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  1. Andrzej Pietruszczak (2014). A General Concept of Being a Part of a Whole. 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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  2. Marek Nasieniewski & Andrzej Pietruszczak (2013). On Modal Logics Defining Jaśkowski's D2-Consequence. In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. 141--161.
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  3. Marek Nasieniewski & Andrzej Pietruszczak (2012). On the Weakest Modal Logics Defining Jaśkowski's Logic D2 and the D2-Consequence. Bulletin of the Section of Logic 41 (3/4):215-232.
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  4. Andrzej Pietruszczak (2012). Semantical Investigations on Some Weak Modal Logics. Part II. Bulletin of the Section of Logic 41 (3/4):109-130.
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  5. Marek Nasieniewski & Andrzej Pietruszczak (2011). A Method of Generating Modal Logics Defining Jaśkowski's Discussive Logic D₂. Studia Logica 97 (1):161-182.
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  6. Andrzej Pietruszczak (2011). Laudacja na 90-lecie profesora Leona Gumańskiego - redaktora Ruchu Filozoficznego w latach 1981-2008. Ruch Filozoficzny 4 (4).
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  7. Rafał Gruszczyński & Andrzej Pietruszczak (2010). How to Define a Mereological (Collective) Set. 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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  8. Andrzej Pietruszczak (2010). Simplified Kripke Style Semantics for Some Very Weak Modal Logics. 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. Rafał Gruszczyński & Andrzej Pietruszczak (2009). Space, Points and Mereology. On Foundations of Point-Free Euclidean Geometry. 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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  10. Tomasz Jarmużek & Andrzej Pietruszczak (2009). The Tense Logic for Master Argument in Prior's Reconstruction. 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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  11. Marek Nasieniewski & Andrzej Pietruszczak (2009). New Axiomatizations of the Weakest Regular Modal Logic Defining Jaskowski's Logic D 2'. Bulletin of the Section of Logic 38 (1/2):45-50.
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  12. Marek Nasieniewski & Andrzej Pietruszczak (2009). Semantics for Regular Logics Connected with Jaskowski's Discussive Logic D 2'. Bulletin of the Section of Logic 38 (3/4):173-187.
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  13. Andrzej Pietruszczak (2009). Simplified Kripke Style Semantics for Modal Logics K45, KB4 and KD45. Bulletin of the Section of Logic 38 (3/4):163-171.
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  14. Rafał Gruszczyński & Andrzej Pietruszczak (2008). Full Development of Tarski's Geometry of Solids. 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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  15. Marek Nasieniewski & Andrzej Pietruszczak (2008). The Weakest Regular Modal Logic Defining Jaskowski's Logic D2. Bulletin of the Section of Logic 37 (3/4):197-210.
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  16. Tomasz Jarmużek, Maciej Nowicki & Andrzej Pietruszczak (2006). An Outline of the Anselmian Theory of God. 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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  17. Jacek Malinowski & Andrzej Pietruszczak (2006). Editorial Introduction. Logic in Torun: 1992-2003. Poznan Studies in the Philosophy of the Sciences and the Humanities 91:9.
     
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  18. Andrzej Pietruszczak (2006). On Applications of Truth-Value Connectives for Testing Arguments with Natural Connectives. 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. Andrzej Pietruszczak (2005). Pieces of Mereology. Logic and Logical Philosophy 14 (2):211-234.
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  20. Tomasz Jarmużek & Andrzej Pietruszczak (2004). Completeness of Minimal Positional Calculus. 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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  21. Andrzej Pietruszczak (2004). The Axiomatization of Horst Wessel's Strict Logical Consequence Relation. 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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  22. Andrzej Pietruszczak (2004). The Consequence Relation Preserving Logical Information. 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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  23. Jerzy Perzanowski & Andrzej Pietruszczak (2003). Aim, the Scope and Editorial Policy of the Journal. 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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  24. Andrzej Pietruszczak (2003). Mereological Sets of Distributive Classes. 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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  25. Jacek Malinowski & Andrzej Pietruszczak (eds.) (2000). Wokół Filozofii Logicznej. Uniwersytet Mikołaja Kopernika.
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