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 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)

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)

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)

Resumen El objetivo del presente artículo es analizar en la historia del español dos tipos de fórmulas de saludo, entendidas como unidades discursivas propias del acto de habla expresivo que sirven para abrir el canal comunicativo de las relaciones sociales. A través de la búsqueda sistemática en textos del CORDE de hasta finales del siglo XIX, intentaremos hallar (i) los factores sociopragmáticos que desempeñan el papel más importante en cada tipo de saludo, (ii) el origen paradigmático de cada fórmula, (iii) (...) su distribución sociocultural y las preferencias discursivas e informativas, y (iv) su nivel de predominio en determinadas épocas. (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)

The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...) independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)

This is a study about man who is a part of the world of physical events, including actions. As a bunch of actions which are conditioned by beliefs and other attitudes, man co-creates communities which emerge and vanish along time. While generating and undergoing changes man is potentially a dynamic and flexible creature who at least partially manages relations with the world, including other men. This study is of an interdisciplinary nature, where the author merges philosophy and cultural anthropology with (...) insight into sociology and communication studies. At the same time, the author takes an anti-essentialist position, where the study is a hypothetical construct. While doing this, the author assembles a particular vocabulary, where action, belief and community are addressed by communication, culture, thickness and the like concepts. (shrink)

We present a detailed proof of the admissibility of cut in sequent calculus for some congruent modal logics. The result was announced much earlier during the Trends in Logic Conference, Toruń 2006 and the proof for monotonic modal logics was provided already in Indrzejczak [5]. Also some tableau and natural deduction formalizations presented in Indrzejczak [6] and Indrzejczak [7] were based on this result but the proof itself was not published so far. In this paper we are going to fill (...) this gap. The delay was partly due to the fact that the author from time to time was trying to improve the result and extend it to some additional logics by testing other methods of proving cut elimination. Unfortunately all these attempts failed and cut elimination holds only for these logics which were proved to satisfy this property already in 2005. (shrink)

The status of the equality predicate as a logical constant is problematic. In the paper we look at the problem from the proof-theoretic standpoint and survey several ways of treating equality in formal systems of different sorts. In particular, we focus on the framework of sequent calculus and examine equality in the light of criteria of logicality proposed by Hacking and Došen. Both attempts were formulated in terms of sequent calculus rules, although in the case of Došen it has a (...) nonstandard character. It will be shown that equality can be characterised in a way which satisfies Došen’s criteria of logicality. In the case of Hacking’s approach the fully satisfying result can be obtained only for languages with a nonempty, finite set of predicate constants other than equality. Otherwise, cut elimination theorem fails to hold. (shrink)

The presented Research Topic explores the potential of citizen science to contribute to the development of social innovations. It sets the ground for analysis of mutual relations between two strong and embedded in the literature concepts: citizen science and social innovation. Simultaneously, the collection opens a discussion on how these two ideas are intertwined, what are the significant barriers, and the need to use citizen science for social innovation.

The problem of precise characterisation of traditional forms of reasoning applied in mathematics was independently investigated and successfully resolved by Jaśkowski and Gentzen in 1934. However, there are traces of earlier interests in this field exhibited by the members of the Lvov-Warsaw School. We focus on the results obtained by Jaśkowski and Leśniewski. Jaśkowski provided the first formal system of natural deduction in 1926. Leśniewski also demonstrated in some of his papers how to construct proofs in accordance with intuitively correct (...) principles. (shrink)

We present a uniform characterisation of three-valued logics by means of a bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as the weakest kind of system in the rich family of generalised SC operating on items being some collections of ordinary sequents, like hypersequent and nested sequent calculi. It seems that for many non-classical logics, including some many-valued, paraconsistent and modal logics, (...) the reasonably modest generalisation of standard SC offered by BSC is sufficient. In this paper, we examine a variety of three-valued logics and show how they can be formalised in the framework of BSC. We present a constructive syntactic proof that these systems are cut-free, satisfy the subformula property, and allow one to prove the interpolation theorem in many cases. (shrink)

We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD exploited here is essentially based on the approach of Russell, but with descriptions treated as genuine terms. However, the reductionist aspect of the Russellian approach is retained in several ways. Moreover, a special form of tense definite descriptions is formally developed. A constructive proof (...) of the interpolation theorem for this calculus is given, which is an extension of the result provided by Blackburn and Marx. (shrink)

Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus T H(@,E,D, ♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality (...) and the inverse modality as well as the corresponding sequent calculus S H(@,E,D, ♦ −) . They not only uniformly cover relatively wide range of various hybrid logics but they are also conceptually simple and enable effective search for a minimal model for a satisfiable formula. The main novelty is the exploitation of the unrestricted blocking mechanism introduced as an explicit, sound tableau rule. (shrink)

The central - and philosophically important - question connected with selectivity is the question of the nature of this phenomenon as a specific feature of human cognitive system. It is revealed in acts of two types. Acts of the first type are selective extraction of concrete as well as symbolic informations derived from the external world, and contained in sensoric representations. Acts of the second type are selective actualization of informations preserved in an individual permanent memory. The hypothesis of existing (...) general mental disposition common to acts of both the types is very attractive. The author analyzes some psychological (empirical) and philosophical aspects of these problems. (shrink)

The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful (...) marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions. (shrink)

We discuss the methods for providing sequent calculi for Suszko’s basic non-Fregean Logic with sentential identity SCI. After examination of possible strategies and already proposed systems we focus on the new calculus and its modification. It does not satisfy full cut elimination but a slightly generalised form of the subformula property holds for it. It is also standard in the sense of satisfying several conditions on rules formulated by Gentzen and his followers. We examine also the problem of providing a (...) constructive proof of the interpolation theorem in the setting of this sequent calculus. (shrink)

The aim of this paper is to investigate the causes influencing the length and duration of online media discourse, which may also mean its “quality” or a kind of “attractiveness”. This goal sets out the issues and basic research questions related to these causes. What causes some discourses take a long time and others end as soon as they begin? What makes one discourse attract the attention of other participants in the discussion, and what causes less interest in the proposed (...) topics? In order to obtain answers to the above questions we study the structure of the text, stylistics, topics of discourses and social interaction of forum participants. (shrink)

The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.

SummaryStarting from late Classical-early Hellenistic age a series of witty, lighthearted and irreverent funerary verse-inscriptions aiming to produce some effect of amusement or laughter appeared on a number of monuments, reaching their apogee during Greek-Roman era. Most of them originated in Asia Minor and Rome. Some earliest examples were related to widespread hedonistic exhortations on tombs. Their later ramifications, consisting of ironical or playful expressions, amusing puns and instances of black humour, were written in a more satirical vein, except with (...) inscriptions dedicated for animals that were rife with sentimental motifs. Remarkably diverse as they were, such verse-inscriptions cannot be defined in terms of a distinctly separate, continuous tradition, but they shared some common features. Lacking – for the most part – conventional and formulaic elements, they struck us as heavily individualised, which sets them apart from the mainstream tradition of funerary poetry. This in turn might shed some light on social standing or/and mentality of individuals who opted for such expressive ways of remembering the dead. (shrink)

The subject of this paper is the controversy between cognitivist philosophy and phenomenology concerning the nature of emotions. This article has a limited scope restricted to the domain of the aesthetic emotions usually dependent on the works of art and literature. The author raises the criticism against the cognitivist stance, this criticism based chiefly on the principles of Max Scheler's phenomenology of emotions.

Philosophy in this text is considered under the model of mise en abyme, which is used in particular in the art of fiction narration. A novel about the process of novel writing is an example of mise en abyme. A film about movie directing is also an example of mise en abyme. A painting showing the artist working on the work of art also has features of mise en abyme. Likewise, mise en abyme philosophy is philosophy that discusses how philosophy (...) is created. Philosophy in such a shape is no longer understood as an endless space “inhabited” by situations, concepts, assertions, philosophical theses which are, however, perceived as if from the inside of that space; by contrast, it starts to be perceived from the outside, from the perspective of activities that form its frame, that frame it. For example, two such framing activities are considered – refining situations which is responsible for the “splendor of truth” that shines forth in them and defying the passage of time when constructing situations which is decisive for their isolation from the stream of life. Philosophy that notices its own frame is anchored in the foundations of everyday life which is something irrefutable in relation to the very inside of philosophy; as a consequence, the idea of epistemological foundationalism may be renewed and recovered for philosophy. (shrink)

Social innovations are usually understood as new ideas, initiatives, or solutions that make it possible to meet the challenges of societies in fields such as social security, education, employment, culture, health, environment, housing, and economic development. On the one hand, many citizen science activities serve to achieve scientific as well as social and educational goals. Thus, these actions are opening an arena for introducing social innovations. On the other hand, some social innovations are further developed, adapted, or altered after the (...) involvement of scientist-supervised citizens in research and with the use of the citizen science tools and methods such as action research, crowdsourcing, and community-based participatory research. Such approaches are increasingly recognized as crucial for gathering data, addressing community needs, and creating engagement and cooperation between citizens and professional scientists. However, there are also various barriers to both citizen science and social innovation. For example, management, quality and protection of data, funding difficulties, non-recognition of citizens’ contributions, and limited inclusion of innovative research approaches in public policies. In this volume, we open theoretical as well as empirically-based discussion, including examples, practices, and case studies of at least three types of relations between citizen science and social innovation: domination of the citizen science features over social innovation aspects; domination of the social innovation features over the citizen science aspects; and the ways to achieve balance and integration between the social innovation and citizen science features. Each of these relationships highlights factors that influence the development of the main scales of sustainability of innovations in the practice. These innovations are contributing to a new paradigm of learning and sharing knowledge as well as interactions and socio-psychological development of participants. Also, there are factors that influence the development of platforms, ecosystems, and sustainability of innovations such as broad use of the information and communications technologies including robotics and automation; emerging healthcare and health promotion models; advancements in the development and governance of smart, green, inclusive and age-friendly cities and communities; new online learning centers; agri-food, cohousing or mobility platforms; and engagement of citizens into co-creation or co-production of services delivered by public, private, non-governmental organizations as well as non-formal entities. (shrink)

The following discussion of the situation in the Soviet Union as perceived by the author in two visits, in March?April 1991 and September 1991, was not written in the vain hope of presenting an up?to?date account of the changing events there. Rather, it is an attempt to begin to identify elements of continuity as well as change in the transition to postcommunism, and to assess both what led to the attempted coup and its defeat and factors bearing on the postcommunist (...) future. (shrink)

We consider structures of the form, where Φ and Ψ are non-empty sets and is a relation whose domain is Ψ. In particular, by using a special kind of a diagonal argument, we prove that if Φ is a denumerable recursive set, Ψ is a denumerable r.e. set, and R is an r.e. relation, then there exists an infinite family of infinite recursive subsets of Φ which are not R -images of elements of Ψ. The proof is a very elementary (...) one, without any reference even to e.g. the -theorem. Some consequences of the main result are also discussed. (shrink)