8 found
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  1.  59
    Abstract logics, logic maps, and logic homomorphisms.Steffen Lewitzka - 2007 - Logica Universalis 1 (2):243-276.
    . What is a logic? Which properties are preserved by maps between logics? What is the right notion for equivalence of logics? In order to give satisfactory answers we generalize and further develop the topological approach of [4] and present the foundations of a general theory of abstract logics which is based on the abstract concept of a theory. Each abstract logic determines a topology on the set of theories. We develop a theory of logic maps and show in what (...)
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  2.  33
    Minimally generated abstract logics.Steffen Lewitzka & Andreas B. M. Brunner - 2009 - Logica Universalis 3 (2):219-241.
    In this paper we study an alternative approach to the concept of abstract logic and to connectives in abstract logics. The notion of abstract logic was introduced by Brown and Suszko —nevertheless, similar concepts have been investigated by various authors. Considering abstract logics as intersection structures we extend several notions to their κ -versions, introduce a hierarchy of κ -prime theories, which is important for our treatment of infinite connectives, and study different concepts of κ -compactness. We are particularly interested (...)
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  3.  11
    $${\in_K}$$ : a Non-Fregean Logic of Explicit Knowledge.Steffen Lewitzka - 2011 - Studia Logica 97 (2):233-264.
    We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom Kiφ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit (...)
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  4.  26
    ∈ I : An Intuitionistic Logic without Fregean Axiom and with Predicates for Truth and Falsity.Steffen Lewitzka - 2009 - Notre Dame Journal of Formal Logic 50 (3):275-301.
    We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the quantifier-free language by (...)
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  5.  25
    Denotational Semantics for Modal Systems S3–S5 Extended by Axioms for Propositional Quantifiers and Identity.Steffen Lewitzka - 2015 - Studia Logica 103 (3):507-544.
    There are logics where necessity is defined by means of a given identity connective: \ is a tautology). On the other hand, in many standard modal logics the concept of propositional identity \ can be defined by strict equivalence \}\). All these approaches to modality involve a principle that we call the Collapse Axiom : “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the identity axioms of Suszko’s non-Fregean logic SCI. (...)
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  6.  27
    Reasoning about proof and knowledge.Steffen Lewitzka - 2019 - Annals of Pure and Applied Logic 170 (2):218-250.
  7.  15
    Topological Representation of Intuitionistic and Distributive Abstract Logics.Andreas Bernhard Michael Brunner & Steffen Lewitzka - 2017 - Logica Universalis 11 (2):153-175.
    We continue work of our earlier paper :219–241, 2009) where abstract logics and particularly intuitionistic abstract logics are studied.logics can be topologized in a direct and natural way. This facilitates a topological study of classes of concrete logics whenever they are given in abstract form. Moreover, such a direct topological approach avoids the often complex algebraic and lattice-theoretic machinery usually applied to represent logics. Motivated by that point of view, we define in this paper the category of intuitionistic abstract logics (...)
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  8.  18
    On dividing chains in simple theories.Steffen Lewitzka & Ruy J. G. B. De Queiroz - 2005 - Archive for Mathematical Logic 44 (7):897-911.
    Dividing chains have been used as conditions to isolate adequate subclasses of simple theories. In the first part of this paper we present an introduction to the area. We give an overview on fundamental notions and present proofs of some of the basic and well-known facts related to dividing chains in simple theories. In the second part we discuss various characterizations of the subclass of low theories. Our main theorem generalizes and slightly extends a well-known fact about the connection between (...)
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