This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

Artykuł przedstawia interpretację Emila Rousseau jako koncepcję jednego z czterech miejsc — obok republiki, małej wspólnoty ulokowanej poza społeczeństwem i pełnej samotności — w których człowiek może wyzwolić się z alienacji. Emil żyje w społeczeństwie, ale zachowuje duchowy dystans wobec jego członków; w istocie żyje na pograniczu społeczności, bardziej obok ludzi niż z nimi. Tak jak „obcego”, o którym pisał Simmel, łączy go z jej członkami to, co wspólne wszystkim ludziom, dzieli natomiast to, co ich właśnie łączy we wspólnotę. Emil (...) jest więc obcy ludziom, ale nie jest wyobcowany, gdyż to właśnie on, a nie oni, żyje zgodnie z naturą. Jakkolwiek Rousseau zapewnia, że Emil jest potencjalnie zdolny do zajęcia wszystkich pozostałych miejsc, autor tekstu dowodzi, że kierując się zasadą dobrowolności stowarzyszeń Emil skazany jest na życie samotne, do którego jest też najlepiej przygotowany. (shrink)

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.

This book introduces the English-speaking reader to the thought of Stanislaw Brzozowski (1878-1911), the outstanding Polish philosopher and literary critic. Although practically unknown in the West, Brzozowski is an important but neglected forerunner of the intellectual tradition of `Western Marxism', most commonly associated with Georg Lukács and Antonio Gramsci. -/- Concentrating first on the early phase of Brzozowski's thought, Professor Walicki goes on to analyse his ideas on the working class and its relation to the intelligentsia and contemporary working-class ideologies. (...) Finally he deals with aspects of his thought which go beyond the Marxian problematic and round off the intellectual portrait of the man. -/- Brzozowski's anti-naturalistic approach resulted in a radical reinterpretation of Marxism which dealt with many of the problems of the revolt against positivism in European philosophy. Professor Walicki argues that the retrieval of the philosophical and humanist aspect of Marxism, and its separation from the Engels-inspired `scientific Marxism', was the achievement of Brzozowski and not, as frequently assumed, of Lukács, who came to similar conclusions only some ten years later. -/- By placing Brzozowski within the cross-currents of the various philosophical, sociological, literary, and political streams of Western and Eastern European thought in which Marxism was situated, Professor Walicki produces a fascinating study of an early East European challenge to orthodox Marxism. (shrink)

This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.

We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of (...) varying strength. For all presented calculi a constructive cut elimination is provided. (shrink)

W artykule proponuje się aksjomatyzację fragmentu klasycznej logiki zdań, który zostaje nazwany logiką niesymplifikacyjną. Nazwa pochodzi stąd, że unika się w nim, jak przypuszcza pewna ilość badaczy – wskazanych w tekście – paradoksalnych własności klasycznej implikacji i równoważności. Twierdzenie o niewyprowadzalności tez paradoksalnych nie jest jeszcze definitywnie udowodnione. Ale cały bieg myśli wydaje się interesujący z filozoficznego punktu widzenia ze względu na możliwość odróżnienia kilku rodzajów implikacji i równoważności.

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.

National healthcare systems in all countries do not act effectively. Therefore, especially strategies for introducing organizational innovation to public organization should be considered. The problem is how to organize the research in this field. One of the generally accepted solutions is the systemic approach to healthcare systems. In this paper multiagent systems theory and autonomous systems theory are applied to the analysis of main types of healthcare systems. Such analysis allows us to consider the system properties: the level of the (...) autonomy, energy dissipation in the system, the payoff specificity, functional role of the agents in the system, the level of the agents’ cooperation, and delays in flows of money, requests, rules, and controls. As a result, some new functionalities of the healthcare system on the national level have been found and analysed. The aforementioned parameters are good tools to analyse the system functionality. (shrink)

entailment; families of sets; logic of questions.

There are many religions in the human world, and people manifest their religiousness in many different ways. The main problem this paper addresses concerns the possibility of sorting out this complex world of human religiousness by showing that it can be phenomenologically reduced to a few very basic existential attitudes. These attitudes express the main types of ways in which a human being relates to his or herself and the world, independently of the worldview or religion professed by the individual. (...) I use Kierkegaard’s theories of the stages of existence and subjective truth as a model. The theory of the stages of existence provides five basic existential attitudes on the basis of which religious attitudes can develop: spiritlessness, the aesthetic, the ethical, religiousness A, and religiousness B. The theory of subjective truth shows how the concept of truth functions in an ethical and existential sense as the personal truth of an individual engaged in building their religious identity. In turn, I discuss the problem of the relation of Kierkegaard’s philosophy to phenomenology, briefly introduce his concept of subjective truth and the stages of existence, and show how existential attitudes can be transformed into religious ones. I also consider the problem of the demonic as the inverted order of this anthropological and existential model. Finally, I argue that the model developed herein may be useful for further research into the phenomenology of religious attitudes. (shrink)

This history of Russian thought was first published in Polish in 1973 and subsequently appeared 2005 in a revised and expanded publication. The current volume begins with Enlightenment thought and Westernization in Russia in the 17<SUP>th century and moves to the religious-philosophical renaissance of first decade of the 20<SUP>th century. This book provides readers with an exhaustive account of relationships between various Russian thinkers with an examination of how those thinkers relate to a number of figures and trends in Western (...) philosophy and in the broader history of ideas. (shrink)

The paper provides a proof theoretic characterization of the Russellian theory of definite descriptions (RDD) as characterized by Kalish, Montague and Mar (KMM). To this effect three sequent calculi are introduced: LKID0, LKID1 and LKID2. LKID0 is an auxiliary system which is easily shown to be equivalent to KMM. The main research is devoted to LKID1 and LKID2. The former is simpler in the sense of having smaller number of rules and, after small change, satisfies cut elimination but fails to (...) satisfy the subformula property. In LKID2 an additional analysis of different kinds of identities leads to proliferation of rules but yields the subformula property. This refined proof theoretic analysis leading to fully analytic calculus with constructive proof of cut elimination is the main contribution of the paper. (shrink)

In this paper the life phenomenon is analysed from cybernetic point of view. The Korzeniewski’s approach is discussed and complemented. The analysis is based on autonomous systems theory and information metabolism theory. Philosophical aspects of the problem are taken into consideration as well.

In this paper, the concept of structural information is presented. The mathematical foundation of the concept is put forward, and the nature of information encoded in a structure is studied. A method for calculating the amount of structural information is introduced. An application to the analysis of cognitive maps is also presented and discussed.

Visages de l'histoire. Essais de l'entour de la méthodologie et d'histoire de l'historiographie.