Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "Pietruszczak, Andrzej" wg kryterium: Autor

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-5 z 5
    Tytuł:
    On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
    Autorzy:
    Pietruszczak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/749944.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    first-degree theses of modal logics
    theses without iterated modalities
    Pollack’s theory of Basic Modal Logic
    basic theories for modal logics between C1 and S5
    Opis:
    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: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).
    Źródło:
    Bulletin of the Section of Logic; 2017, 46, 1/2
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2
    Autorzy:
    Pietruszczak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/750008.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    first-degree theses of modal logics
    theses without iterated modalities
    Pollack’s theory of Basic Modal Logic
    basic theories for modal logics between C1 and S5
    Opis:
    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: (N), (T), (D), ⌜(T)∨☐q⌝, and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and (T) and (altn) have no common atom. We generalize Pollack’s result from [1], where he proved that all modal logics between S1 and S5 have the same theses which does not involve iterated modalities (i.e., the same first-degree theses).
    Źródło:
    Bulletin of the Section of Logic; 2017, 46, 3/4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories
    Autorzy:
    Łyczak, Marcin
    Pietruszczak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/749926.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    elementary ontology
    quantifier-free fragment of ontology
    ontology-like theories
    copula ‘is’
    calculus of names
    Leśniewski's ontology
    subtheories of Leśniewski’s ontology
    Opis:
    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 (which corresponds to the universal name ‘object’) and we prove its adequacy with respect to the set-theoretic interpretation (again using an epimorphism theorem). Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we examine for both our theories their quantifier extensions and their connections with Leśniewski’s classical quantified ontology.
    Źródło:
    Bulletin of the Section of Logic; 2018, 47, 4
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A comparison of two systems of point-free topology
    Autorzy:
    Gruszczyński, Rafał
    Pietruszczak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/articles/749986.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    point-free topology
    region-based topology
    foundations of topology
    mereology
    mereological structures
    separation structures
    connection structures
    Grzegorczyk structures
    Biacino-Gerla structures.
    Opis:
    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 the sense that their axioms are satisfied in the same class of structures) in presence of axiom stipulating non-existence of atoms.
    Źródło:
    Bulletin of the Section of Logic; 2018, 47, 3
    0138-0680
    2449-836X
    Pojawia się w:
    Bulletin of the Section of Logic
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Rachunki sekwentowe w logice klasycznej
    Autorzy:
    Indrzejczak, Andrzej
    Pietruszczak, Andrzej
    Powiązania:
    https://bibliotekanauki.pl/books/28323571.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Opis:
    Prezentowana praca jest pomyślana jako wprowadzenie do niezwykle bogatej i złożonej problematyki związanej z teorią i zastosowaniami rachunków sekwentowych. Chcąc zachować rozsądne rozmiary książki siłą rzeczy dokonano w niej wyboru zagadnień, które w przekonaniu autora są najważniejsze, czy po prostu interesujące. Nacisk został położony na metodologiczne aspekty RS, toteż nie jest to praca z zakresu teorii dowodu, w której RS jest narzędziem do prezentacji wyników tej teorii. Książka zawiera detaliczną prezentację podstawowych zastosowań RS, najważniejszych twierdzeń i technik dowodzenia tych rezultatów. W szczególności, czytelnik może znaleźć poniżej różne dowody podstawowych twierdzeń oraz ich porównanie. Najwięcej uwagi poświęcamy dowodzeniu fundamentalnego twierdzenia o eliminowalności (Cut), czyli reguły cięcia, które często traktowane jest jako najważniejszy wynik z zakresu teorii dowodu. W pracy poświęcamy tez sporo miejsca wyjaśnieniu, dlaczego wynik ten jest tak ważny. Staraliśmy się, by praca była przystępnie napisana, ale nie kosztem nadmiernego upraszczania czy poświęcania rygorów formalnych. Adresatem jest czytelnik z pewnym przygotowaniem formalno-logicznym, ale nie przekraczającym poziomu standardowego kursu logiki w zakresie oferowanym na studiach filozoficznych, czy wstępu do matematyki (dyskretnej) na studiach matematycznych lub informatycznych. Ze wstępu
    In 1934 Jaśkowski and Gentzen independently published their groundbreaking works on natural deduction. Moreover, Gentzen introduced in his paper another formal system LK, nowadays commonly called sequent calculus. Although Gentzen presented sequent calculus as a kind of auxiliary system for showing some properties of natural deduction it appeared soon that it is a system of a great importance. Modern proof theory is developed mainly in Gentzen’s tradition with sequent calculi as the basic tool for application. Unfortunately, in Poland, the country with great logical tradition, this approach is not very popular. The book is meant as a detailed introduction to the subject of sequent calculi and their applications. However, it differs strongly from well known books on proof theory which use sequent calculi as a tool for exploration and presentation of metalogical results. Instead, this book focuses on sequent calculi, their properties, and techniques of proof. Hence it is not a book on proof theory as such, but rather methodological study of basic tools of modern proof theory. In particular, we pay special attention to different techniques of proving cut-elimination theorem which is often seen as the most fundamental result in the field. We restrict considerations to classical logic, hence we do not present generalizations of sequent calculi provided for nonclassical logics. We hope that these matters will be treated in the sequel to this volume. Since the book is self-contained the first chapter contains the brief introduction to classical propositional logic (CPL). We describe propositional languages and notation, Hilbert calculus for CPL and standard semantics. Special attention is paid to adequacy proofs for Hilbert calculus; we present several approaches due to Post, Henkin, Asser, Hintikka and Smullyan. Finally, some properties of CPL, like decidability and interpolation are discussed and formalization in terms of natural deduction. The general introduction to sequent calculi is provided in chapter 2. In particular, we discuss the notion of a sequent, sequent rules and sequent calculus; in each case several variants and generalizations of basic notions are presented. Finally, we discuss different possible interpretions of sequents and sequent rules and the connections with the theory of consequence relations. Chapter 3 is devoted to detailed description of original Gentzen’s calculus LK and its basic properties. Syntactical equivalence with Hilbert formalization of CPL as well as soundness with respect to standard semantics is shown. In the next chapter we introduce a plethora of variants of sequent calculi for CPL. In particular, analytical sequent calculus is introduced with no structural rules and with invertible rules. Finally, we present a general result concerning equivalence of rules of several shapes on the basis of standard sequent calculus, and discuss the most interesting properties of rules. The cornerstone of the book is chaper 5 which contains a detailed description of different proofs of cut-elimination. After informal discussion of the general idea of proving cut-elimination/admissibility, we present the original proof of Gentzen. Next, we introduce three different proofs due to Dragalin, Schütte and Smullyan. Despite the differences all are based on local transformation steps in proofs, similarly as Gentzen’s proof. Rather different approach to the problem is represented by Curry and Buss. Their proofs, although different, are based on the strategy of global transformation of input proof containing applications of cut. A discussion of properties of presented proofs and their comparison finishes the chapter. The next chapter focuses on some consequences of cut-elimination. First of all, we discuss subformula-property, several senses of analyticity, decidability of CPL and strategies of proof-search. Additionaly, the proof of interpolation for CPL by means of Maehara strategy is presented. In chapter 7 we show that sequent calculus may be applied succesfully also for presenting semantical results. We restrict our considerations to completeness proof. Firstly, Henkin-style non-constructive proof is presented in two variants for sequent calculus with cut. Next, Hintikka-style constructive proofs (also in two variants) are provided for cut-free sequent calculus. We present also a completeness proof for sequent calculus with analytical cut which mixes the properties of Henkin’s and Hintikka’s proofs. Finally, Post method based on normal forms is adapted to cut-free sequent calculus. Next we turn to first-order logic. Chapter 8 has similar character to chapter 1; it is an introduction to first-order classical logic with special attention paid to some language-oriented problems important in the context of sequent calculi. In chapter 9 we extend to first-order logic the techniques and results introduced in chapters 3-7 for propositional logic. We focus on questions particularly important for, or hard to prove in the context of sequent formalization of first-order logic. In particular, we discuss in detail two approaches to characterization of the language (free variables versus paramaters) and the problem of semi-decidability and proof-search strategies. Except ordinary cut-elimination theorem (in Gentzen’s and Dragalin’s version) we present the strengtened version of this result (mid-sequent theorem) which may be seen as a version of Herbrand’s theorem. Also four different approaches to formalization of elementary theories on the basis of sequent calculi are discussed. The last chapter is devoted to brief presentation of some other kinds of sequent calculi which are essentially different from ordinary Gentzen’s calculi explored so far. The first type is based on the idea of characterization of constants by means of rules, and in this respect is similar to ordinary Gentzen’s calculi. The difference is that several calculi of this sort admit rules of different character than cumulative Gentzen’s introduction rules. The second type is based on the idea of characterization of constants by means of primitive sequents, with structural rules only. The third type is of mixed character with rules and sequents equally applicable. We finish with an Appendix presenting briefly set-theoretical, algebraic and arithmetical notions used in the book; in particular, we pay special attentention to inductive proofs.
    Dostawca treści:
    Biblioteka Nauki
    Książka
      Wyświetlanie 1-5 z 5

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies