Results for 'First‐order topological structure'

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  1. First order topological structures and theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.
    In this paper we introduce the notion of a first order topological structure, and consider various possible conditions on the complexity of the definable sets in such a structure, drawing several consequences thereof.Our aim is to develop, for a restricted class of unstable theories, results analogous to those for stable theories. The “material basis” for such an endeavor is the analogy between the field of real numbers and the field of complex numbers, the former being a “nicely (...)
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  2.  48
    Groups, group actions and fields definable in first‐order topological structures.Roman Wencel - 2012 - Mathematical Logic Quarterly 58 (6):449-467.
    Given a group , G⊆Mm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V⊆G and define a new topology τ on G with which becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory (...)
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  3.  55
    Expressive power in first order topology.Paul Bankston - 1984 - Journal of Symbolic Logic 49 (2):478-487.
    A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces (...)
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  4.  13
    On ultrafilter extensions of first-order models and ultrafilter interpretations.Nikolai L. Poliakov & Denis I. Saveliev - 2021 - Archive for Mathematical Logic 60 (5):625-681.
    There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...)
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  5.  47
    Intuitionistic completeness of first-order logic.Robert Constable & Mark Bickford - 2014 - Annals of Pure and Applied Logic 165 (1):164-198.
    We constructively prove completeness for intuitionistic first-order logic, iFOL, showing that a formula is provable in iFOL if and only if it is uniformly valid in intuitionistic evidence semantics as defined in intuitionistic type theory extended with an intersection operator.Our completeness proof provides an effective procedure that converts any uniform evidence into a formal iFOL proof. Uniform evidence can involve arbitrary concepts from type theory such as ordinals, topological structures, algebras and so forth. We have implemented that procedure in (...)
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  6. First-order swap structures semantics for some Logics of Formal Inconsistency.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Journal of Logic and Computation 30 (6):1257-1290.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  7.  25
    First-order topological axioms.R. D. Kopperman - 1981 - Journal of Symbolic Logic 46 (3):475-489.
    We exhibit a finite list of first-order axioms which may be used to define topological spaces. For most separation axioms we discover a first-order equivalent statement.
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  8. A note on universally free first order quantification theory ap Rao.Universally Free First Order Quantification - forthcoming - Logique Et Analyse.
     
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  9.  16
    Logic, partial orders and topology.Hugo Mariano & Francisco Miraglia - 2005 - Manuscrito 28 (2):449-546.
    We give a version of L´os’ ultraproduct result for forcing in Kripke structures in a first-order language with equality and discuss ultrafilters in a topology naturally associated to a partial order. The presentation also includes background material so as to make the exposition accessible to those whose main interest is Computer Science, Artificial Intelligence and/or Philosophy.
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  10.  11
    Ordering Acyclic Connected Structures of Trees Having Greatest Degree-Based Invariants.S. Kanwal, M. K. Siddiqui, E. Bonyah, T. S. Shaikh, I. Irshad & S. Khalid - 2022 - Complexity 2022:1-16.
    Being building block of data sciences, link prediction plays a vital role in revealing the hidden mechanisms that lead the networking dynamics. Since many techniques depending in vertex similarity and edge features were put forward to rule out many well-known link prediction challenges, many problems are still there just because of unique formulation characteristics of sparse networks. In this study, we applied some graph transformations and several inequalities to determine the greatest value of first and second Zagreb invariant, S K (...)
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  11.  21
    First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
    The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...)
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  12.  28
    A topology for galois types in abstract elementary classes.Michael Lieberman - 2011 - Mathematical Logic Quarterly 57 (2):204-216.
    We present a way of topologizing sets of Galois types over structures in abstract elementary classes with amalgamation. In the elementary case, the topologies thus produced refine the syntactic topologies familiar from first order logic. We exhibit a number of natural correspondences between the model-theoretic properties of classes and their constituent models and the topological properties of the associated spaces. Tameness of Galois types, in particular, emerges as a topological separation principle. © 2011 WILEY-VCH Verlag GmbH & Co. (...)
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  13.  14
    First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
    The transition semantics presented in Rumberg :77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language \ are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves \-validity w.r.t. transition structures. As a consequence, for a certain fragment of \, validity w.r.t. transition structures turns (...)
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  14.  49
    Continuous first order logic for unbounded metric structures.Itaï Ben Yaacov - 2008 - Journal of Mathematical Logic 8 (2):197-223.
    We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with results from cite{BenYaacov:Perturbations} regarding (...)
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  15.  31
    First-order and counting theories of ω-automatic structures.Dietrich Kuske & Markus Lohrey - 2008 - Journal of Symbolic Logic 73 (1):129-150.
    The logic L (Qu) extends first-order logic by a generalized form of counting quantifiers ("the number of elements satisfying... belongs to the set C"). This logic is investigated for structures with an injectively ω-automatic presentation. If first-order logic is extended by an infinity-quantifier, the resulting theory of any such structure is known to be decidable [6]. It is shown that, as in the case of automatic structures [21], also modulo-counting quantifiers as well as infinite cardinality quantifiers ("there are χ (...)
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  16.  7
    The profinite topology of free groups and weakly generic tuples of automorphisms.Gábor Sági - 2021 - Mathematical Logic Quarterly 67 (4):432-444.
    Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from (...)
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  17.  26
    Minimal first-order structures.Predrag Tanović - 2011 - Annals of Pure and Applied Logic 162 (11):948-957.
    We prove a dichotomy theorem for minimal structures and use it to prove that the number of non-isomorphic countable elementary extensions of an arbitrary countable, infinite first-order structure is infinite.
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  18.  55
    First order logic with empty structures.Mohamed A. Amer - 1989 - Studia Logica 48 (2):169 - 177.
    For first order languages with no individual constants, empty structures and truth values (for sentences) in them are defined. The first order theories of the empty structures and of all structures (the empty ones included) are axiomatized with modus ponens as the only rule of inference. Compactness is proved and decidability is discussed. Furthermore, some well known theorems of model theory are reconsidered under this new situation. Finally, a word is said on other approaches to the whole problem.
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  19.  35
    Inverse topological systems and compactness in abstract model theory.Daniele Mundici - 1986 - Journal of Symbolic Logic 51 (3):785-794.
    Given an abstract logic L = L(Q i ) i ∈ I generated by a set of quantifiers Q i , one can construct for each type τ a topological space S τ exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set $S_T = \{(S_\tau, \pi^\tau_\sigma)\mid\sigma, \tau \in T, \sigma \subset \tau\}$ is an inverse topological system whose bonding mappings π τ σ are naturally (...)
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  20. Knowledge Logics.Frank Wolter First Order Common - forthcoming - Studia Logica.
  21.  25
    The First-Order Structure of Weakly Dedekind-Finite Sets.A. C. Walczak-Typke - 2005 - Journal of Symbolic Logic 70 (4):1161 - 1170.
    We show that infinite sets whose power-sets are Dedekind-finite can only carry N₀-categorical first order structures. We identify other subclasses of this class of Dedekind-finite sets, and discuss their possible first order structures.
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  22.  28
    First order properties on nowhere dense structures.Nešetřil Jaroslav & Ossona De Mendez Patrice - 2010 - Journal of Symbolic Logic 75 (3):868-887.
    A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Ajtai and Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special classes of structures (such as minor closed classes). (...)
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  23.  23
    The indiscernible topology: A mock zariski topology.Markus Junker & Daniel Lascar - 2001 - Journal of Mathematical Logic 1 (01):99-124.
    We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies. The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.
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  24.  20
    First Order Logics for Metric Structures.Bernd I. Dahn - 1980 - Mathematical Logic Quarterly 26 (1‐6):77-88.
  25.  32
    First Order Logics for Metric Structures.Bernd I. Dahn - 1980 - Mathematical Logic Quarterly 26 (1-6):77-88.
  26.  14
    Undecidability of the Real-Algebraic Structure of Scott's Model.Miklós Erdélyi-Szabó - 1998 - Mathematical Logic Quarterly 44 (3):344-348.
    We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows.
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  27.  22
    Landscape as a Topology of Being and Appearance.Beatrice Nunold - 2008 - Proceedings of the Xxii World Congress of Philosophy 1:191-226.
    Our reality constitutes itself as being one of pictures. Landscape is a product of aesthetic reflection as well as the perception of reality and virtual reality of the first order (VR 1). Pictorial representation of a landscape is virtual reality of the second order (VR 2). A picture is a structure of relations with a specific topology or an interrelationship. A picture is set in relation. Topology relates to relational similarities and differences as well as their transfer into other (...)
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  28.  15
    Proof Theory of First Order Abduction: Sequent Calculus and Structural Rules.Seyed Ahmad Mirsanei - 2021 - Eighth Annual Conference of Iranian Association for Logic (Ial).
    The logical formalism of abductive reasoning is still an open discussion and various theories have been presented about it. Abduction is a type of non-monotonic and defeasible reasonings, and the logic containing such a reasoning is one of the types of non-nonmonotonic and defeasible logics, such as inductive logic. Abduction is a kind of natural reasoning and it is a solution to the problems having this form "the phenomenon of φ cannot be explained by the theory of Θ" and we (...)
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  29.  22
    Variations in definition of ultraproducts of a family of first order relational structures.Wilfred G. Malcolm - 1972 - Notre Dame Journal of Formal Logic 13 (3):394-398.
  30.  5
    Pregeometry over locally o‐minimal structures and dimension.Masato Fujita - forthcoming - Mathematical Logic Quarterly.
    We define a discrete closure operator for definably complete locally o‐minimal structures. The pair of the underlying set of and the discrete closure operator forms a pregeometry. We define the rank of a definable set over a set of parameters using this fact and call it ‐dimension. A definable set X is of dimension equal to the ‐dimension of X. The structure is simultaneously a first‐order topological structure. The dimension rank of a set definable in the (...)
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  31.  13
    First-order definability on finite structures.M. Ajtai - 1989 - Annals of Pure and Applied Logic 45 (3):211-225.
  32.  12
    Computing Some Degree-Based Topological Indices of Honeycomb Networks.Lili Gu, Shamaila Yousaf, Akhlaq Ahmad Bhatti, Peng Xu & Adnan Aslam - 2022 - Complexity 2022:1-13.
    A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n, silicate (...)
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  33.  71
    A calculus for first order discourse representation structures.Hans Kamp & Uwe Reyle - 1996 - Journal of Logic, Language and Information 5 (3-4):297-348.
    This paper presents a sound and complete proof system for the first order fragment of Discourse Representation Theory. Since the inferences that human language users draw from the verbal input they receive for the most transcend the capacities of such a system, it can be no more than a basis on which more powerful systems, which are capable of producing those inferences, may then be built. Nevertheless, even within the general setting of first order logic the structure of the (...)
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  34.  32
    Structural proof theory for first-order weak Kleene logics.Andreas Fjellstad - 2020 - Journal of Applied Non-Classical Logics 30 (3):272-289.
    This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.
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  35.  19
    Topological Completeness of First-Order Modal Logics.Steve Awodey & Kohei Kishida - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 1-17.
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  36.  18
    Topological Completeness of First-Order Modal Logics.Steve Awodey & Kohei Kishida - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 1-17.
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  37.  19
    Combinatorics of first order structures and propositional proof systems.Jan Krajíček - 2004 - Archive for Mathematical Logic 43 (4):427-441.
    We define the notion of a combinatorics of a first order structure, and a relation of covering between first order structures and propositional proof systems. Namely, a first order structure M combinatorially satisfies an L-sentence Φ iff Φ holds in all L-structures definable in M. The combinatorics Comb(M) of M is the set of all sentences combinatorially satisfied in M. Structure M covers a propositional proof system P iff M combinatorially satisfies all Φ for which the associated (...)
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  38. Spatial localisation: Interpolation of first-order and second-order visual structure.P. McGraw, D. R. Badcock, J. McArthur & R. I. Bridle - 2004 - In Robert Schwartz (ed.), Perception. Malden Ma: Blackwell. pp. 175-175.
     
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  39. Topology and modality: The topological interpretation of first-order modal logic: Topology and modality.Steve Awodey - 2008 - Review of Symbolic Logic 1 (2):146-166.
    As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for propositional modal logic, in which the “necessity” operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such (...) semantics. (shrink)
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  40.  6
    Fragments of first-order logic.Ian Pratt-Hartmann - 2023 - Oxford: Oxford University Press.
    A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are (...)
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  41.  17
    Structural completeness of the first‐order predicate calculus.W. A. Pogorzelski & T. Prucnal - 1975 - Mathematical Logic Quarterly 21 (1):315-320.
  42. First-order modal logic in the necessary framework of objects.Peter Fritz - 2016 - Canadian Journal of Philosophy 46 (4-5):584-609.
    I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only (...)
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  43.  15
    Successor-invariant first-order logic on finite structures.Benjamin Rossman - 2007 - Journal of Symbolic Logic 72 (2):601-618.
    We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (.
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  44.  11
    Ordered completion for first-order logic programs on finite structures.Vernon Asuncion, Fangzhen Lin, Yan Zhang & Yi Zhou - 2012 - Artificial Intelligence 177-179 (C):1-24.
  45. Tractarian First-Order Logic: Identity and the N-Operator.Brian Rogers & Kai F. Wehmeier - 2012 - Review of Symbolic Logic 5 (4):538-573.
    In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on early work of Hintikka’s, we (...)
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  46. A First-Order Modal Theodicy: God, Evil, and Religious Determinism.Gesiel Borges da Silva & Fábio Bertato - 2019 - South American Journal of Logic 5 (1):49-80.
    Edward Nieznanski developed in 2007 and 2008 two different systems in formal logic which deal with the problem of evil. Particularly, his aim is to refute a version of the logical problem of evil associated with a form of religious determinism. In this paper, we revisit his first system to give a more suitable form to it, reformulating it in first-order modal logic. The new resulting system, called N1, has much of the original basic structure, and many axioms, definitions, (...)
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  47.  16
    Cohen-like first order structures.Ziemowit Kostana - 2023 - Annals of Pure and Applied Logic 174 (1):103172.
  48.  52
    Formal topologies on the set of first-order formulae.Thierry Coquand, Sara Sadocco, Giovanni Sambin & Jan M. Smith - 2000 - Journal of Symbolic Logic 65 (3):1183-1192.
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  49. First-order logical duality.Steve Awodey - 2013 - Annals of Pure and Applied Logic 164 (3):319-348.
    From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...)
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  50.  12
    Fibred algebraic semantics for a variety of non-classical first-order logics and topological logical translation.Yoshihiro Maruyama - 2021 - Journal of Symbolic Logic 86 (3):1189-1213.
    Lawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics. This yields uniform hyperdoctrinal completeness results for numerous logics such as different types of relevant predicate logics and beyond, which are new results on their own; i.e., we give uniform categorical semantics for a broad variety of non-classical predicate logics. And (...)
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