Results for 'algebra of contextual sets'

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  1.  30
    Calculus of Contextual Rough Sets in Contextual Spaces.Edward Bryniarski & Urszula Wybraniec-Skardowska - 1998 - Journal of Applied Non-Classical Logics 8 (1):9-26.
    The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included (...)
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  2.  54
    Contextual semantics in quantum mechanics from a categorical point of view.Vassilios Karakostas & Elias Zafiris - 2017 - Synthese 194 (3).
    The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, (...)
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  3.  23
    Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems.Prosenjit Howlader & Mohua Banerjee - 2023 - Journal of Logic, Language and Information 32 (1):117-146.
    The notion of a context in formal concept analysis and that of an approximation space in rough set theory are unified in this study to define a Kripke context. For any context (G,M,I), a relation on the set G of objects and a relation on the set M of properties are included, giving a structure of the form ((G,R), (M,S), I). A Kripke context gives rise to complex algebras based on the collections of protoconcepts and semiconcepts of the underlying context. (...)
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  4.  47
    On łukasiewicz-moisil algebras of fuzzy sets.Sergiu Rudeanu - 1993 - Studia Logica 52 (1):95 - 111.
    The set (X, J) of fuzzy subsetsf:XJ of a setX can be equipped with a structure of -valued ukasiewicz-Moisil algebra, where is the order type of the totally ordered setJ. Conversely, every ukasiewicz-Moisil algebra — and in particular every Post algebra — is isomorphic to a subalgebra of an algebra of the form (X, J), whereJ has an order type . The first result of this paper is a characterization of those -valued ukasiewicz-Moisil algebras which are (...)
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  5.  45
    On the Boolean algebras of definable sets in weakly o‐minimal theories.Stefano Leonesi & Carlo Toffalori - 2004 - Mathematical Logic Quarterly 50 (3):241-248.
    We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove (...)
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  6.  42
    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 (...)
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  7.  40
    Finite algebras of relations are representable on finite sets.H. Andréka, I. Hodkinson & I. Németi - 1999 - Journal of Symbolic Logic 64 (1):243-267.
    Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have the `finite base property' and have decidable universal theories, and that any finite algebra in each class is representable on a finite set.
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  8. Finite Algebras of Relations are Representable on Finite Sets.H. Andreka, I. Hodkinson & I. Nemeti - 1999 - Journal of Symbolic Logic 64 (1):243-267.
    Using a combinatorial theorem of Herwig on extending partial isomorphisms of relational structures, we give a simple proof that certain classes of algebras, including Crs, polyadic Crs, and WA, have the `finite base property' and have decidable universal theories, and that any finite algebra in each class is representable on a finite set.
     
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  9. Decidability of cylindric set algebras of dimension two and first-order logic with two variables.Maarten Marx & Szabolcs Mikulás - 1999 - Journal of Symbolic Logic 64 (4):1563-1572.
    The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on a finite (...)
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  10. Decidability of Cylindric Set Algebras of Dimension Two and First-Order Logic with Two Variables.Maarten Marx & Szabolcs Mikulas - 1999 - Journal of Symbolic Logic 64 (4):1563-1572.
    The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables, using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two. The new proof also shows the known results that the universal theory of Pse$_2$ is decidable and that every finite Pse$_2$ can be represented on a finite base. Since the class Cs$_2$ of cylindric set (...)
     
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  11. An Overview of Plithogenic Set and Symbolic Plithogenic Algebraic Structures.Florentin Smarandache - 2023 - Journal of Fuzzy Extension and Applications 4 (1):48–55.
    This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.
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  12. The Tarski–Lindenbaum algebra of the class of strongly constructivizable models with $$\omega $$-stable theories.Mikhail Peretyat’kin - forthcoming - Archive for Mathematical Logic:1-12.
    We study the class of all strongly constructivizable models having \(\omega \) -stable theories in a fixed finite rich signature. It is proved that the Tarski–Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean \(\Sigma ^1_1\) -algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of all Boolean \(\Sigma ^1_1\) -algebras. This gives a characterization (...)
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  13.  8
    Algebraic Structure of the Set Theory of Unanalysed Propositions.André Deprit - 1953 - Philosophical Studies (Dublin) 3:67-75.
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  14.  6
    Algebraic Structure of the Set Theory of Unanalysed Propositions.André Deprit - 1953 - Philosophical Studies (Dublin) 3:67-75.
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  15.  4
    Algebraic Structure of the Set Theory of Unanalysed Propositions.André Deprit - 1953 - Philosophical Studies (Dublin) 3:67-75.
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  16.  23
    Towards the algebraization of set theory. Set-theoretic domains.Janusz Czelakowski - 2004 - Bulletin of the Section of Logic 33 (3):157-178.
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  17.  10
    Carry-over of attentional settings between distinct tasks: A transient effect independent of top-down contextual biases.Catherine Thompson, Alessia Pasquini & Peter J. Hills - 2021 - Consciousness and Cognition 90 (C):103104.
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  18.  31
    Dimension of definable sets, algebraic boundedness and Henselian fields.Lou Van den Dries - 1989 - Annals of Pure and Applied Logic 45 (2):189-209.
  19.  64
    On an algebra of sets of finite sequences.J. Donald Monk - 1970 - Journal of Symbolic Logic 35 (1):19-28.
  20.  15
    A new symbolic representation for the algebra of sets.Jerome Frazee - 1990 - History and Philosophy of Logic 11 (1):67-75.
    The algebra of sets has, basically, two different types of symbols. One type of symbol (∩, ?, +, ?) defines another set from two other sets. A second type of symbol (?, ?, =, ?) makes a proposition about two sets. When the construction of these two types of symbols is based on the same four-dot matrix as the logic symbols described in a previous paper, the three symbol types then dovetail together into a harmonious whole (...)
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  21.  29
    On the role of contextual factors in cognitive neuroscience experiments: a mechanistic approach.Abel Wajnerman-Paz & Daniel Rojas-Líbano - 2022 - Synthese 200 (5):1-26.
    Experiments in cognitive neuroscience build a setup whose set of controlled stimuli and rules elicits a cognitive process in a participant. This setup requires researchers to decide the value of quite a few parameters along several dimensions. We call ‘’contextual factors’’ the parameters often assumed not to change the cognitive process elicited and are free to vary across the experiment’s repetitions. Against this assumption, empirical evidence shows that many of these contextual factors can significantly influence cognitive performance. Nevertheless, (...)
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  22.  25
    A certain conception of rough sets in topological Boolean algebras.Marek Chuchro - 1993 - Bulletin of the Section of Logic 22 (1):9-12.
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  23.  30
    An algebraic characterization of power set in countable standard models of ZF.George Metakides & J. M. Plotkin - 1975 - Journal of Symbolic Logic 40 (2):167-170.
  24. Level Theory, Part 3: A Boolean Algebra of Sets Arranged in Well-Ordered Levels.Tim Button - 2022 - Bulletin of Symbolic Logic 28 (1):1-26.
    On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; (...)
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  25. is a set B with Boolean operations a∨ b (join), a∧ b (meet) and− a (complement), partial ordering a≤ b defined by a∧ b= a and the smallest and greatest element, 0 and 1. By Stone's Representation Theorem, every Boolean algebra is isomorphic to an algebra of subsets of some nonempty set S, under operations a∪ b, a∩ b, S− a, ordered by inclusion, with 0=∅. [REVIEW]Mystery Of Measurability - 2006 - Bulletin of Symbolic Logic 12 (2).
  26.  13
    On an algebra of sets of finite sequences.J. Donald Monk - 1970 - Journal of Symbolic Logic 35 (1):19-28.
  27.  37
    The number of one-generated cylindric set algebras of dimension greater than two.Jean A. Larson - 1985 - Journal of Symbolic Logic 50 (1):59-71.
    S. Ulam asked about the number of nonisomorphic projective algebras with k generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of nonisomorphic one-generated structures of finite dimension n, where n is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, cylindric set algebras, and cylindric algebras. The results of this paper extend earlier (...)
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  28.  25
    An extension of the algebra of sets.Jerzy Słupecki & Krystyna Piróg-Rzepecka - 1973 - Studia Logica 31 (1):7 - 37.
  29.  63
    Full algebra of generalized functions and non-standard asymptotic analysis.Todor D. Todorov & Hans Vernaeve - 2008 - Logic and Analysis 1 (3-4):205-234.
    We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a (...)
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  30.  99
    Algebras of intervals and a logic of conditional assertions.Peter Milne - 2004 - Journal of Philosophical Logic 33 (5):497-548.
    Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an (...)
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  31.  26
    Topological representations of post algebras of order ω+ and open theories based on ω+-valued post logic.Helena Rasiowa - 1985 - Studia Logica 44 (4):353 - 368.
    Post algebras of order + as a semantic foundation for +-valued predicate calculi were examined in [5]. In this paper Post spaces of order + being a modification of Post spaces of order n2 (cf. Traczyk [8], Dwinger [1], Rasiowa [6]) are introduced and Post fields of order + are defined. A representation theorem for Post algebras of order + as Post fields of sets is proved. Moreover necessary and sufficient conditions for the existence of representations preserving a given (...)
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  32.  39
    Set-Theoretical Methods in the Algebra of Logic.A. Adam & U. I. Zuravlev - 1970 - Journal of Symbolic Logic 35 (1):162.
  33. Indistinguishability and the origins of contextuality in physics.José Acacio De Barros, Federico Holik & Décio Krause - 2019 - Philosophical Transactions of the Royal Society A 377 (2157): 20190150.
    In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new (...)
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  34.  22
    The Role of Contextual Values in the Formation of Ecological Behaviours.Camila Horst Toigo, Neil Ravenscroft & Ely José De Mattos - 2023 - Environmental Values 32 (4):385-409.
    It is commonly understood that over-arching transcendental values (TVs) play a major role in directly influencing individual and group behaviours, including those relating to the environment. This paper challenges this approach, by arguing that there is good evidence to indicate that personal contexts – rather than TVs – inform many decisions that individuals need to make. As such, the paper argues that individuals use their TVs as a guide to forming contextual values, in a way that TVs only influence (...)
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  35.  27
    Lindenbaum algebras of intuitionistic theories and free categories.Peter Freyd, Harvey Friedman & Andre Scedrov - 1987 - Annals of Pure and Applied Logic 35 (C):167-172.
    We consider formal theories synonymous with various free categories . Their Lindenbaum algebras may be described as the lattices of subobjects of a terminator. These theories have intuitionistic logic. We show that the Lindenbaum algebras of second order and higher order arithmetic , and set theory are not isomorphic to the Lindenbaum algebras of first order theories such as arithmetic . We also show that there are only five kernels of representations of the free Heyting algebra on one generator (...)
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  36.  82
    The Oxford handbook of contextual political analysis.Robert E. Goodin & Charles Tilly (eds.) - 2006 - Oxford : New York: Oxford University Press.
    The Oxford Handbooks of Political Science is a ten-volume set of reference books offering authoritative and engaging critical overviews of the state of political science. This volume, The Oxford Handbook of Contextual Political Analysis, sets out to synthesize and critique for the first time those approaches to political science that offer a more fine-grained qualitative analysis of the political world. The work in the volume has a common aim in being sensitive to the thoughts of contextual nuances (...)
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  37.  32
    Groups and algebras of binary relations.Steven Givant & Hajnal Andréka - 2002 - Bulletin of Symbolic Logic 8 (1):38-64.
    In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if (...)
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  38.  97
    Prepositional aspect and the algebra of paths.Joost Zwarts - 2005 - Linguistics and Philosophy 28 (6):739 - 779.
    The semantics of directional prepositions is investigated from the perspective of aspect. What distinguishes telic PPs (like to the house) from atelic PPs (like towards the house), taken as denoting sets of paths, is their algebraic structure: atelic PPs are cumulative, closed under the operation of concatenation, telic PPs are not. Not only does this allow for a natural and compositional account of how PPs contribute to the aspect of a sentence, but it also guides our understanding of the (...)
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  39.  14
    Conceptual Distance and Algebras of Concepts.Mohamed Khaled & Gergely Székely - forthcoming - Review of Symbolic Logic:1-16.
    We show that the conceptual distance between any two theories of first-order logic is the same as the generator distance between their Lindenbaum–Tarski algebras of concepts. As a consequence of this, we show that, for any two arbitrary mathematical structures, the generator distance between their meaning algebras (also known as cylindric set algebras) is the same as the conceptual distance between their first-order logic theories. As applications, we give a complete description for the distances between meaning algebras corresponding to structures (...)
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  40.  32
    Compositionality in context.Dag Westerståhl, Alexandru Baltag & Johan van Benthem - 2021 - In A. Palmigiano & M. Zadrzadeh (eds.), Outstanding Contributions to Logic: Samson Abramsky. Springer.
    Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language expressions in a systematic manner following syntactic construction, thereby allowing for a perspicuous algebraic view of the syntax-semantics interface. Yet the status of the principle remains under debate, with positions ranging from compositionality always being achievable to its having genuine empirical content. This paper attempts to sort out some major issues in all this from a logical perspective. First, we stress the fundamental (...)
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  41.  80
    The Effects of Contextual and Wrongdoing Attributes on Organizational Employees' Whistleblowing Intentions Following Fraud.Shani N. Robinson, Jesse C. Robertson & Mary B. Curtis - 2012 - Journal of Business Ethics 106 (2):213-227.
    Recent financial fraud legislation such as the Dodd–Frank Act and the Sarbanes–Oxley Act (U.S. House of Representatives, Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010, [H.R. 4173], 2010 ; U.S. House of Representatives, The Sarbanes–Oxley Act of 2002, Public Law 107-204 [H.R. 3763], 2002 ) relies heavily on whistleblowers for enforcement, and offers protection and incentives for whistleblowers. However, little is known about many aspects of the whistleblowing decision, especially the effects of contextual and wrongdoing attributes on (...)
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  42.  31
    Contextualism and the role of contextual frames.Anne Bezuidenhout - 2009 - Manuscrito 32 (1):59-84.
    Some part of the debate between minimalists and contextualists can be construed as merely terminological and can be resolved by agreeing to a certain division of labor. Minimalist claims are to be understood as claims about what is needed for adequate formal compositional semantic models of language understood in abstraction from real conversational contexts. Contextualist claims are ones about how language users produce and understand utterances by manipulating features of the psychological and discourse contexts of the conversational participants in real (...)
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  43.  6
    Model completion of scaled lattices and co‐Heyting algebras of p‐adic semi‐algebraic sets.Luck Darnière - 2019 - Mathematical Logic Quarterly 65 (3):305-331.
    Let p be prime number, K be a p‐adically closed field, a semi‐algebraic set defined over K and the lattice of semi‐algebraic subsets of X which are closed in X. We prove that the complete theory of eliminates quantifiers in a certain language, the ‐structure on being an extension by definition of the lattice structure. Moreover it is decidable, contrary to what happens over a real closed field for. We classify these ‐structures up to elementary equivalence, and get in particular (...)
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  44.  23
    Isomorphisms of finite cylindric set algebras of characteristic zero.György Serény - 1993 - Notre Dame Journal of Formal Logic 34 (2):284-294.
  45.  22
    Prenex Normal Form in the Modal Predicate Logic PS*S and the Grosseteste Algebra of Sets GS*S.Robert L. Wilson - 1974 - Mathematical Logic Quarterly 20 (13‐18):271-280.
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  46.  24
    Prenex Normal Form in the Modal Predicate Logic PS*S and the Grosseteste Algebra of Sets GS*S.Robert L. Wilson - 1974 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 20 (13-18):271-280.
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  47.  31
    Compositionality in Context.Alexandru Baltag, Johan van Benthem & Dag Westerståhl - 2023 - In Alessandra Palmigiano & Mehrnoosh Sadrzadeh (eds.), Samson Abramsky on Logic and Structure in Computer Science and Beyond. Springer Verlag. pp. 773-812.
    Compositionality is a principle used in logic, philosophy, mathematics, linguistics, and computer science for assigning meanings to language expressions in a systematic manner following syntactic construction, thereby allowing for a perspicuous algebraic view of the syntax-semantics interface. Yet the status of the principle remains under debate, with positions ranging from compositionality always being achievable to its having genuine empirical content. This paper attempts to sort out some major issues in all this from a logical perspective. First, we stress the fundamental (...)
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  48.  26
    Algebraic Models of Sets and Classes in Categories of Ideals.Steve Awodey, Henrik Forssell & Michael A. Warren - unknown
    We introduce a new sheaf-theoretic construction called the ideal completion of a category and investigate its logical properties. We show that it satisfies the axioms for a category of classes in the sense of Joyal and Moerdijk [17], so that the tools of algebraic set theory can be applied to produce models of various elementary set theories. These results are then used to prove the conservativity of different set theories over various classical and constructive type theories.
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  49.  16
    Multipartite Composition of Contextuality Scenarios.Ana Belén Sainz & Elie Wolfe - 2018 - Foundations of Physics 48 (8):925-953.
    Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how separate contextuality scenarios combine into a joint scenario. Under the premise that the the allowed probabilistic models satisfy the No Signalling principle, Foulis and Randall defined the unique possible way to compose two contextuality scenarios. When composing strictly-more than two test spaces, however, a (...)
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  50.  28
    A too brief set of postulates for the algebra of logic.C. I. Lewis - 1915 - Journal of Philosophy, Psychology and Scientific Methods 12 (19):523-525.
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