Wyniki wyszukiwania - Biblioteka Nauki

1

Towards a Pragmatic Mereology

100%

Janicki R. , Le D. T. M.

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2007

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tom Vol. 75, nr 1-4

295-314

EN

A version of mereology (i.e. theory of parts and fusions) is presented. Some applications to model software structures are discussed.

2

Mereology and truth-making

51%

Simons P.

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2016

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tom 25

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nr 3 Mereology and Beyond (II)

245-258

EN

Many mereological propositions are true contingently, so we are entitled to ask why they are true. One frequently given type of answer to such questions evokes truth-makers, that is, entities in virtue of whose existence the propositions in question are true. However, even without endorsing the extreme view that all contingent propositions have truth-makers, it turns out to be puzzlingly hard to provide intuitively convincing candidate truth-makers for even a core class of basic mereological propositions. Part of the problem is that the relation of part to whole is ontologically intimate in a way reminiscent of identity. Such intimacy bespeaks a formal or internal relation, which typically requires no truth-makers beyond its terms. But truth-makers are held to necessitate their truths, so whence the contingency when A is part of B but need not be, or B need not have A as part? This paper addresses and attempts to disentangle the conundrum.

3

On a Notion of Extensionality for Artifacts

51%

Semeniuk-Polkowska M. , Polkowski L.

Fundamenta Informaticae

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2013

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tom Vol. 127, nr 1-4

65--80

EN

The notion of extensionality means in plain sense that properties of complex things can be expressed by means of their simple components, in particular, that two things are identical if and only if certain of their components or features are identical; e.g., the Leibniz Identitas Indiscernibilium Principle: two things are identical if each applicable to them operator yields the same result on either; or, extensionality for sets, viz., two sets are identical if and only if they consist of identical elements. In mereology, this property is expressed by the statement that two things are identical if their parts are the same. However, building a thing from parts may proceed in various ways and this, unexpectedly, yields various extensionality principles. Also, building a thing may lead to things identical with respect to parts but distinct with respect, e.g., to usage. We address the question of extensionality for artifacts, i.e., things produced in some assembling or creative process in order to satisfy a chosen purpose of usage, and, we formulate the extensionality principle for artifacts which takes into account the assembling process and requires for identity of two artifacts that assembling graphs for the two be isomorphic in a specified sense. In parallel, we consider the design process and design things showing the canonical correspondence between abstracta as design products and concreta as artifacts. In the end, we discuss approximate artifacts as a result of assembling with spare parts which analysis does involve rough mereology.

4

Mereology and Infinity

51%

Niebergall K.-G.

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2016

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tom 25

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nr 3 Mereology and Beyond (II)

309-350

EN

This paper deals with the treatment of infinity and finiteness in mereology. After an overview of some first-order mereological theories, finiteness axioms are introduced along with a mereological definition of “x is finite” in terms of which the axioms themselves are derivable in each of those theories. The finiteness axioms also provide the background for definitions of “(mereological theory) T makes an assumption of infinity”. In addition, extensions of mereological theories by the axioms are investigated for their own sake. In the final part, a definition of “x is finite” stated in a second-order language is also presented, followed by some concluding remarks on the motivation for the study of the (first-order) extensions of mereological theories dealt with in the paper.

5

Notes on models of first-order mereological theories

51%

Tsai H.-c.

Logic and Logical Philosophy

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2015

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tom 24

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nr 4 Mereology and Beyond

469-482

EN

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable.

6

Notes on models of first-order mereological theories

51%

Tsai H.-c.

Logic and Logical Philosophy

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2015

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tom 24

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nr 4 Mereology and Beyond

469–482

EN

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable.

7

Set-theoretic mereology

51%

Hamkins J. D. , Kikuchi M.

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2016

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tom 25

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nr 3 Mereology and Beyond (II)

285-308

EN

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by adding the singleton operator, are foundationally robust.

8

Composition, identity, and emergence

51%

Calosi C.

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2016

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tom 25

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nr 3 Mereology and Beyond (II)

429-443

EN

Composition as Identity (CAI) is the thesis that a whole is, strictly and literally, identical to its parts, considered collectively. McDaniel [2008] argues against CAI in that it prohibits emergent properties. Recently Sider [2014] exploited the resources of plural logic and extensional mereology to undermine McDaniel’s argument. He shows that CAI identifies extensionally equivalent pluralities – he calls it the Collapse Principle (CP) – and then shows how this identification rescues CAI from the emergentist argument. In this paper I first give a new generalized version of both the arguments. It is more general in that it does not presuppose an atomistic mereology. I then go on to argue that the consequences of CP are rather radical. It entails mereological nihilism, the view that there are only mereological atoms. I finally show that, given a mild assumption about property instantiation, namely that there are no un-instantiated properties, this argument entails that CAI and emergent properties are incompatible after all.

9

The p-semisimple property for some generalizations of BCI algebras and its applications

51%

Obojska L. , Walendziak A.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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2020

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tom 19

79-94

EN

This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.

10

A categorical axiomatisation of Region-Based Geometry

51%

Bennett B.

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2001

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tom Vol. 46, nr 1,2

145-158

EN

Region Based Geometry (RBG) is an axiomatic theory of qualitative configurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1st-order axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over \mathbbR.

11

Boundaries, Borders, Fences, Hedges

51%

Polkowski L. , Semeniuk-Polkowska M.

Fundamenta Informaticae

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2014

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tom Vol. 129, nr 1/2

149--159

EN

In this essay, we analyze various often semantically identified notions of separating things. In doing this, we contrast the set–theoretical approach based on the notion of an element/point with the mereological approach based on the notion of a part, hence, pointless. We address time aspect of the notion of a boundary and related notions as well as approximate notions defined in the realm of rough (approximate) mereology.

12

Czy monady mają części? Witkiewicz i jego krytyka mereologii jako ontologii

44%

Szachniewicz A.

Analiza i Egzystencja. Czasopismo Filozoficzne

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2017

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tom 37

79-99

EN

This paper reconstructs Stanisław Ignacy Witkiewicz’s understanding of logic, accentuating the differences in his evaluation of logic and systems of ‘logistics’. Leśniewski’s theory of collective sets (mereology) exemplifies logistics as understood by Witkiewicz. I present an outline of Leśniewski’s nominalism, which entails a belief in a non-abstract nature of sets. I focus on these features of mereology that could have led Witkiewicz to interpreting it as an ontological system. Witkacy (Witkiewicz’s penname) was skeptical of the usefulness of formal systems (or logistics), and of mereology in particular, for the purposes of designing a unified ontological system describing essential properties of objects (the world). According to Witkiewicz, such formal systems assumed the role of ontology but severely lacked in philosophical justification. I argue that regardless of his nominalism and corporeal conception of individuals, mereology cannot be considered a formal theory of Witkiewicz’s monads.

13

The Notion of the Diameter of Mereological Ball in Tarski's Geometry of Solids

44%

Sitek G.

Logic and Logical Philosophy

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2017

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tom 26

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nr 4

531–562

EN

In the paper "Full development of Tarski's geometry of solids" Gruszczyński and Pietruszczak have obtained the full development of Tarski’s geometry of solids that was sketched in [14, 15]. In this paper 1 we introduce in Tarski’s theory the notion of congruence of mereological balls and then the notion of diameter of mereological ball. We prove many facts about these new concepts, e.g., we give a characterization of mereological balls in terms of its center and diameter and we prove that the set of all diameters together with the relation of inequality of diameters is the dense linearly ordered set without the least and the greatest element.

14

More on The Decidability of Mereological Theories

44%

Tsai H.-c.

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tom 20

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nr 3

251-265

EN

Quite a few results concerning the decidability of mereological theories have been given in my previous paper. But many mereological theories are still left unaccounted for. In this paper I will refine a general method for proving the undecidability of a theory and then by making use of it, I will show that most mereological theories that are strictly weaker than CEM are finitely inseparable and hence undecidable. The same results might be carried over to some extensions of those weak theories by adding the fusion axiom schema. Most of the proofs to be presented in this paper take finite lattices as the base models when applying the refined method. However, I shall also point out the limitation of this kind of reduction and make some observations and conjectures concerning the decidability of stronger mereological theories.

15

On connection synthesis via rough mereology

44%

Polkowski L.

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2001

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tom Vol. 46, nr 1,2

83-96

EN

Rough mereology is a paradigm for reasoning under uncertainty whose primitive notion is that of being a part to a degree; hence, rough mereology falls in the province of mereology-based theories for reasoning about complex objects. Among mereological theories of objects, theories based on the primitive notion of a connection distinguish themselves by a variety of applications of which we would like to mention the area of Qualitative Spatial Reasoning. In this paper, we define rough mereologies within the realm of mereologies based on the primitive notion of a part and we show that in this framework one may induce notions of connection closely related to initial rough mereologies in the sense that they induce the same notion of a part. We also address the distributed environment proving some results about connection preservation throughout the reasoning system.

16

Composition as identity and plural Cantor's theorem

44%

Bohn E. D.

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2016

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tom 25

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nr 3 Mereology and Beyond (II)

411-428

EN

In this paper, I argue that the thesis of Composition as Identity blocks the plural version of Cantor’s Theorem, and that this in turn has implications for our use of Cantor’s theorem in metaphysics. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano, and might be turned around to become an abductive argument for Composition as Identity

17

Ontological Models Based on Mereology, Topology and Theoretical Data

44%

Vasyliuk J. , Teslyuk V. , Mykhailiuk A.

Machine Dynamics Research

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2013

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tom Vol. 37, No. 2

91-96

EN

In this paper the ontological models based on mereology, topology and theoretical data about microelectromechanical system as ontology is described throughout the spectrum of mereology, topological principles. As result, it was illustrated the elementary structure, the interaction between microsystems components and internal processes between them.

18

Mereological foundations of point-free geometry via multi-valued logic

38%

Coppola C. , Gerla G.

Logic and Logical Philosophy

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2015

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tom 24

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nr 4 Mereology and Beyond

535-553

EN

We suggest possible approaches to point-free geometry based on multi-valued logic. The idea is to assume as primitives the notion of a region together with suitable vague predicates whose meaning is geometrical in nature, e.g. ‘close’, ‘small’, ‘contained’. Accordingly, some first-order multi-valued theories are proposed. We show that, given a multi-valued model of one of these theories, by a suitable definition of point and distance we can construct a metrical space in a natural way. Taking into account that interesting metrical approaches to geometry exist, this looks to be promising for a point-free foundation of the notion of space. We hope also that this way to face point-free geometry provides a tool to illustrate the passage from a naïve and ‘qualitative’ approach to geometry to the ‘quantitative’ approach of advanced science.

19

The Notion of Cube in theTheory of Squares

38%

Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2000/2001

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tom Vol. 8

67--79

20

On the Problem of Boundaries from Mereology and Rough Mereology Points of View

38%

Polkowski L. , Semeniuk-Polkowska M.

Fundamenta Informaticae

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2014

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tom Vol. 133, nr 2/3

241--255

EN

The notion of a boundary belongs in the canon of the most important notions of mereotopology, the topological theory induced by mereological structures; the importance of this notion rests not only in its applications to practical spatial reasoning, e.g., in geographical information systems, where it is usually couched under the term of a contour and applied in systems related to economy, welfare, climate, wildlife etc., but also in its impact on reasoning schemes elaborated for reasoning about spatial objects, represented as regions, about spatial locutions etc. The difficulty with this notion lies primarily in the fact that boundaries are things not belonging in mereological universa of things of which they are boundaries. Various authors, from philosophers through mathematicians to logicians and computer scientists proposed schemes for defining and treating boundaries. We propose two approaches to boundaries; the first aims at defining boundaries as things possibly in the universe in question, i.e., composed of existing things, whereas the second defines them as things in a meta–space built over the mereological universe in question, i.e., we assume a priori that boundaries are in a sense ‘things at infinity’, in an agreement with the topological nature of boundaries. Of the two equivalent topological definitions of a boundary, the first, global, defining the boundary as the difference between the closure and the interior of the set, and the second, local, defining it as the set of boundary points whose all neighborhoods transect the set, the first calls for the first type of the boundary and the second is best fitted for the meta–boundary. In the text that follows, we discuss mereology and rough mereology notions (sects. 2, 3), the topological approach to the notion of a boundary and the model ROM with which we illustrate our discussion (sect. 4), the mereology approach (sect. 5), and the approach based on rough mereology and granular computing in the framework of rough mereology (sect. 6).