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  1. Advances in Modal Logic, Vol. 13.Nicola Olivetti & Rineke Verbrugge (eds.) - 2020 - College Publications.
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  • Another Problem in Possible World Semantics.Yifeng Ding & Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 13. College Publications. pp. 149-168.
    In "A Problem in Possible-World Semantics," David Kaplan presented a consistent and intelligible modal principle that cannot be validated by any possible world frame (in the terminology of modal logic, any neighborhood frame). However, Kaplan's problem is tempered by the fact that his principle is stated in a language with propositional quantification, so possible world semantics for the basic modal language without propositional quantifiers is not directly affected, and the fact that on careful inspection his principle does not target the (...)
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  • Topological Foundations of Cognitive Science.Carola Eschenbach, Christopher Habel & Barry Smith (eds.) - 1984 - Hamburg: Graduiertenkolleg Kognitionswissenschaft.
    A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda (...)
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  • Probabilistic Opinion Pooling with Imprecise Probabilities.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Journal of Philosophical Logic 47 (1):17-45.
    The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...)
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  • Orthospaces and quantum logic.J. L. Bell - 1985 - Foundations of Physics 15 (12):1179-1202.
    In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical completion of (...)
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  • Realism, operationalism, and quantum mechanics.D. Foulis, C. Piron & C. Randall - 1983 - Foundations of Physics 13 (8):813-841.
    A comprehensive formal system is developed that amalgamates the operational and the realistic approaches to quantum mechanics. In this formalism, for example, a sharp distinction is made between events, operational propositions, and the properties of physical systems.
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  • Truthlikeness for Theories on Countable Languages.Thomas Mormann - 2006 - In Ian Jarvie, Karl Milford & David Miller (eds.), Karl Popper: A Centenary Assessment vol. 3.
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  • Description, Construction and Representation. From Russell and Carnap to Stone.Thomas Mormann - 2006 - In Guido Imagire & Christine Schneider (eds.), Untersuchungen zur Ontologie.
    The first aim of this paper is to elucidate Russell’s construction of spatial points, which is to be <br>considered as a paradigmatic case of the "logical constructions" that played a central role in his epistemology and theory of science. Comparing it with parallel endeavours carried out by Carnap and Stone it is argued that Russell’s construction is best understood as a structural representation. It is shown that Russell’s and Carnap’s representational constructions may be considered as incomplete and sketchy harbingers of (...)
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  • Zorn's lemma and complete Boolean algebras in intuitionistic type theories.J. L. Bell - 1997 - Journal of Symbolic Logic 62 (4):1265-1279.
    We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some (...)
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  • Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
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  • Naturalness, intrinsicality, and duplication.Theodore R. Sider - 1993 - Dissertation, University of Massachusetts
    This dissertation explores the concepts of naturalness, intrinsicality, and duplication. An intrinsic property is had by an object purely in virtue of the way that object is considered in itself. Duplicate objects are exactly similar, considered as they are in themselves. The perfectly natural properties are the most fundamental properties of the world, upon which the nature of the world depends. In this dissertation I develop a theory of intrinsicality, naturalness, and duplication and explore their philosophical applications. Chapter 1 introduces (...)
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  • Mass terms and quantification.Jan Tore Lønning - 1987 - Linguistics and Philosophy 10 (1):1 - 52.
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  • Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
    This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that (...)
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  • Evo-Devo as a Trading Zone.Rasmus Grønfeldt Winther - 2014 - In Alan C. Love (ed.), Conceptual Change in Biology: Scientific and Philosophical Perspectives on Evolution and Development. Berlin: Springer Verlag, Boston Studies in the Philosophy of Science.
    Evo-Devo exhibits a plurality of scientific “cultures” of practice and theory. When are the cultures acting—individually or collectively—in ways that actually move research forward, empirically, theoretically, and ethically? When do they become imperialistic, in the sense of excluding and subordinating other cultures? This chapter identifies six cultures – three /styles/ (mathematical modeling, mechanism, and history) and three /paradigms/ (adaptationism, structuralism, and cladism). The key assumptions standing behind, under, or within each of these cultures are explored. Characterizing the internal structure of (...)
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  • Propositional manifolds and logical cohomology.J. Kouneiher & A. P. M. Balan - 2000 - Synthese 125 (1-2):147-154.
    In this note, we outline a definition of propositional manifold and logical cohomology. An application is also considered for mathematics: two Boole algebras of mathematical propositions are non equivalent if their two cohomologies are not isomorphic.
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  • The Logical Basis of the Tractarian Ontology.Natan Berber - 2007 - Axiomathes 17 (2):185-196.
    This paper focuses on the relation between logic and ontology. In particular, it demonstrates how classical logical theory can clarify the ontological part of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. To this end, the work examines the adequacy of a formal system that was devised by the Polish logician, mathematician and philosopher Roman Suszko (1919–1979) as a model for the Tractatus. Following a brief explanation of the Tractarian ontology, the main ideas of Suszko’s system and its philosophical significance will be considered. The (...)
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  • On 2nd Order Calculi of Individuals.Karl-Georg Niebergall - 2009 - Theoria 24 (2):169-202.
    From early work of N. Goodman to recent approaches by H. Field and D. Lewis, there have been attempts to combine 2nd order languages with calculi of individuals. This paper is a contribution, containing basic definitions and distinctions and some metatheorems, to the development of a general metatheory of such theories.
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  • Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics.David P. Ellerman - 1995 - Rowman & Littlefield Publishers.
    Dramatic changes or revolutions in a field of science are often made by outsiders or 'trespassers,' who are not limited by the established, 'expert' approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.
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  • Symmetrical Heyting algebras with operators.Luisa Iturrioz - 1983 - Mathematical Logic Quarterly 29 (2):33-70.
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  • Formalized Token Models and Duality in Semantics: An Algebraic Approach.Lars Hansen - 2004 - Journal of Symbolic Logic 69 (2):443 - 477.
    Employing the theory of Birkhoff polarities as a model of model theory yields an inductively defined dual structure which is a formalization of semantics and which allows for simple proofs of some new results for model theory.
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  • Region-based topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
    A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...)
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  • Extension of relatively |sigma-additive probabilities on Boolean algebras of logic.Mohamed A. Amer - 1985 - Journal of Symbolic Logic 50 (3):589 - 596.
    Contrary to what is stated in Lemma 7.1 of [8], it is shown that some Boolean algebras of finitary logic admit finitely additive probabilities that are not σ-additive. Consequences of Lemma 7.1 are reconsidered. The concept of a C-σ-additive probability on B (where B and C are Boolean algebras, and $\mathscr{B} \subseteq \mathscr{C}$ ) is introduced, and a generalization of Hahn's extension theorem is proved. This and other results are employed to show that every S̄(L)-σ-additive probability on s̄(L) can be (...)
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  • Representation of symmetric probability models.Peter H. Krauss - 1969 - Journal of Symbolic Logic 34 (2):183-193.
    This paper is a sequel to the joint publication of Scott and Krauss in which the first aspects of a mathematical theory are developed which might be called "First Order Probability Logic". No attempt will be made to present this additional material in a self-contained form. We will use the same notation and terminology as introduced and explained in Scott and Krauss, and we will frequently refer to the theorems stated and proved in the preceding paper. The main objective of (...)
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  • Effects, Observables, States, and Symmetries in Physics.David J. Foulis - 2007 - Foundations of Physics 37 (10):1421-1446.
    We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.
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  • Distributive lattices with a dual homomorphic operation.Alasdair Urquhart - 1979 - Studia Logica 38 (2):201 - 209.
    The lattices of the title generalize the concept of a De Morgan lattice. A representation in terms of ordered topological spaces is described. This topological duality is applied to describe homomorphisms, congruences, and subdirectly irreducible and free lattices in the category. In addition, certain equational subclasses are described in detail.
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  • Categories of frames for modal logic.S. K. Thomason - 1975 - Journal of Symbolic Logic 40 (3):439-442.
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  • Rings which admit elimination of quantifiers.Bruce I. Rose - 1978 - Journal of Symbolic Logic 43 (1):92-112.
    We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy ≠ 0). Theorem (...)
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  • Standardization principle of nonstandard universes.Masahiko Murakami - 1999 - Journal of Symbolic Logic 64 (4):1645-1655.
    A bounded ultrasheaf is a nonstandard universe constructed from a superstructure in a Boolean valued model of set theory. We consider the bounded elementary embeddings between bounded ultrasheaves. Then the standardization principle is true if and only if the ultrafilters are comparable by the Rudin-Frolik order. The base concept is that the bounded elementary embeddings correspond to the complete Boolean homomorphisms. We represent this by the Rudin-Keisler order of ultrafilters of Boolean algebras.
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  • (1 other version)An Axiomatization of Topological Boolean Algebras.Joel Kagan - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (7):103-106.
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  • A Boolean model of ultrafilters.Thierry Coquand - 1999 - Annals of Pure and Applied Logic 99 (1-3):231-239.
    We introduce the notion of Boolean measure algebra. It can be described shortly using some standard notations and terminology. If B is any Boolean algebra, let BN denote the algebra of sequences , xn B. Let us write pk BN the sequence such that pk = 1 if i K and Pk = 0 if k < i. If x B, denote by x* BN the constant sequence x* = . We define a Boolean measure algebra to be a Boolean (...)
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  • Boolean-valued set theory and forcing.Richard Mansfield & John Dawson - 1976 - Synthese 33 (2-4):223 - 252.
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  • Conceptual change and evolutionary developmental biology.A. C. Love - 2014 - In Alan C. Love (ed.), Conceptual Change in Biology: Scientific and Philosophical Perspectives on Evolution and Development. Berlin: Springer Verlag, Boston Studies in the Philosophy of Science. pp. 1-54.
    The 1981 Dahlem conference was a catalyst for contemporary evolutionary developmental biology (Evo-devo). This introductory chapter rehearses some of the details of the history surrounding the original conference and its associated edited volume, explicates the philosophical problem of conceptual change that provided the rationale for a workshop devoted to evaluating the epistemic revisions and transformations that occurred in the interim, explores conceptual change with respect to the concept of evolutionary novelty, and highlights some of the themes and patterns in the (...)
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  • (1 other version)An Axiomatization of Topological Boolean Algebras.Joel Kagan - 1972 - Mathematical Logic Quarterly 18 (7):103-106.
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  • Operational logics and the Hahn-Jordan property.Yewande Olubummo & Thurlow A. Cook - 1990 - Foundations of Physics 20 (7):905-913.
    The main result established in this paper is the following: If the base normed spaceV of completely additive weights is a norm-determining subspace of the space of finitely additive weights V acting on the order unit space spanning the operational logic, thenV has the ε-Jordan-Hahn property iff V has the approximate Jordan-Hahn property. Several examples illustrating the theory are given.
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  • 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.
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  • Small infinitary epistemic logics.Tai-wei Hu, Mamoru Kaneko & Nobu-Yuki Suzuki - 2019 - Review of Symbolic Logic 12 (4):702-735.
    We develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL are presented for ordinal α up to a given αo so that GL is finitary KDn with n agents and GL allows conjunctions of certain countably infinite formulae. GL is small in that the language is countable and can be constructive. The set of formulae Lα is increasing up (...)
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  • Mathematical quantum theory I: Random ultrafilters as hidden variables.William Boos - 1996 - Synthese 107 (1):83 - 143.
    The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a (...)
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  • On Boolean Algebras and their Recursive Completions.E. W. Madison - 1985 - Mathematical Logic Quarterly 31 (31-34):481-486.
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  • Construction of models for algebraically generalized recursive function theory.H. R. Strong - 1970 - Journal of Symbolic Logic 35 (3):401-409.
    The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable Boolean algebra (...)
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  • The completeness theorem for infinitary logic.Richard Mansfield - 1972 - Journal of Symbolic Logic 37 (1):31-34.
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  • The existence of countable totally nonconstructive extensions of the countable atomless Boolean algebra.E. W. Madison - 1983 - Journal of Symbolic Logic 48 (1):167-170.
    Our results concern the existence of a countable extension U of the countable atomless Boolean algebra B such that U is a "nonconstructive" extension of B. It is known that for any fixed admissible indexing φ of B there is a countable nonconstructive extension U of B (relative to φ). The main theorem here shows that there exists an extension U of B such that for any admissible indexing φ of B, U is nonconstructive (relative to φ). Thus, in this (...)
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  • A Study in Grzegorczyk Point-Free Topology Part II: Spaces of Points.Rafał Gruszczyński & Andrzej Pietruszczak - 2019 - Studia Logica 107 (4):809-843.
    In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show (...)
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  • Horn sentences.Fred Galvin - 1970 - Annals of Mathematical Logic 1 (4):389.
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  • Automorphisms of Finite Order.D. A. Anapolitanos - 1979 - Mathematical Logic Quarterly 25 (33):565-575.
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  • Using mathematica to understand the computer proof of the Robbins conjecture.Branden Fitelson - manuscript
    mathematicians for over 60 years. Amazingly, the Argonne team's automated theorem-proving program EQP took only 8 days to find a proof of it. Unfortunately, the proof found by EQP is quite complex and difficult to follow. Some of the steps of the EQP proof require highly complex and unintuitive substitution strategies. As a result, it is nearly impossible to reconstruct or verify the computer proof of the Robbins conjecture entirely by hand. This is where the unique symbolic capabilities of Mathematica (...)
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  • An algorithm for deriving tautologies of logic of classes and relations from those of sentential calculus.Michele Malatesta - 2000 - Metalogicon 13 (2):89-123.
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