This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. (...) Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

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.

The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)

We present a proof-theoretical analysis of the theory of definite descriptions which emerges from Frege’s approach and was formally developed by Kalish and Montague. This theory of definite descriptions is based on the assumption that all descriptions are treated as genuine terms. In particular, a special object is chosen as a designatum for all descriptions which fail to designate a unique object. Kalish and Montague provided a semantical treatment of such theory as well as complete axiomatic and natural deduction formalization. (...) In the paper we provide a sequent calculus formalization of this logic and prove cut elimination theorem in the constructive manner. (shrink)

The paper presents a uniform proof-theoretic treatment of several kinds of free logic, including the logics of existence and definedness applied in constructive mathematics and computer science, and called here quasi-free logics. All free and quasi-free logics considered are formalised in the framework of sequent calculus, the latter for the first time. It is shown that in all cases remarkable simplifications of the starting systems are possible due to the special rule dealing with identity and existence predicate. Cut elimination is (...) proved in a constructive way for sequent calculi adequate for all logics under consideration. (shrink)

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

Singh asserts that the parent–child relationship engenders a moral responsibility for the newborn. Simultaneously, he contends, drawing on the argument from potentiality, that the fetal stage of human development does not establish the parent–child relationship. Consequently, within Singh’s proposed relational framework, moral responsibility for the developing fetus does not manifest. Thus, Singh advocates for abortion, citing the absence of moral responsibilities arising for the pregnant woman for the fetus. In this article, I critique Singh’s argument from potentiality, identifying flaws and (...) highlight the incoherence of the argument pertaining to the parent–child relationship. (shrink)

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

Provability, Computability and Reflection.

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)

In several applications of sequent calculi going beyond pure logic, an introduction of suitably defined rules seems to be more profitable than addition of extra axiomatic sequents. A program of formalization of mathematical theories via rules of special sort was developed successfully by Negri and von Plato. In this paper a general theorem on possible ways of transforming axiomatic sequents into rules in sequent calculi is proved. We discuss its possible applications and provide some case studies for illustration.

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.

The studies of health care systems are conducted intensively on various levels. They are important because the systems suffer from numerous pathologies. The health care is analyzed, first of all, in economic aspects but their functionality in the framework of systems theory is studied, as well. There are also attempts to work out some general values on which health care systems should be based. Nevertheless, the aforementioned studies, however, are fragmentary ones. In this paper holistic approach to the philosophical basis (...) of health care is presented. The levels on which the problem can be considered are specified explicitly and relations between them are analyzed, as well. The philosophical basis on which the national health care systems could be based is proposed. Personalism is the basis for the proposal. First of all, the values, that are derived from the personalistic philosophy, are specified as the basic ones for health care systems. Then, general organizational and functional properties of the system are derived from the assumed values. The possibility of adaptation of solutions from other fields of social experiences are also mentioned. The existing health care systems are analyzed within the frame of the introduced proposal. (shrink)

The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called (...) Gentzen’s type, we have a subtype of standard SC due to Gentzen. Hence by nonstandard ones we mean all these ordinary SC where other kinds of rules are applied than those admitted in standard Gentzen’s sequent calculi. We describe briefly some of the most interesting or important nonstandard SC belonging to the three abovementioned types. (shrink)

In this brief note we would like to outline the main events of life and the main achievements of Stanisław Jaśkowski one of the important Polish logician and mathematician of the first half of twentieth century.

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)

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 (...) all formulae and all worlds, V preserves classical conditions for truth-value operators; (ii) for the world w and any formula ϕ, V(⬜ϕ,w) = 1 iff ∀x∈A V(ϕ,x) = 1; (iii) for other worlds formula ⬜ϕ has an arbitrary value. Moreover, for rte-versions of considered logics we must add the following condition: (iv) V(⬜χ,w) = V(⬜χ[ϕ/ψ],w), if ϕ and ψ are tautological equivalent. Finally, for C1, D1and E1 we must add queer models of the form in which: (i) holds and (ii') V(⬜ϕ,w) = 0, for any formula ϕ. We prove that considered logics are determined by some classes of above models. (shrink)

This is a sequel article to [10] where a hypersequent calculus for some temporal logics of linear frames includingKt4.3and its extensions for dense and serial flow of time was investigated in detail. A distinctive feature of this approach is that hypersequents are noncommutative, i.e., they are finite lists of sequents in contrast to other hypersequent approaches using sets or multisets. Such a system in [10] was proved to be cut-free HC formalization of respective logics by means of semantical argument. In (...) this article we present an equivalent variant of this calculus for which a constructive syntactical proof of cut elimination is provided. (shrink)

This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ + (for a strongly inaccessible cardinal λ).

In 1934 Stanisław Jaśkowski published his groundbreaking work on natural deduction. At the same year Gerhard Gentzen also published a work on the same topic. We aim at presenting of Jaśkowski’s system and provide a comparison with Gentzen’s approach. We also try to outline the influence of Jaśkowski’s approach on the later development of natural deduction systems.

Among issues considered in contemporary ethics, apart from concepts such as good, value and justice, there is also the concept of care, discussed extensively in feminism. The article presents and analyses this ethical concept. It shows some problems with the translation of the English word ‘care’ into the Polish equivalent ‘troska’. The focus here, however, is mainly on the way of understanding the concept of care among feminist ethicists, such as Virginia Held, Nel Noddings, Joan Tronto, Diemut Bubeck, and Sara (...) Ruddick. For all of them, care is a relation, though they differ in their account of the specificity and meaning of this relation. (shrink)

This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat application of hybrid logics (...) may remarkably improve the situation inmodal proof theory. (shrink)

In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but (...) with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form. (shrink)

This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.

The epidemiological situation resulting from the SARS-CoV-2 pandemic caused the Polish universities to fully switch to distance education in March 2020. Medical e-learning has not yet been broadly implemented into the education process. Therefore, examples of successful e-learning implementations or the organization of the process of medical e-learning offer a valuable source of knowledge today, which is needed immediately. The article presents e-learning practices at the Polish medical universities during the SARS-CoV-2 epidemic during the period from March to September 2020, (...) covering seven universities in Poland that offer medical and health studies. The organization and implementation of e-learning classes is presented, including knowledge evaluation practices, providing example decisions issued by university rectors, on which the teaching process was based. A detailed presentation of the schools’ organizational units or workgroups that played an important role in the process of coordination of measures supporting e-education is also included. The article also presents a description of the software applications, utilities, and services used at the schools in the course of the process of online education. Below are some examples of specific such implementations in selected university courses. (shrink)

This is a summary of a talk delivered at the Winter School of Logic held in Rabka, 24.02 – 04.03.1986 by the Department of Logic of the Jagiellonian University. We wish to announce here several results on embeddability of quotient algebras of certain kind into algebras of some varieties related to the class of Heyting algebras. A “by product” is the deduction theorem for a large family of intermediate consequence operations.

Internet increasingly serves not only to communication between it’s users. The emergence of Web 2.0 platforms which are peculiar to publication of various content allowed to release of activity and commitment of millions of people worldwide. Study contains sociological analysis of already existing visual materials dealing with old age, which were made by users of the deviantART.com. It’s one of the longest established online community bringing together artists from around the world. Article draws attention to the multiplicity of contemporary forms (...) of presentation of old age and difficulties and methodological guidelines related to the study of resources from new media. ** Sieć internet coraz czȩściej służy nie tylko komunikacji miȩdzy jej użytkownikami. Pojawienie siȩ serwisów Web 2.0 stanowi¸a}cych swoiste platformy do publikacji najrozmaitszych treści pozwoliło na uwolnienie pokładów aktywności i zaangażowania milionów ludzi na świecie. Praca traktuje o próbie socjologicznej analizy wizualnych materiałów zastanych traktuj¸a}cych o starości, które zostały udostȩpnione publicznie przez osoby korzystaj¸a}ce z witryny deviantART.com. Jest to jedna z najdłużej funkcjonuj¸a}cych społeczności internetowych zrzeszaj¸acych artystów z całego świata. Artykuł zwraca uwagȩ na wielość współczesnych form prezentacji starości oraz trudności i wskazówki metodologiczne zwi¸azane z badaniem zasobów nowych mediów. (shrink)

The paper presents a comparison of two generalised sequent calculi for temporal logics. In both cases the main technical solution is the multiplication of the sorts of sequents and, additionally, the application of some kind of labelling to formulae. The first approach was proposed by Kaziemierz Trzęsicki at the 1980s. The second, called Multiple Sequent Calculus (MSC), was proposed in the beginning of the present century. Both approaches are examples of the family of multisequent calculi.

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)

In this article, an analysis was made of what’s new in the debate on the condition of the contemporary political community brought up by the discussion about the relationship between care and justice. The author introduces the category of care in philosophy and its understanding and with particular emphasis on the views of Virginia Held. He analyzes the importance of a relationship of care as the foundation for the proper functioning of the socio-political community and criticism of the idea of (...) a social contract undertaken by representatives of the ethics of care. Critically, he presents the consequences of the assumptions of the civic community accepted by Held. (shrink)