which the judge can look at thecontestants in an attempt to determine which is a robot and which aperson. But what if we confront the judge with an animal, and arobot striving to pass for one, and then challenge him to peg which iswhich? (...)
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  • Creativity, the Turing test, and the (better) Lovelace test.Selmer Bringsjord, P. Bello & David A. Ferrucci - 2001 - Minds and Machines 11 (1):3-27.
    The Turing Test is claimed by many to be a way to test for the presence, in computers, of such ``deep'' phenomena as thought and consciousness. Unfortunately, attempts to build computational systems able to pass TT have devolved into shallow symbol manipulation designed to, by hook or by crook, trick. The human creators of such systems know all too well that they have merely tried to fool those people who interact with their systems into believing that these systems really have (...)
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  • Thoughts about Thoughts: The Structure of Fregean Propositions.Nathan Bice - 2019 - Dissertation, Columbia University
    This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...)
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  • Aspectos metafísicos na física de Newton: Deus.Bruno Camilo de Oliveira - 2011 - In Luiz Henrique de Araújo Dutra & Alexandre Meyer Luz (eds.), Coleção rumos da epistemologia. pp. 186-201.
    CAMILO, Bruno. Aspectos metafísicos na física de Newton: Deus. In: DUTRA, Luiz Henrique de Araújo; LUZ, Alexandre Meyer (org.). Temas de filosofia do conhecimento. Florianópolis: NEL/UFSC, 2011. p. 186-201. (Coleção rumos da epistemologia; 11). Através da análise do pensamento de Isaac Newton (1642-1727) encontramos os postulados metafísicos que fundamentam a sua mecânica natural. Ao deduzir causa de efeito, ele acreditava chegar a uma causa primeira de todas as coisas. A essa primeira causa de tudo, onde toda a ordem e leis (...)
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  • Dedekind's Logicism.Ansten Mørch Klev - 2015 - Philosophia Mathematica:nkv027.
    A detailed argument is provided for the thesis that Dedekind was a logicist about arithmetic. The rules of inference employed in Dedekind's construction of arithmetic are, by his lights, all purely logical in character, and the definitions are all explicit; even the definition of the natural numbers as the abstract type of simply infinite systems can be seen to be explicit. The primitive concepts of the construction are logical in their being intrinsically tied to the functioning of the understanding.
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  • By Disanalogy, Cyberwarfare Is Utterly New.Selmer Bringsjord & John Licato - 2015 - Philosophy and Technology 28 (3):339-358.
    We provide an underlying theory of argument by disanalogy, in order to employ it to show that cyberwarfare is fundamentally new. Once this general case is made, the battle is won: we are well on our way to establishing our main thesis: that Just War Theory itself must be modernized. Augustine and Aquinas had a stunningly long run, but today’s world, based as it is on digital information and increasingly intelligent information-processing, points the way to a beast so big and (...)
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  • (2 other versions)Logic TK: Algebraic Notions from Tarski’s Consequence Operator.Hércules A. Feitosa, Mauri C. Do Nascimento & Maria Claudia C. Grácio - 2010 - Principia: An International Journal of Epistemology 14 (1):47-70.
    Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.
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  • The physics and metaphysics of identity and individuality: Steven French and Décio Krause: Identity in physics: A historical, philosophical, and formal analysis. Oxford: Clarendon Press, 2006, 440 pp, £68.00 HB.Don Howard, Bas C. van Fraassen, Otávio Bueno, Elena Castellani, Laura Crosilla, Steven French & Décio Krause - 2010 - Metascience 20 (2):225-251.
    The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, 50139 (...)
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  • A refutation of Penrose's Godelian case against artificial intelligence.Selmer Bringsjord - 2000
    Having, as it is generally agreed, failed to destroy the computational conception of mind with the G\"{o}delian attack he articulated in his {\em The Emperor's New Mind}, Penrose has returned, armed with a more elaborate and more fastidious G\"{o}delian case, expressed in and 3 of his {\em Shadows of the Mind}. The core argument in these chapters is enthymematic, and when formalized, a remarkable number of technical glitches come to light. Over and above these defects, the argument, at best, is (...)
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  • Are we evolved computers?: A critical review of Steven Pinker's how the mind works. [REVIEW]Selmer Bringsjord - 2001 - Philosophical Psychology 14 (2):227 – 243.
    Steven Pinker's How the mind works (HTMW) marks in my opinion an historic point in the history of humankind's attempt to understand itself. Socrates delivered his "know thyself" imperative rather long ago, and now, finally, in this behemoth of a book, published at the dawn of a new millennium, Pinker steps up to have psychology tell us what we are: computers crafted by evolution - end of story; mystery solved; and the poor philosophers, having never managed to obey Socrates' command, (...)
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  • Proof verification and proof discovery for relativity.Naveen Sundar Govindarajalulu, Selmer Bringsjord & Joshua Taylor - 2015 - Synthese 192 (7):2077-2094.
    The vision of machines autonomously carrying out substantive conjecture generation, theorem discovery, proof discovery, and proof verification in mathematics and the natural sciences has a long history that reaches back before the development of automatic systems designed for such processes. While there has been considerable progress in proof verification in the formal sciences, for instance the Mizar project’ and the four-color theorem, now machine verified, there has been scant such work carried out in the realm of the natural sciences—until recently. (...)
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  • Analogy, explanation, and proof.John E. Hummel, John Licato & Selmer Bringsjord - 2014 - Frontiers in Human Neuroscience 8.
    People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the inference that the milk is sour have in common with the proof that, say, the square root of two (...)
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  • A Neighbourhood Semantics for the Logic TK.Cezar A. Mortari & Hércules de Araújo Feitosa - 2011 - Principia: An International Journal of Epistemology 15 (2):287.
    The logic TK was introduced as a propositional logic extending the classical propositional calculus with a new unary operator which interprets some conceptions of Tarski’s consequence operator. TK-algebras were introduced as models to TK . Thus, by using algebraic tools, the adequacy (soundness and completeness) of TK relatively to the TK-algebras was proved. This work presents a neighbourhood semantics for TK , which turns out to be deductively equivalent to the non-normal modal logic EMT4 . DOI:10.5007/1808-1711.2011v15n2p287.
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  • A new solution to the paradoxes of rational acceptability.Igor Douven - 2002 - British Journal for the Philosophy of Science 53 (3):391-410.
    The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...)
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  • The preface paradox revisited.Igor Douven - 2003 - Erkenntnis 59 (3):389 - 420.
    The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version (...)
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  • Atomic ontology.Andrew Parisi - 2020 - Synthese 197 (1):355-379.
    The aim of this article is to offer a method for determining the ontological commitments of a formalized theory. The second section shows that determining the consequence relation of a language model-theoretically entails that the ontology of a theory is tied very closely to the variables that feature in that theory. The third section develops an alternative way of determining the ontological commitments of a theory given a proof-theoretic account of the consequence relation for the language that theory is in. (...)
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  • Computation, among other things, is beneath us.Selmer Bringsjord - 1994 - Minds and Machines 4 (4):469-88.
    What''s computation? The received answer is that computation is a computer at work, and a computer at work is that which can be modelled as a Turing machine at work. Unfortunately, as John Searle has recently argued, and as others have agreed, the received answer appears to imply that AI and Cog Sci are a royal waste of time. The argument here is alarmingly simple: AI and Cog Sci (of the Strong sort, anyway) are committed to the view that cognition (...)
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  • Cognition is not computation: The argument from irreversibility.Selmer Bringsjord - 1997 - Synthese 113 (2):285-320.
    The dominant scientific and philosophical view of the mind – according to which, put starkly, cognition is computation – is refuted herein, via specification and defense of the following new argument: Computation is reversible; cognition isn't; ergo, cognition isn't computation. After presenting a sustained dialectic arising from this defense, we conclude with a brief preview of the view we would put in place of the cognition-is-computation doctrine.
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  • Zero-place operations and functional completeness, and the definition of new connectives.I. L. Humberstone - 1993 - History and Philosophy of Logic 14 (1):39-66.
    Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...)
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  • Computer Science as Immaterial Formal Logic.Selmer Bringsjord - 2020 - Philosophy and Technology 33 (2):339-347.
    I critically review Raymond Turner’s Computational Artifacts – Towards a Philosophy of Computer Science by placing beside his position a rather different one, according to which computer science is a branch of, and is therefore subsumed by, immaterial formal logic.
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  • The Quasi-lattice of Indiscernible Elements.Mauri Cunha do Nascimento, Décio Krause & Hércules Araújo Feitosa - 2011 - Studia Logica 97 (1):101-126.
    The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice ( $${\mathfrak{I}}$$ -lattice), which can be modeled by an algebraic structure built in quasi-set theory $${\mathfrak{Q}}$$. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that ‘naturally’ arises is non distributive.
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  • Toward a formal philosophy of hypercomputation.Selmer Bringsjord & Michael Zenzen - 2002 - Minds and Machines 12 (2):241-258.
    Does what guides a pastry chef stand on par, from the standpoint of contemporary computer science, with what guides a supercomputer? Did Betty Crocker, when telling us how to bake a cake, provide an effective procedure, in the sense of `effective' used in computer science? According to Cleland, the answer in both cases is ``Yes''. One consequence of Cleland's affirmative answer is supposed to be that hypercomputation is, to use her phrase, ``theoretically viable''. Unfortunately, though we applaud Cleland's ``gadfly philosophizing'' (...)
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  • The Elementary Classes of Direct and Boolean Products.Daniel Gluschankof - 1994 - Mathematical Logic Quarterly 40 (2):191-203.
    We characterize the elementary classes generated from a distinguished subclass closing by taking direct products and elementary equivalence. In the second part we give the same characterization in terms of atomic Boolean products. In the last part, we study the cases when the class of Boolean products is elementary but is not given by a discriminator.
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  • Typical ambiguity and elementary equivalence.Daniel Dzierzgowski - 1993 - Mathematical Logic Quarterly 39 (1):436-446.
    A sentence of the usual language of set theory is said to be stratified if it is obtained by “erasing” type indices in a sentence of the language of Russell's Simple Theory of Types. In this paper we give an alternative presentation of a proof the ambiguity theorem stating that any provable stratified sentence has a stratified proof. To this end, we introduce a new set of ambiguity axioms, inspired by Fraïssé's characterization of elementary equivalence; these axioms can be naturally (...)
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  • Generalized logical consequence: Making room for induction in the logic of science. [REVIEW]Samir Chopra & Eric Martin - 2002 - Journal of Philosophical Logic 31 (3):245-280.
    We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class of structures in (...)
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  • A First Order Theory of Functional Parthood.Pawel Garbacz - 2007 - Journal of Philosophical Logic 36 (3):309-337.
    This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states of affairs. The (...)
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  • Generalized quantifiers.Dag Westerståhl - 2008 - Stanford Encyclopedia of Philosophy.
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  • Logic and artificial intelligence: Divorced, still married, separated ...? [REVIEW]Selmer Bringsjord & David A. Ferrucci - 1998 - Minds and Machines 8 (2):273-308.
    Though it''s difficult to agree on the exact date of their union, logic and artificial intelligence (AI) were married by the late 1950s, and, at least during their honeymoon, were happily united. What connubial permutation do logic and AI find themselves in now? Are they still (happily) married? Are they divorced? Or are they only separated, both still keeping alive the promise of a future in which the old magic is rekindled? This paper is an attempt to answer these questions (...)
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  • Quantifiers and the Foundations of Quasi-Set Theory.Jonas R. Becker Arenhart & Décio Krause - 2009 - Principia: An International Journal of Epistemology 13 (3):251-268.
    In this paper we discuss some questions proposed by Prof. Newton da Costa on the foundations of quasi-set theory. His main doubts concern the possibility of a reasonable semantical understanding of the theory, mainly due to the fact that identity and difference do not apply to some entities of the theory’s intended domain of discourse. According to him, the quantifiers employed in the theory, when understood in the usual way, rely on the assumption that identity applies to all entities in (...)
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  • Intertheory relations from unified theories.Gebhard Geiger - 1991 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 22 (2):263-282.
    Summary The concept of unified theory is defined in logical and abstract semantic terms, and employed in the analysis of relations between empirical scientific theories. The conceptual framework of the approach applies to binary relations such as the reduction or replacement of one theory by another, and to multiple intertheory relations. Historically, unified theories tend to arise within the contexts of scientific conflicts which they may show susceptible of solution even in the most controversial cases of the logical incompatibility or (...)
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  • Searle on the Brink.Selmer Bringsjord - 1994 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 1.
    In his recent _The Rediscovery of the Mind_ John Searle tries to destroy cognitive science _and_ preserve a future in which a ``perfect science of the brain'' (1992, p. 235) arrives. I show that Searle can't accomplish both objectives. The ammunition he uses to realise the first stirs up a maelstrom of consciousness so wild it precludes securing the second.
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  • The expressive power of memory logics.Carlos Areces, Diego Figueira, Santiago Figueira & Sergio Mera - 2011 - Review of Symbolic Logic 4 (2):290-318.
    We investigate the expressive power of memory logics. These are modal logics extended with the possibility to store (or remove) the current node of evaluation in (or from) a memory, and to perform membership tests on the current memory. From this perspective, the hybrid logic (↓), for example, can be thought of as a particular case of a memory logic where the memory is an indexed list of elements of the domain.
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  • Is Gödelian Model-based Deductive Reasoning Computational?Selmer Bringsjord - 1998 - Philosophica 61 (1).
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  • (1 other version)On Fork Arrow Logic and Its Expressive Power.Paulo A. S. Veloso, Renata P. De Freitas, Petrucio Viana, Mario Benevides & Sheila R. M. Veloso - 2007 - Journal of Philosophical Logic 36 (5):489 - 509.
    We compare fork arrow logic, an extension of arrow logic, and its natural first-order counterpart (the correspondence language) and show that both have the same expressive power. Arrow logic is a modal logic for reasoning about arrow structures, its expressive power is limited to a bounded fragment of first-order logic. Fork arrow logic is obtained by adding to arrow logic the fork modality (related to parallelism and synchronization). As a result, fork arrow logic attains the expressive power of its first-order (...)
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