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  1. The Logic of Hyperlogic. Part A: Foundations.Alexander W. Kocurek - 2024 - Review of Symbolic Logic 17 (1):244-271.
    Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...)
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  2. (What) Is Feminist Logic? (What) Do We Want It to Be?Catharine Saint-Croix & Roy T. Cook - 2024 - History and Philosophy of Logic 45 (1):20-45.
    ‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance (...)
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  3. Towards the Inevitability of Non-Classical Probability.Giacomo Molinari - 2023 - Review of Symbolic Logic 16 (4):1053-1079.
    This paper generalises an argument for probabilism due to Lindley [9]. I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set $\{0,1\}$, and where logical consequence $\models $ is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an agent values (...)
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  4. Logics for AI and Law: Joint Proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, September 8-9 and 11-12, 2023, Hangzhou.Bruno Bentzen, Beishui Liao, Davide Liga, Reka Markovich, Bin Wei, Minghui Xiong & Tianwen Xu (eds.) - 2023 - College Publications.
    This comprehensive volume features the proceedings of the Third International Workshop on Logics for New-Generation Artificial Intelligence and the International Workshop on Logic, AI and Law, held in Hangzhou, China on September 8-9 and 11-12, 2023. The collection offers a diverse range of papers that explore the intersection of logic, artificial intelligence, and law. With contributions from some of the leading experts in the field, this volume provides insights into the latest research and developments in the applications of logic in (...)
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  5. Non-transitive counterparts of every Tarskian logic.Damian E. Szmuc - forthcoming - Analysis.
    The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive counterpart of (...)
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  6. Inferential Constants.Camillo Fiore, Federico Pailos & Mariela Rubin - 2022 - Journal of Philosophical Logic 52 (3):767-796.
    A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years, much attention has been paid to the study of metainferences—and, in particular, to the question of what are the valid metainferences of a given logic. So far, however, this study has been done in quite a poor language. Our usual sequent calculi have no way to represent, e.g. negations, disjunctions or conjunctions of inferences. (...)
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  7. Logic for Exact Entailment.Kit Fine & Mark Jago - 2019 - Review of Symbolic Logic 12 (3):536-556.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...)
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  8. Conditionals, Support and Connexivity.Hans Rott - manuscript
    In natural language, conditionals are frequently used for giving explanations. Thus the antecedent of a conditional is typically understood as being connected to, being relevant for, or providing evidential support for the conditional's consequent. This aspect has not been adequately mirrored by the logics that are usually offered for the reasoning with conditionals: neither in the logic of the material conditional or the strict conditional, nor in the plethora of logics for suppositional conditionals that have been produced over the past (...)
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  9. The Laws of Thought and the Laws of Truth as Two Sides of One Coin.Ulf Hlobil - 2022 - Journal of Philosophical Logic 52 (1):313-343.
    Some think that logic concerns the “laws of truth”; others that logic concerns the “laws of thought.” This paper presents a way to reconcile both views by building a bridge between truth-maker theory, à la Fine, and normative bilateralism, à la Restall and Ripley. The paper suggests a novel way of understanding consequence in truth-maker theory and shows that this allows us to identify a common structure shared by truth-maker theory and normative bilateralism. We can thus transfer ideas from normative (...)
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  10. Nāgārjuna’s Tetralemma in Yamauchi Tokuryū’s Philosophy.Romaric Jannel - 2022 - The Eastern Buddhist. Third Series 2.
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  11. Grado de dependencia e independencia de los (sub) componentes de Conjuntos Borrosos y Neutrosóficos.Florentin Smarandache - 2019 - Neutrosophic Computing and Machine Learning 5 (1):1-6.
    La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia, Por tal motivo el objetivo del presente (...)
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  12. Degree of Dependence and Independence of the (Sub)Components of Fuzzy Set and Neutrosophic Set.Florentin Smarandache - 2016 - Neutrosophic Sets and Systems 11 (1):95-97.
    We have introduced for the first time the degree of dependence (and consequently the degree of independence) between the components of the fuzzy set, and also between the components of the neutrosophic set in our 2006 book’s fifth edition [1]. Now we extend it for the first time to the refined neutrosophic set considering the degree of dependence or independence of subcomponets.
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  13. Nidus Idearum. Scilogs, I: De neutrosophia.Florentin Smarandache - 2016 - Brussels, Belgium: Pons.
    In this first books of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others dead or waiting, referring to neutrosophy – email messages to research colleagues, or replies, notes about authors, articles or books, so on.
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  14. Nidus Idearum. Scilogs, II: de rerum consectatione.Florentin Smarandache - 2016 - Brussels, Belgium: Pons.
    In this second book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, some of them already put at work, others dead or waiting, referring to many topics (see Topics) in different fields of research – email messages to research colleagues, or replies, notes about authors, articles, or books, so on – in an eager pursuit (consectatio) for meanings, reasons, and purports of (scientific) things (res).
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  15. Nidus Idearum. Scilogs, III: Viva la Neutrosophia!Florentin Smarandache - 2017 - Brussels, Belgium: Pons.
    In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas!
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  16. Nidus Idearum. Scilogs, IV: vinculum vinculorum.Florentin Smarandache - 2019 - Brussels, Belgium: Pons.
    In this fourth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring mostly to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas!
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  17. Nidus Idearum. Scilogs, V: joining the dots.Florentin Smarandache - 2019 - Brussels, Belgium: Pons.
    In this fifth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, mostly referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas!
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  18. Nidus Idearum. Scilogs, VI: annotations on neutrosophy.Florentin Smarandache - 2019 - Brussels, Belgium: Pons.
    In this sixth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, and so on. Feel free to budge in or just use the scilogs as open source for your own ideas!
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  19. Nidus Idearum. Scilogs, VII: superluminal physics.Florentin Smarandache - 2019 - Brussels, Belgium: Pons.
    In this seventh book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to different scientific topics – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. -/- Exchanging ideas with Akeem Adesina A. Agboola, Muhammad Akram, Octavian Blaga, Said Broumi, Kajal Chatterjee, Vic Christianto, Octavian Cira, Mihaela Colhon, B. Davvaz, Luu Quoc Dat, R. Dhavaseelan, Jean Dezert, Hoda Esmail, Reza Farhadian, Ervin Goldfain, Muhammad Gulistan, (...)
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  20. Definición Mejorada de Lógica Neutrosófica No Estándar e Introducción a los Hiperreales Neutrosóficos (Quinta versión). Improved Definition of Non-Standard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals (Fifth Version).Florentin Smarandache - 2022 - Neutrosophic Computing and Machine Learning 23 (1):1-20.
    In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise they would (...)
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  21. Automating Reasoning with Standpoint Logic via Nested Sequents.Tim Lyon & Lucía Gómez Álvarez - 2018 - In Michael Thielscher, Francesca Toni & Frank Wolter (eds.), Proceedings of the Sixteenth International Conference on Principles of Knowledge Representation and Reasoning (KR2018). pp. 257-266.
    Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...)
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  22. A Framework for Intuitionistic Grammar Logics.Tim Lyon - 2021 - In Pietro Baroni, Christoph Benzmüller & Yὶ N. Wang (eds.), Lecture Notes in Computer Science. 93413 Cham, Germany: pp. 495-503.
    We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.
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  23. How to Adopt a Logic.Daniel Cohnitz & Carlo Nicolai - forthcoming - Dialectica.
    What is commonly referred to as the Adoption Problem is a challenge to the idea that the principles of logic can be rationally revised. The argument is based on a reconstruction of unpublished work by Saul Kripke. As the reconstruction has it, Kripke extends the scope of Willard van Orman Quine's regress argument against conventionalism to the possibility of adopting new logical principles. In this paper we want to discuss the scope of this challenge. Are all revisions of logic subject (...)
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  24. What Can You Say? Measuring the Expressive Power of Languages.Alexander Kocurek - 2018 - Dissertation, University of California, Berkeley
    There are many different ways to talk about the world. Some ways of talking are more expressive than others—that is, they enable us to say more things about the world. But what exactly does this mean? When is one language able to express more about the world than another? In my dissertation, I systematically investigate different ways of answering this question and develop a formal theory of expressive power, translation, and notational variance. In doing so, I show how these investigations (...)
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  25. Three Short Arguments Against Goff’s Grounding of Logical Laws in Universal Consciousness.Andrew Thomas - 2021 - Kriterion - Journal of Philosophy (3):237-246.
    In this paper, I argue that Goff's view that universal consciousness grounds logical laws such as the law of non-contradiction cannot be true on the grounds that we cannot guarantee the classical logic loving nature of universal consciousness that Goff desires in order to ground logical laws. I will present three arguments to show this.
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  26. Logic talk.Alexander W. Kocurek - 2021 - Synthese 199 (5-6):13661-13688.
    Sentences about logic are often used to show that certain embedding expressions are hyperintensional. Yet it is not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. In this paper, I develop a formal system called hyperlogic that is designed to do just that. I provide a hyperintensional semantics for hyperlogic that doesn’t appeal to logically impossible worlds, as traditionally understood, but instead uses a shiftable parameter that determines the (...)
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  27. Imperative Inference and Practical Rationality.Daniel W. Harris - 2021 - Philosophical Studies (4):1065-1090.
    Some arguments include imperative clauses. For example: ‘Buy me a drink; you can’t buy me that drink unless you go to the bar; so, go to the bar!’ How should we build a logic that predicts which of these arguments are good? Because imperatives aren’t truth apt and so don’t stand in relations of truth preservation, this technical question gives rise to a foundational one: What would be the subject matter of this logic? I argue that declaratives are used to (...)
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  28. Paraconsistent Logic as Model Building.Ricardo Sousa Silvestre - 2018 - South American Journal of Logic 1 (4):195-217.
    The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical logic. (...)
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  29. On the Correspondence between Nested Calculi and Semantic Systems for Intuitionistic Logics.Tim Lyon - 2021 - Journal of Logic and Computation 31 (1):213-265.
    This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...)
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  30. G. Priest's An Introduction to Non-Classical Logic (2001). [REVIEW]Hans-Peter Leeb - 2003 - History and Philosophy of Logic 24:65-66.
    The review gives a short description of the content of the book and discusses the treatment of conditionals in it.
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  31. Representing the Zoo World and the Traffic World in the language of the causal calculator.Varol Akman, Selim T. Erdoğan, Joohyung Lee, Vladimir Lifschitz & Hudson Turner - 2004 - Artificial Intelligence 153 (1-2):105-140.
    The work described in this report is motivated by the desire to test the expressive possibilities of action language C+. The Causal Calculator (CCalc) is a system that answers queries about action domains described in a fragment of that language. The Zoo World and the Traffic World have been proposed by Erik Sandewall in his Logic Modelling Workshop—an environment for communicating axiomatizations of action domains of nontrivial size. -/- The Zoo World consists of several cages and the exterior, gates between (...)
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  32. Impossible Worlds, by Francesco Berto and Mark Jago. [REVIEW]Koji Tanaka - 2022 - Mind 131 (521):292-301.
    Book Review of Impossible Worlds, by Francesco Berto and Mark Jago. Oxford: Oxford University Press, 2019.
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  33. The symbolic epistemological implications of the different mythological set up of the (Egyptian)-Mesopotamian culture compared to the Grecian one.Donato Santarcangelo - 2017 - Enkelados 6.
    The Mesopotamian peoples were never really dominated by the reason the way we conceptualize it. It's to the revelation as direct emanation of the divine that they ascribed the appearance of knowledge.
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  34. The Logical Web.Matheus Silva - manuscript
    Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...)
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  35. The logic of ground.Adam Lovett - 2020 - Journal of Philosophical Logic 49 (1):13-49.
    I explore the logic of ground. I first develop a logic of weak ground. This logic strengthens the logic of weak ground presented by Fine in his ‘Guide to Ground.’ This logic, I argue, generates many plausible principles which Fine’s system leaves out. I then derive from this a logic of strict ground. I argue that there is a strong abductive case for adopting this logic. It’s elegant, parsimonious and explanatorily powerful. Yet, so I suggest, adopting it has important consequences. (...)
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  36. Hyperlogic: A System for Talking about Logics.Alexander W. Kocurek - 2019 - Proceedings for the 22nd Amsterdam Colloquium.
    Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which (...)
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  37. A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics.Antonio Lieto & Gian Luca Pozzato - 2019 - Journal of Experimental and Theoretical Artificial Intelligence:1-39.
    We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of the combination of prototypical concepts. The proposed logic relies on the logic of typicality ALC + TR, whose semantics is based on the notion of rational closure, as well as on the distributed semantics of probabilistic Description Logics, and is equipped with a cognitive heuristic used by humans for concept composition. We first extend the logic of typicality ALC + TR by typicality inclusions of the (...)
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  38. An Argument for Minimal Logic.Nils Kürbis - 2019 - Dialectica 73 (1-2):31-63.
    The problem of negative truth is the problem of how, if everything in the world is positive, we can speak truly about the world using negative propositions. A prominent solution is to explain negation in terms of a primitive notion of metaphysical incompatibility. I argue that if this account is correct, then minimal logic is the correct logic. The negation of a proposition A is characterised as the minimal incompatible of A composed of it and the logical constant ¬. A (...)
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  39. Two Indian dialectical logics: saptabhangi and catuskoti.Fabien Schang - 2010 - Journal of the Indian Council of Philosophical Research 27 (1):45-75.
    A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhaṅgī, and the Mādhyamika catuṣkoṭi. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing theory of judgment within a common conceptual framework.
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  40. Non classical concept representation and reasoning in formal ontologies.Antonio Lieto - 2012 - Dissertation, Università Degli Studi di Salerno
    Formal ontologies are nowadays widely considered a standard tool for knowledge representation and reasoning in the Semantic Web. In this context, they are expected to play an important role in helping automated processes to access information. Namely: they are expected to provide a formal structure able to explicate the relationships between different concepts/terms, thus allowing intelligent agents to interpret, correctly, the semantics of the web resources improving the performances of the search technologies. Here we take into account a problem regarding (...)
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  41. A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences.Jared Millson - 2019 - Studia Logica (6):1-34.
    In recent years, the e ffort to formalize erotetic inferences (i.e., inferences to and from questions) has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and regular erotetic implication. While an attempt has been made to (...)
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  42. Composing Prototypes - AISC 18.Antonio Lieto & Gian Luca Pozzato - 2018 - In Proceedings of AISC 2018, 15th Annual Conference of the Italian Association for Cognitive Sciences The new era of Artificial Intelligence: a cognitive perspective. 27100 Pavia, Province of Pavia, Italy: pp. 8-10.
    Combining typical knowledge to generate novel concepts is an important creative trait of human cognition. Dealing with such ability requires, from an AI perspective, the harmonization of two conflicting requirements that are hardly accommodated in symbolic systems: the need of a syntactic compositionality (typical of logical systems) and that one concerning the exhibition of typicality effects (see Frixione and Lieto, 2012). In this work we provide a logical framework able to account for this type of human-like concept combination. We propose (...)
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  43. A Description Logic of Typicality for Conceptual Combination.Antonio Lieto & Gian Luca Pozzato - 2018 - In Proceedings of ISMIS 18. Springer.
    We propose a nonmonotonic Description Logic of typicality able to account for the phenomenon of combining prototypical concepts, an open problem in the fields of AI and cognitive modelling. Our logic extends the logic of typicality ALC + TR, based on the notion of rational closure, by inclusions p :: T(C) v D (“we have probability p that typical Cs are Ds”), coming from the distributed semantics of probabilistic Description Logics. Additionally, it embeds a set of cognitive heuristics for concept (...)
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  44. Genuine Process Logic.Wolfgang Sohst - 2017 - Collected Lectures of MoMo Berlin.
    The Genuine Process Logic described here (abbreviation: GPL) places the object-bound process itself at the center of formalism. It should be suitable for everyday use, i.e. it is not primarily intended for the formalization of computer programs, but instead, as a counter-conception to the classical state logics. The new and central operator of the GPL is an action symbol replacing the classical state symbols, e.g. of equivalence or identity. The complete renunciation of object-language state expressions also results in a completely (...)
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  45. ‘Chasing’ the diagram—the use of visualizations in algebraic reasoning.Silvia de Toffoli - 2017 - Review of Symbolic Logic 10 (1):158-186.
    The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...)
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  46. ”John P. Burgess, Philosophical Logic, Princeton University Press, 2009”. [REVIEW]Constantin C. Brîncuș - 2013 - Romanian Journal of Analytic Philosophy 8 (1):90-92.
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  47. Categorical harmony and path induction.Patrick Walsh - 2017 - Review of Symbolic Logic 10 (2):301-321.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...)
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  48. Strong Completeness and Limited Canonicity for PDL.Gerard Renardel de Lavalette, Barteld Kooi & Rineke Verbrugge - 2009 - Journal of Logic, Language and Information 18 (2):291-292.
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  49. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  50. Causality and attribution in an Aristotelian Theory.Srećko Kovač - 2015 - In Arnold Koslow & Arthur Buchsbaum (eds.), The Road to Universal Logic: Festschrift for 50th Birthday of Jean-Yves Béziau, vol. 1. Cham, Heidelberg, etc.: Springer-Birkhäuser. pp. 327-340.
    Aristotelian causal theories incorporate some philosophically important features of the concept of cause, including necessity and essential character. The proposed formalization is restricted to one-place predicates and a finite domain of attributes (without individuals). Semantics is based on a labeled tree structure, with truth defined by means of tree paths. A relatively simple causal prefixing mechanism is defined, by means of which causes of propositions and reasoning with causes are made explicit. The distinction of causal and factual explanation are elaborated, (...)
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