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  1. Ontologies and Worlds in Category Theory: Implications for Neural Systems.Michael John Healy & Thomas Preston Caudell - 2006 - Axiomathes 16 (1):165-214.
    We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to providing mathematical rigor, this approach has several advantages. It allows the incremental analysis of ontologies by basing them in an interconnected hierarchy of theories, with an operation on (...)
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  • Johan van Benthem on Logic and Information Dynamics.Alexandru Baltag & Sonja Smets (eds.) - 2014 - Cham, Switzerland: Springer International Publishing.
    This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...)
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  • Neither Mereology nor Whiteheadian Account of Space yet Convicted.Thomas Mormann - 1999 - Analysis 59 (3):174–182.
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  • Formal Learning Theory.Oliver Schulte - 2008 - Stanford Encyclopedia of Philosophy.
    Formal learning theory is the mathematical embodiment of a normative epistemology. It deals with the question of how an agent should use observations about her environment to arrive at correct and informative conclusions. Philosophers such as Putnam, Glymour and Kelly have developed learning theory as a normative framework for scientific reasoning and inductive inference.
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  • Natural Deduction, Hybrid Systems and Modal Logics.Andrzej Indrzejczak - 2010 - Dordrecht, Netherland: Springer.
    This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
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  • Leo Esakia on Duality in Modal and Intuitionistic Logics.Guram Bezhanishvili (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations (...)
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  • Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell.David DeVidi, Michael Hallett & Peter Clark (eds.) - 2011 - Dordrecht, Netherland: Springer.
    The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematics and decision theory and foundations of economics. (...)
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  • The introduction of topology into analytic philosophy: two movements and a coda.Samuel C. Fletcher & Nathan Lackey - 2022 - Synthese 200 (3):1-34.
    Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...)
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  • Modes of Convergence to the Truth: Steps Toward a Better Epistemology of Induction.Hanti Lin - forthcoming - Review of Symbolic Logic:1-34.
    Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...)
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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. Florianópolis, SC, Brasil: NEL/UFSC. 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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  • Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
    This is a companion paper to Braüner where a natural deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our natural deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.
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  • Logic of Justified Beliefs Based on Argumentation.Chenwei Shi, Sonja Smets & Fernando R. Velázquez-Quesada - forthcoming - Erkenntnis:1-37.
    This manuscript presents a topological argumentation framework for modelling notions of evidence-based belief. Our framework relies on so-called topological evidence models to represent the pieces of evidence that an agent has at her disposal, and it uses abstract argumentation theory to select the pieces of evidence that the agent will use to define her beliefs. The tools from abstract argumentation theory allow us to model agents who make decisions in the presence of contradictory information. Thanks to this, it is possible (...)
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  • A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer International Publishing. pp. 289-337.
    This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...)
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  • Realism, Rhetoric, and Reliability.Kevin T. Kelly, Konstantin Genin & Hanti Lin - 2016 - Synthese 193 (4):1191-1223.
    Ockham’s razor is the characteristic scientific penchant for simpler, more testable, and more unified theories. Glymour’s early work on confirmation theory eloquently stressed the rhetorical plausibility of Ockham’s razor in scientific arguments. His subsequent, seminal research on causal discovery still concerns methods with a strong bias toward simpler causal models, and it also comes with a story about reliability—the methods are guaranteed to converge to true causal structure in the limit. However, there is a familiar gap between convergent reliability and (...)
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  • Newton Versus Leibniz: Intransparency Versus Inconsistency.Karin Verelst - 2014 - Synthese 191 (13):2907-2940.
    In this paper I argue that inconsistencies in scientific theories may arise from the type of causality relation they—tacitly or explicitly—embody. All these seemingly different causality relations can be subsumed under a general strategy developed to defeat the paradoxes which inevitably occur in our experience of the real. With respect to this, scientific theories are just a subclass of the larger class of metaphysical theories, construed as theories that attempt to explain a (part of) the world consistently. All metaphysical theories (...)
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  • The Continuum as a Formal Space.Sara Negri & Daniele Soravia - 1999 - Archive for Mathematical Logic 38 (7):423-447.
    A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.
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  • Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics. [REVIEW]Piero Pagliani - 1997 - Journal of Logic, Language and Information 6 (1):63-99.
    Semantics connected to some information based metaphor are well-known in logic literature: a paradigmatic example is Kripke semantic for Intuitionistic Logic. In this paper we start from the concrete problem of providing suitable logic-algebraic models for the calculus of attribute dependencies in Formal Contexts with information gaps and we obtain an intuitive model based on the notion of passage of information showing that Kleene algebras, semi-simple Nelson algebras, three-valued ukasiewicz algebras and Post algebras of order three are, in a sense, (...)
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  • Incompatible Empirically Equivalent Theories: A Structural Explication.Thomas Mormann - 1995 - Synthese 103 (2):203 - 249.
    The thesis of the empirical underdetermination of theories (U-thesis) maintains that there are incompatible theories which are empirically equivalent. Whether this is an interesting thesis depends on how the term incompatible is understood. In this paper a structural explication is proposed. More precisely, the U-thesis is studied in the framework of the model theoretic or emantic approach according to which theories are not to be taken as linguistic entities, but rather as families of mathematical structures. Theories of similarity structures are (...)
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  • The Development of Categorical Logic.John L. Bell - unknown
    5.5. Every topos is linguistic: the equivalence theorem.
     
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  • Announcement as Effort on Topological Spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - 2019 - Synthese 196 (7):2927-2969.
    We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and (...)
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  • Mathematical Aspects of Similarity and Quasi-Analysis - Order, Topology, and Sheaves.Thomas Mormann - manuscript
    The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many empirical (...)
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  • Domains for Computation in Mathematics, Physics and Exact Real Arithmetic.Abbas Edalat - 1997 - Bulletin of Symbolic Logic 3 (4):401-452.
    We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and (...)
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  • Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders.Jouni Järvinen, Piero Pagliani & Sándor Radeleczki - 2013 - Studia Logica 101 (5):1073-1092.
    In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the quasiorder R forms (...)
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  • The Geometry of Knowledge.Johan van Benthem & Darko Sarenac - unknown
    The most widely used attractive logical account of knowledge uses standard epistemic models, i.e., graphs whose edges are indistinguishability relations for agents. In this paper, we discuss more general topological models for a multi-agent epistemic language, whose main uses so far have been in reasoning about space. We show that this more geometrical perspective affords greater powers of distinction in the study of common knowledge, defining new collective agents, and merging information for groups of agents.
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  • Vagueness, Kant and Topology: A Study of Formal Epistemology.Giovanni Boniolo & Silvio Valentini - 2008 - Journal of Philosophical Logic 37 (2):141-168.
    In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.
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  • On What Ontology is and Not-Is.Karin Verelst - 2008 - Foundations of Science 13 (3):347-370.
    In this paper I investigate the relation between physics and metaphysics in Plato’s participation theory. I show that the logic shoring up Plato’s metaphysics in paraconsistent, as had been suggested already by Graham Priest. The transformation of the paradoxical One-and-Many of the pre-Socratics into a paraconsistent Great-and-Small bridges the abyss between archaic rationality and the world of classical logic based ultimately on the principle of contradiction. Indeed, language is an organ of perception, not simply a means of communication. J. Jaynes, (...)
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  • Positive Monotone Modal Logic.Jim de Groot - 2021 - Studia Logica 109 (4):829-857.
    Positive monotone modal logic is the negation- and implication-free fragment of monotone modal logic, i.e., the fragment with connectives and. We axiomatise positive monotone modal logic, give monotone neighbourhood semantics based on posets, and prove soundness and completeness. The latter follows from the main result of this paper: a duality between so-called \-spaces and the algebraic semantics of positive monotone modal logic. The main technical tool is the use of coalgebra.
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  • Private Announcements on Topological Spaces.Hans van Ditmarsch, Sophia Knight & Aybüke Özgün - 2018 - Studia Logica 106 (3):481-513.
    In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \, while all the other agents observe that group G is informed, but are uncertain whether the information provided is \ or \. This article follows up on our prior work where the dynamics were public events. We provide a complete axiomatization (...)
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  • Natural Predicates and Topological Structures of Conceptual Spaces.Thomas Mormann - 1993 - Synthese 95 (2):219 - 240.
    In the framework of set theory we cannot distinguish between natural and non-natural predicates. To avoid this shortcoming one can use mathematical structures as conceptual spaces such that natural predicates are characterized as structurally nice subsets. In this paper topological and related structures are used for this purpose. We shall discuss several examples taken from conceptual spaces of quantum mechanics (orthoframes), and the geometric logic of refutative and affirmable assertions. In particular we deal with the problem of structurally distinguishing between (...)
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  • The Logic of Information in State Spaces.Levin Hornischer - forthcoming - Review of Symbolic Logic:1-32.
    State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn’s aboutness interpretation of fde, to the space of open sets of a spectral space. We show that these information structures induce so-called hype models (...)
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  • The Common Order-Theoretic Structure of Version Spaces and ATMSs.Carl A. Gunter, Teow-Hin Ngair & Devika Subramanian - 1997 - Artificial Intelligence 95 (2):357-407.
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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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  • Programming Interfaces and Basic Topology.Peter Hancock & Pierre Hyvernat - 2006 - Annals of Pure and Applied Logic 137 (1-3):189-239.
    A pattern of interaction that arises again and again in programming is a 'handshake', in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent--the client or Angel--and concluded by the other--the server or Demon. We present a category in which the objects--called interaction structures in the paper--serve as descriptions of services provided across such handshaken interfaces. The morphisms--called (general) simulations--model components that provide one such service, relying (...)
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  • Typ-Ken (an Amalgam of Type and Token) Drives Infosphere.Yukio-Pegio Gunji, Takayuki Niizato, Hisashi Murakami & Iori Tani - 2010 - Knowledge, Technology & Policy 23 (1-2):227-251.
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  • Continuous Lattices and Whiteheadian Theory of Space.Thomas Mormann - 1998 - Logic and Logical Philosophy 6:35 - 54.
    In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers yielding the real numbers . The argument of the paper relies on the theories of continuous lattices and “pointless” (...)
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  • 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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  • A Grim Semantics For Logics of Belief.Christopher Steinsvold - 2008 - Journal of Philosophical Logic 37 (1):45-56.
    Patrick Grim has presented arguments supporting the intuition that any notion of a totality of truths is incoherent. We suggest a natural semantics for various logics of belief which reflect Grim’s intuition. The semantics is a topological semantics, and we suggest that the condition can be interpreted to reflect Grim’s intuition. Beyond this, we present a natural canonical topological model for K4 and KD4.
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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 (J-lattice), which can be modeled by an algebraic structure built in quasi-set theory 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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  • Mereotopology in 2nd-Order and Modal Extensions of Intuitionistic Propositional Logic.Paolo Torrini, John G. Stell & Brandon Bennett - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):495-525.
    We show how mereotopological notions can be expressed by extending intuitionistic propositional logic with propositional quantification and a strong modal operator. We first prove completeness for the logics wrt Kripke models; then we trace the correspondence between Kripke models and topological spaces that have been enhanced with an explicit notion of expressible region. We show how some qualitative spatial notions can be expressed in topological terms. We use the semantical and topological results in order to show how in some extensions (...)
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  • Domain Theory in Logical Form.Samson Abramsky - 1991 - Annals of Pure and Applied Logic 51 (1-2):1-77.
    Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 1–77. The mathematical framework of Stone duality is used to synthesise a number of hitherto separate developments in theoretical computer science.• Domain theory, the mathematical theory of computation introduced by Scott as a foundation for detonational semantics• The theory of concurrency and systems behaviour developed by Milner, Hennesy based on operational semantics.• Logics of programsStone duality provides a junction between semantics and logics . Moreover, the underlying (...)
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  • Typ-Ken (an Amalgam of Type and Token) Drives Infosphere.Yukio-Pegio Gunji, Takayuki Niizato, Hisashi Murakami & Iori Tani - 2010 - Knowledge, Technology & Policy 23 (1-2):227-251.
    Floridi’s infosphere consisting of informational reality is estimated and delineated by introducing the new notion of Typ-Ken, an undifferentiated amalgam of type and token that can be expressed as either type or token dependent on contingent ontological commitment. First, we elaborate Floridi’s system, level of abstraction (LoA), model, and structure scheme, which is proposed to reconcile ontic with epistemic structural reality, and obtain the duality of type and token inherited in the relationship between LoA and model. While we focus on (...)
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  • Intuitionistic Hybrid Logic.Torben Braüner & Valeria de Paiva - 2006 - Journal of Applied Logic 4 (3):231-255.
    Hybrid logics are a principled generalization of both modal logics and description logics, a standard formalism for knowledge representation. In this paper we give the first constructive version of hybrid logic, thereby showing that it is possible to hybridize constructive modal logics. Alternative systems are discussed, but we fix on a reasonable and well-motivated version of intuitionistic hybrid logic and prove essential proof-theoretical results for a natural deduction formulation of it. Our natural deduction system is also extended with additional inference (...)
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