37 found
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  1. Pieces of Mereology.Andrzej Pietruszczak - 2005 - Logic and Logical Philosophy 14 (2):211-234.
    In this paper† we will treat mereology as a theory of some structures that are not axiomatizable in an elementary langauge and we will use a variable rangingover the power set of the universe of the structure). A mereological structure is an ordered pair M = hM,⊑i, where M is a non-empty set and ⊑is a binary relation in M, i.e., ⊑ is a subset of M × M. The relation ⊑ isa relation of being a mereological part . We (...)
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  2.  44
    A General Concept of Being a Part of a Whole.Andrzej Pietruszczak - 2014 - Notre Dame Journal of Formal Logic 55 (3):359-381.
    The transitivity of the relation of part to whole is often questioned. But it is among the most basic principles of mereology. In this paper we present a general solution to the problem of transitivity of parthood which may be satisfactory for both its advocates and its opponents. We will show that even without the transitivity of parthood one can define—basic in mereology—the notion of being a mereological sum of some objects. We formulate several proposals of general approaches to the (...)
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  3.  17
    Classical Mereology is Not Elementarily Axiomatizable.Andrzej Pietruszczak - 2015 - Logic and Logical Philosophy 24 (4).
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  4. Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry.Rafał Gruszczyński & Andrzej Pietruszczak - 2009 - Logic and Logical Philosophy 18 (2):145-188.
    This article is devoted to the problem of ontological foundations of three-dimensional Euclidean geometry. Starting from Bertrand Russell’s intuitions concerning the sensual world we try to show that it is possible to build a foundation for pure geometry by means of the so called regions of space. It is not our intention to present mathematically developed theory, but rather demonstrate basic assumptions, tools and techniques that are used in construction of systems of point-free geometry and topology by means of mereology (...)
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  5.  9
    A Study in Grzegorczyk Point-Free Topology Part I: Separation and Grzegorczyk Structures.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Studia Logica 106 (6):1197-1238.
    This is the first, out of two papers, devoted to Andrzej Grzegorczyk’s point-free system of topology from Grzegorczyk :228–235, 1960. https://doi.org/10.1007/BF00485101). His system was one of the very first fully fledged axiomatizations of topology based on the notions of region, parthood and separation. Its peculiar and interesting feature is the definition of point, whose intention is to grasp our geometrical intuitions of points as systems of shrinking regions of space. In this part we analyze separation structures and Grzegorczyk structures, and (...)
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  6.  9
    On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1.Andrzej Pietruszczak - 2017 - Bulletin of the Section of Logic 46 (1/2).
    This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group:,,, ⌜∨ ☐q⌝,and for any n > 0 a formula ⌜ ∨ ⌝, where has not the atom ‘q’, and and have no common atom. We generalize Pollack’s result from [12],where (...)
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  7.  7
    A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D2.Marek Nasieniewski & Andrzej Pietruszczak - 2011 - Studia Logica 97 (1):161-182.
    Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows : \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where • is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = \{A \in (...)
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  8.  42
    Simplified Kripke Style Semantics for Some Very Weak Modal Logics.Andrzej Pietruszczak - 2009 - Logic and Logical Philosophy 18 (3-4):271-296.
    In the present paper we examine very weak modal logics C1, D1, E1, S0.5◦, S0.5◦+(D), S0.5 and some of their versions which are closed under replacement of tautological equivalents (rte-versions). We give semantics for these logics, formulated by means of Kripke style models of the form , where w is a «distinguished» world, A is a set of worlds which are alternatives to w, and V is a valuation which for formulae and worlds assigns the truth-vales such that: (i) for (...)
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  9. How to Define a Mereological (Collective) Set.Rafał Gruszczyński & Andrzej Pietruszczak - 2010 - Logic and Logical Philosophy 19 (4):309-328.
    As it is indicated in the title, this paper is devoted to the problem of defining mereological (collective) sets. Starting from basic properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we present and motivate basic axioms for (...)
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  10.  3
    On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 2.Andrzej Pietruszczak - 2017 - Bulletin of the Section of Logic 46 (3/4).
    This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following formulas are theses of all logics from this group:,,, ⌜∨☐q⌝, and for any n > 0 a formula ⌜ ∨ ⌝, where has not the atom ‘q’, and and have no common atom. We generalize Pollack’s result (...)
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  11.  43
    Full Development of Tarski's Geometry of Solids.Rafał Gruszczyński & Andrzej Pietruszczak - 2008 - Bulletin of Symbolic Logic 14 (4):481-540.
    In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 can be (...)
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  12.  51
    Completeness of Minimal Positional Calculus.Tomasz Jarmużek & Andrzej Pietruszczak - 2004 - Logic and Logical Philosophy 13:147-162.
    In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could (...)
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  13.  18
    The Weakest Regular Modal Logic Defining Jaskowski's Logic D2.Marek Nasieniewski & Andrzej Pietruszczak - 2008 - Bulletin of the Section of Logic 37 (3/4):197-210.
  14.  16
    On the Weakest Modal Logics Defining Jaśkowski's Logic D2 and the D2-Consequence.Marek Nasieniewski & Andrzej Pietruszczak - 2012 - Bulletin of the Section of Logic 41 (3/4):215-232.
  15.  57
    The Axiomatization of Horst Wessel's Strict Logical Consequence Relation.Andrzej Pietruszczak - 2004 - Logic and Logical Philosophy 13:121-138.
    In his book from 1984 Horst Wessel presents the system of strict logical consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the relation |=s of strict logical consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical consequence relation in CPC. The relation |=s is defined as follows: phi |=s psi iff phi |= psi, every variable from psi occurs in phi and neither phi is a contradiction nor psi is a tautology. (...)
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  16.  10
    Simplified Kripke Style Semantics for Modal Logics K45, KB4 and KD45.Andrzej Pietruszczak - 2009 - Bulletin of the Section of Logic 38 (3/4):163-171.
  17.  40
    The Consequence Relation Preserving Logical Information.Andrzej Pietruszczak - 2004 - Logic and Logical Philosophy 13:89-120.
    Information is contained in statements and «flows» from their structure and meaning of expressions they contain. The information that flows only from the meaning of logical constants and logical structure of statements we will call logical information. In this paper we present a formal explication of this notion which is proper for sentences being Boolean combination of atomic sentences. 1 Therefore we limit ourselves to analyzing logical information flowing only from the meaning of truth-value connectives and logical structure of sentences (...)
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  18. On Applications of Truth-Value Connectives for Testing Arguments with Natural Connectives.Andrzej Pietruszczak - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):143-156.
    In introductory logic courses the authors often limit their considerations to the truth-value operators. Then they write that conditionals and biconditionals of natural language ("if" and "if and only if") may be represented as material implications and equivalences ("⊃" and "≡"), respectively. Yet material implications are not suitable for conditionals. Lewis' strict implications are much better for this purpose. Similarly, strict equivalences are better for representing biconditionals (than material equivalences). In this paper we prove that the methods from standard first (...)
     
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  19.  20
    A Method of Generating Modal Logics Defining Jaśkowski’s Discussive Logic D2.Marek Nasieniewski & Andrzej Pietruszczak - 2011 - Studia Logica 97 (1):161-182.
    Jaśkowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows : \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A \in {D_{2}}}$$\end{document} iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}$$\end{document}, where • is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm D}_{2} = \{A \in (...)
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  20.  4
    A Comparison of Two Systems of Point-Free Topology.Rafał Gruszczyński & Andrzej Pietruszczak - 2018 - Bulletin of the Section of Logic 47 (3):187.
    This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide in presence of axiom stipulating non-existence of atoms.
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  21.  11
    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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  22. An Outline of the Anselmian Theory of God.Tomasz Jarmużek, Maciej Nowicki & Andrzej Pietruszczak - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):317-330.
    The article presents a formalization of Anselm's so-called Ontological Arguments from Proslogion . The main idea of our research is to stay to the original text as close as is possible. We show, against some common opinions, that (i) the logic necessary for the formalization must be neither a purely sentential modal calculus, nor just non-modal first-order logic, but a modal first-order theory; (ii) such logic cannot contain logical axiom ⌜ A → ⋄ A ⌝; (iii) none of Anselm's reasonings (...)
     
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  23.  55
    The Tense Logic for Master Argument in Prior’s Reconstruction.Tomasz Jarmużek & Andrzej Pietruszczak - 2009 - Studia Logica 92 (1):85 - 108.
    In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...)
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  24.  7
    The Tense Logic for Master Argument in Prior’s Reconstruction.Tomasz Jarmużek & Andrzej Pietruszczak - 2009 - Studia Logica 92 (1):85-108.
    In this paper we examine Prior's reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic $K_t 4$ plus a new axiom $:p \wedge Gp \supset PGp'$. This formula was used by Prior in his original analysis of Master Argument. is usually added as an extra axiom to an axiomatization of the (...)
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  25. Editorial Introduction. Logic in Torun: 1992-2003.Jacek Malinowski & Andrzej Pietruszczak - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91:9.
  26. Wokół Filozofii Logicznej.Jacek Malinowski & Andrzej Pietruszczak (eds.) - 2000 - Uniwersytet Mikołaja Kopernika.
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  27.  18
    A Modal Extension of Jaśkowski’s Discussive Logic $\Textbf{D}_\Textbf{2}$.Krystyna Mruczek-Nasieniewska, Marek Nasieniewski & Andrzej Pietruszczak - 2019 - Logic Journal of the IGPL 27 (4):451-477.
    In Jaśkowski’s model of discussion, discussive connectives represent certain interactions that can hold between debaters. However, it is not possible within the model for participants to use explicit modal operators. In the paper we present a modal extension of the discussive logic $\textbf{D}_{\textbf{2}}$ that formally corresponds to an extended version of Jaśkowski’s model of discussion that permits such a use. This logic is denoted by $\textbf{m}\textbf{D}_{\textbf{2}}$. We present philosophical motivations for the formulation of this logic. We also give syntactic characterizations (...)
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  28.  19
    New Axiomatizations of the Weakest Regular Modal Logic Defining Jaskowski's Logic D 2'.Marek Nasieniewski & Andrzej Pietruszczak - 2009 - Bulletin of the Section of Logic 38 (1/2):45-50.
  29.  3
    On Modal Logics Defining Jaśkowski's D2-Consequence.Marek Nasieniewski & Andrzej Pietruszczak - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 141--161.
  30.  9
    Semantics for Regular Logics Connected with Jaskowski's Discussive Logic D 2'.Marek Nasieniewski & Andrzej Pietruszczak - 2009 - Bulletin of the Section of Logic 38 (3/4):173-187.
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  31.  6
    Aim, the Scope and Editorial Policy of the Journal.Jerzy Perzanowski & Andrzej Pietruszczak - 1993 - Logic and Logical Philosophy 1:3-6.
    Logic, philosophy and science are among the most distinguished achievements of Western civilization. Their occurrence in ancient Greece and further development through the millennia, including long-time cooperation, is indeed the most important legacy of the Greek rationalism.
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  32. Laudacja na 90-lecie profesora Leona Gumańskiego - redaktora Ruchu Filozoficznego w latach 1981-2008.Andrzej Pietruszczak - 2011 - Ruch Filozoficzny 68 (4).
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  33.  11
    Mereological Sets of Distributive Classes.Andrzej Pietruszczak - 1996 - Logic and Logical Philosophy 4:105-122.
    We will present an elementary theory in which we can speak of mereological sets composed of distributive classes. Besides the concept of a distributive class and the membership relation , it will possess the notion of a mereological set and the relation of being a mereological part. In this theory we will interpret Morse’s elementary set theory (cf. Morse [11]). We will show that our theory has a model, if only Morse’s theory has one.
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  34.  9
    Pure Modal Logic of Names and Tableau Systems.Andrzej Pietruszczak & Tomasz Jarmużek - 2018 - Studia Logica 106 (6):1261-1289.
    By a pure modal logic of names we mean a quantifier-free formulation of such a logic which includes not only traditional categorical, but also modal categorical sentences with modalities de re and which is an extension of Propositional Logic. For categorical sentences we use two interpretations: a “natural” one; and Johnson and Thomason’s interpretation, which is suitable for some reconstructions of Aristotelian modal syllogistic :271–284, 1989; Thomason in J Philos Logic 22:111–128, 1993 and J Philos Logic 26:129–141, 1997. In both (...)
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  35.  27
    Semantical Investigations on Some Weak Modal Logics. Part II.Andrzej Pietruszczak - 2012 - Bulletin of the Section of Logic 41 (3/4):109-130.
  36.  18
    Simplified Kripke-Style Semantics for Some Normal Modal Logics.Andrzej Pietruszczak, Mateusz Klonowski & Yaroslav Petrukhin - 2020 - Studia Logica 108 (3):451-476.
    Pietruszczak :163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics \, \ ), \ are determined by suitable classes of simplified Kripke frames of the form \, where \. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of \. Furthermore, a modal logic is a normal extension of \ ; \; \) if and only if it is (...)
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  37.  6
    On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories.Marcin Łyczak & Andrzej Pietruszczak - 2018 - Bulletin of the Section of Logic 47 (4):233-263.
    We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 and we prove its adequacy with respect to the set-theoretic interpretation. Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we (...)
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