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 Research Topic explores the ninth Sustainable Development Goal (SDG), which aims to build resilient infrastructure, promote inclusive and sustainable industrialization, and foster innovation, particularly in the context of post-COVID-19 pandemic recovery. The pandemic significantly impacted the manufacturing sector, leading to a global production drop, job losses, and disrupted supply chains, with less technology-intensive industries taking longer to regain ground. Despite these challenges, the United Nations highlights opportunities to enhance industrialization and technology distribution, emphasizing, among other things, the need to (...) expand mobile broadband networks, increase research and development investment, and improve rural road connectivity. (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)

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 Research Topic addresses the eleventh Sustainable Development Goal (SDG), which is to “make cities and human settlements inclusive, safe, resilient and sustainable.” Several individual targets and indicators measure progress toward this goal. Researchers study, among others, urban inclusion, the influence of urban policy on socioeconomic disparities, and gentrification. This Research Topic primarily addresses the challenges and complexities of sustainable urban planning and development concerning decent work, economic growth, and associated crises due to their significant impact on urban living.

This Research Topic focuses on the first Sustainable Development Goal (SDG) by the UN, which aims to “end poverty in all its forms everywhere.” Progress toward this goal is evaluated through various targets and indicators. The most recent SDG progress report highlighted how poverty reduction has significantly slowed and worsened, mainly due to the COVID-19 pandemic (United Nations, 2024). This unprecedented emergency has particularly affected informal workers, young people, and women. With the goal of eradicating poverty by 2030 currently off (...) track, intensified action is crucial. Moreover, amid a growing climate crisis, significant efforts are needed to bring the 2030 targets within reach. This Research Topic examines SDG1 from a sociological perspective, focusing on its framing, geographic adaptations, stakeholder involvement, and the influence of social mobility and stratification studies, especially in the context of the challenges of the post-COVID-19 pandemic. (shrink)

This Research Topic explores Sustainable Development Goal (SDG) eight, which is to “promote sustained, inclusive, and sustainable economic growth, full and productive employment, and decent work for all.” It highlights the COVID-19 pandemic’s severe impact and triggered global economic recession, worsened gender pay gaps, increased undeclared employment, and significantly raised unemployment (United Nations, 2024). From a sociology-specific perspective, this Research Topic examines the global and local implementation of SDG8, its adaptation to different geographical contexts, stakeholder involvement, and issues related to (...) decent work conditions worldwide. (shrink)

THE METAPHOR OF THE “LINE OF RESISTANCE” AND THE LAW OF CONTRADICTION This essay presents the “idea of God” as a metaphor of the line of resistance – as used in Umberto Eco’s writings. This metaphor is understood in the sense of pure negativity. The pure negative, the pure “not,” is very different from the God of revealed religion. The idea of God is not a proof of the existence of God, but only a device of elocution – in order (...) to give an appropriate name to the thing. Such interpretation is possible thanks to imputing to this idea the law of contradiction. Keywords: THE LAW OF CONTRADICTION, UMBERTO ECO, METAPHOR OF THE LINE OF RESISTANCE, IDEA OF GOD. (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)

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)

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)

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)

The article is trying to present reception not as such, but as a problem which reception is for historian of philosophy. It is clearly visible in the process of formation on neo-Kantianism, which programme distance themselves from any orthodoxy. As a consequence there is a need of treating a neo-philosophy as original and one-off phenomenon and not a renewal of old philosophy. As an example can serve a dead dog motif present at Hegel and Jacobi related to Spinoza.

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 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)

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.

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)

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)

Hypersequent calculi can formalize various non-classical logics. In [9] we presented a non-commutative variant of HC for the weakest temporal logic of linear frames Kt4.3 and some its extensions for dense and serial flow of time. The system was proved to be cut-free HC formalization of respective temporal logics by means of Schütte/Hintikka-style semantical argument using models built from saturated hypersequents. In this paper we present a variant of this calculus for Kt4.3 with a constructive syntactical proof of cut elimination.

The paper studies extensions of t-normal logics S0.5o and S0.5 obtained by means of some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.