In the paper, the authors discuss two kinds of consequence operations characterized axiomatically. The first one are consequence operations of the type Cn + that, in the intuitive sense, are infallible operations, always leading from accepted (true) sentences of a deductive system to accepted (true) sentences of the deductive system (see Tarski in Monatshefte für Mathematik und Physik 37:361–404, 1930, Comptes Rendus des Séances De la Société des Sciences et des Lettres de Varsovie 23:22–29, 1930; (...) Pogorzelski and Słupecki in Stud Logic 9:163–176, 1960, Stud Logic 10:77–95, 1960). The second kind are dual consequence operations of the type Cn − that can be regarded as anti-infallible operations leading from non-accepted (rejected, false) sentences of a deductive system to non-accepted (rejected, false) sentences of the system (see Słupecki in Funkcja Łukasiewicza, 33–40, 1959; Wybraniec-Skardowska in Teoria zdań odrzuconych, 5–131, Zeszyty Naukowe Wyższej Szkoły Inżynierskiej w Opolu, Seria Matematyka 4(81):35–61, 1983, Ann Pure Appl Logic 127:243–266, 2004, in On the notion and function of rejected propositions, 179–202, 2005). The operations of the types Cn + and Cn − can be ordinary finitistic consequence operations or unit consequence operations. A deductive system can be characterized in two ways by the following triple: $$\begin{array}{ll}{\rm by\,the\,triple}:\hspace{1.4cm} (+ , -)\hspace{0,6cm} \\ {\rm or\,by\,the\,triple}:\hspace{1.0cm} (-, +)\hspace{0,6cm} .\end{array}$$ We compare axiom systems for operations of the types Cn + and Cn −, give some methodological properties of deductive systems defined by means of these operations (e.g. consistency, completeness, decidability in Łukasiewicz’s sense), as well as formulate different metatheorems concerning them. (shrink)

BackgroundNon-technical skills are cognitive and interpersonal skills underpinning technical proficiency. Ethical values and respect for human dignity make operating room nurses responsible for nursing decisions that are clinically and technically sound and morally appropriate.AimTo learn what ethical issues operating room nurses perceive as important regarding non-technical skills.Research designQualitative individual in-depth interviews were conducted. The interviews were analysed using Braun and Clarke’s six phases for thematic analysis.Participants and research contextEleven experienced perioperative/operating room nurses working in an operating unit at a (...) Norwegian university hospital.Ethical considerationsApproval was given by The Norwegian Social Science Data Service in care of the hospital’s Data Protection Officer.FindingsThree main themes were found: respect and care for the patient, making the patient feel safe, and respect within the perioperative team. These features or themes, which incorporate collaboration and communication, are closely connected to patient safety.DiscussionDefending the patient’s dignity is part of caring for and respecting the patient. The manner in which the operating room team collaborates is important for the patient to feel safe and secure. Poor teamwork may have dire consequences. Reciprocal respect within the team includes respect for each other’s tasks and responsibilities and to talk to one another in a friendly manner.ConclusionBeing respectful and contributing to a caring atmosphere are central ethical skills in the operating room. To patients, harmonious teamwork translates into a feeling of safety and being cared for. The nurses see respect and patient safety, and respect and reciprocal politeness among the members of the perioperative team as central ethical non-technical skills. Lack of respect influences the team negatively and is detrimental for patient safety. Good communication is an important safety measure during surgery and creates a feeling of good ‘flow’ within the operating room team. (shrink)

The United States Government does not mandate that US based firms follow US social and environmental law in foreign markets. However, because many developing countries do not have strong human rights, labor, and environmental laws, many multinationals have adopted voluntary corporate responsibility initiatives to self-regulate their overseas social and environmental practices. This article argues that voluntary actions, while important, are insufficient to address the magnitude of problems companies confront as they operate in developing countries where governance is often inadequate. The (...) United States can do more to ensure that its multinationals act responsibly everywhere they operate. First, policymakers should define the social and environmental responsibilities of global companies. They must consistently make their expectations for global business clear – and underscore that this objective can often be accomplished without mandates. Second, the US should closely examine the policies that undermine global Corporate Social Responsibility (CSR) and address the many conflicting signals sent by policymakers. Third, the President should make the US government a CSR model by examining how to use its purchasing power to promote human rights. Finally, the US government should require pension funds to report on the social and environmental consequences of their investments. In these ways, Americans can mind our business – and thus make sure that US based firms do not undermine social and environmental progress when they operate in the developing world. (shrink)

The COVID-19 pandemic has upended in-person public education across the United States, a critical infrastructure of care that parents—especially mothers—depend on to work. To understand the nature and magnitude of school closures across states, we collected detailed primary data—the Elementary School Operating Status database —to measure the percentage of school districts offering in-person, remote, and hybrid instruction models for elementary schools by state in September 2020. We link these data to the Current Population Survey to evaluate the association between school (...) reopening and parents’ labor force participation rates, comparing 2020 labor force participation rates to those observed prepandemic in 2019. We find that, across states, the maternal labor force participation rate fell to a greater extent than that of fathers. In 2019, mothers’ rate of labor force participation was about 18 percentage points lower than fathers’. By 2020, this gap grew by 5 percentage points in states where schools offered primarily remote instruction. We show that schools are a vital source of care for young children, and that without in-person instruction, mothers have been sidelined from the labor force. The longer these conditions remain in place, the more difficult it may be for mothers to fully recover from prolonged spells of nonemployment, resulting in reduced occupational opportunities and lifetime earnings. (shrink)

Two major clarifications have greatly abetted the understanding and fruitful expansion of the theory of natural selection in recent years: the acknowledgment that interactors, not replicators, constitute the causal unit of selection; and the recognition that interactors are Darwinian individuals, and that such individuals exist with potency at several levels of organization (genes, organisms, demes, and species in particular), thus engendering a rich hierarchical theory of selection in contrast with Darwin’s own emphasis on the organismic level. But a piece (...) of the argument has been missing, and individuals at levels distinct from organisms have been denied potency (although granted existence within the undeniable logic of the theory), because they do not achieve individuality with the same devices used by organisms and therefore seem weak by comparison. We show here that different features define Darwinian individuality across scales of size and time. In particular, species-individuals may develop few emergent features as direct adaptations. The interactor approach works with emergent fitnesses, not with emergent features; and species, as a consequence of their different mechanism for achieving individuality (reproductive exclusivity among subparts, that is, among organisms), express many effects from other levels. Organisms, by contrast, suppress upwardly cascading effects, because the organismic style of individuality (by functional integration of subparts) does not permit much competition or differential reproduction of parts from within. Species do not suppress the operation of lower levels; such effects therefore become available as exaptations conferring emergent fitness—a primary source of the different strength that species achieve as effective Darwinian individuals in evolution. (shrink)

Four consequence operators based on hypergraph satisfiability are defined. Their properties are explored and interconnections are displayed. Finally their relation to the case of the Classical Propositional Calculus is shown.

Standard quantum mechanics unquestionably violates the separability principle that classical physics (be it point-like analytic, statistical, or field-theoretic) accustomed us to consider as valid. In this paper, quantum nonseparability is viewed as a consequence of the Hilbert-space quantum mechanical formalism, avoiding thus any direct recourse to the ramifications of Kochen-Specker’s argument or Bell’s inequality. Depending on the mode of assignment of states to physical systems – unit state vectors versus non-idempotent density operators – we distinguish between strong/relational and (...) weak/deconstructional forms of quantum nonseparability. The origin of the latter is traced down and discussed at length, whereas its relation to the all important concept of potentiality in forming a coherent picture of the puzzling entangled interconnections among spatially separated systems is also considered. Finally, certain philosophical consequences of quantum non-separability concerning the nature of quantum objects, the question of realism in quantum mechanics, and possible limitations in revealing the actual character of physical reality in its entirety are explored. (shrink)

In the paper, there is presented the theory of logical consequence operators indexed with taboo functions. It describes the mechanisms of logical inference in the environment of forbidden sentences. This kind of processes take place in ideological discourses within which their participants create various narrative worlds (mental worlds). A peculiar feature of ideological discourses is their association with taboo structures of deduction which penalize speech acts. The development of discourse involves, among others, transforming its deduction structure towards the proliferation (...) of consequence operators and modifying penalty functions. The presented theory enables to define various processes of these transformations in the precise way. It may be used in analyses of conflicts between competing elm experts acting within a discourse. (shrink)

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Two characterizations are given of those structural consequence operations on a propositional language which can be defined via proofs from a finite number of polynomial rules.

In this paper we develop an abstract theory of adequacy. In the same way as the theory of consequence operations is a general theory of logic, this theory of adequacy is a general theory of the interactions and connections between consequence operations and its sound and complete semantics. Addition of axioms for the connectives of propositional logic to the basic axioms of consequence operations yields a unifying framework for different systems of classical propositional logic. (...) We present an abstract model-theoretical semantics based on model mappings and theory mappings. Between the classes of models and theories, i.e., the set of sentences verified by a model, it obtains a connection that is well-known within algebra as Galois correspondence. Many basic semantical properties can be derived from this observation. A sentence A is a semantical consequence of T if every model of T is also a model of A. A model mapping is adequate for a consequence operation if its semantical inference operation is identical with the consequence operation. We study how properties of an adequate model mapping reflect the properties of the consequence operation and vice versa. In particular, we show how every concept of the theory of consequence operations can be formulated semantically. (shrink)

Formalization of reasoning which accepts rules of inference leading to conclusions whose logical values are not smaller than the logical value of the “weakest” premise leads to the concept of consequence operation preserving degrees of truth. Several examples of such consequence operation have already been considered . In the present paper we give a general notion of the consequence operation preserving degrees of truth and its characterization in terms of projective generation and selfextensionality.

. We explore a connection between different ways of representing information in computer science. We show that relational databases, modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together with a lattice satisfying these axioms is then called an “information algebra”. We show that any compact consequence operator satisfying the interpolation and the deduction property induces an information algebra. Conversely, each finitary information algebra can be obtained from a consequence operator in this (...) way. Finally we show that arbitrary (not necessarily finitary) information algebras can be represented as some kind of abstract relational database called a tuple system. (shrink)

This paper is a study of similarities and differences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic.

The monograph contains three works on research on the concept of a rejected sentence. This research, conducted under the supervision of Prof. Jerzy Słupecki by U. Wybraniec-Skardowska (1) "Theory of rejected sentences" and G. Bryll (2) "Some supplements of theory of rejected sentences" and (3) "Logical relations between sentences of empirical sciences" led to the construction of a theory rejected sentences and made it possible to formalize certain issues in the methodology of empirical sciences. The concept of a rejected sentence (...) was introduced by J. Łukasiewicz in the course of his inquiry into Aristotelian Syllogistic. It was essentialy generelized by J. Słupecki who, with reference to Tarski's axiomatic theory of deductive systems (1930), gave the formal definition of the rejection function Cn' according to which a sentence y is rejected on the base of a set of sentences X iff at least one sentence which belongs to X can be deduced from the sentence y. Słupecki proved (1959) that the function Cn', which assignes to the set X the set of sentences rejected on the basis of X, is additive and satisfies the axioms of Tarski's general theory of deductive systems. Work (1) uses not only Tarski's general theory of systems but also his the so-called enlarged theory of systems (1930). It constructs a theory T of rejected sentences (propositions), which is created from Tarski's richer theory of systems by adding one axiom and a number of definitions; among them the definition of the rejection function Cn' is fundamental one. Cn' is a function which assignes to every set X of false sentences the set Cn'X whose members are exclusively false senteces. A number of theorems which describes properties of defined concepts have been proved in T. Some of them are necessary for conducting considertions of the concluding section of (1) devoted to the empirical sentences. Section 2 of (1) deals with the theory of the unit consequenses. It is characterized by an axiom from which follow all axioms of Tarski's general theory of deductive systems, additivity and the property that the unit consequence of the set X of sentences is a unit consequence only one sentence of X. An example of unit consequence is the rejection consequence Cn'. In section 3 of (1) the dual theory T' equivalent to T is presented. In T' the primitive concept is the rejection function Cn'. The fundamental axiom of T' states that Cn' is a unit consequence. The concluding section brings a few examples of applications of the definitions and theorems of T in the domain of the scientific methodology. Work (2) corresonds to J. Słupecki paper (1959) and the theory T of rejected propositions given in work (1). In this paper some suplements of the theory T are given. Work (3) is an extension of the theory of rejected propositios given in the paper (1). It is an attempt of formalization some problems of methodology of the empirical sciences which concern to such concepts as: empirical sentence, similar sentence, generalization, inductive conclusion etc. (shrink)

The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...) emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t’Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz’s seminar on mathematicallogi. (shrink)

. In this paper, the significance of using general logic-systems and finite consequence operators defined on non-organized languages is discussed. Results are established that show how properties of finite consequence operators are independent from language organization and that, in some cases, they depend only upon one simple language characteristic. For example, it is shown that there are infinitely many finite consequence operators defined on any non-organized infinite language L that cannot be generated from any finite logic-system. On (...) the other hand, it is shown that for any nonempty language L, a set map is a finite consequence operator if and only if it is defined by a general logic-system. Simple logic-system examples that determine specific consequence operator properties are given. (shrink)

The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.

Tarski’s papers, in which he examines the idea of a consequence operation Cn,divide into two groups. One of them is formed by the papers that offer an analysis of the general idea of the consequence operation. Resorting to fundamental ideas of logical semantics, Tarski explains what, in his view, it means to say that a formula a of a language L is a logical consequence Cn of a set of formulas X of that language. Under the definition (...) he proposed Cn is the strongest operation on sets of formulas of L that preserves truth under all possible interpretations of the language. In the papers belonging to the second group , the consequence operation Cn is treated as an object of abstract studies. More specifically, it is treated as an abstract unary operation defined on the power set of a set S such that the following familiar conditions are satisfied: T1.X⊆Cn)⊆Cnand T2.IfX⊂YthenCn⊂CnActually, Tarski imposed on Cn one more requirement which in more recent investigations is often omitted. It is as follows: T3.Ifα∈Cn,thenforafinitesubsetX′⊆X,α∈Cn is known as the finitaryness condition. (shrink)

In this paper we dene a concept of depth of a consequence operation which seems to have a few useful properties. To make our denition worth- while we shall show that the concept of depth leads to a strengthening of the well-known theorem of R. Wojcicki [4]. For unexplained terminology and notations we refer the reader to R. Wojcicki [5]. Algebras and matrices con- sidered in this paper are of the same similarity type indicating a sequence of nitary (...) class='Hi'>operations. (shrink)

First, we prove that the lattice of all structural strengthenings of a given strongly finite consequence operation is both atomic and coatomic, it has finitely many atoms and coatoms, each coatom is strongly finite but atoms are not of this kind — we settle this by constructing a suitable counterexample. Second, we deal with the notions of hereditary: algebraicness, strong finitisticity and finite approximability of a strongly finite consequence operation. Third, we formulate some conditions which tell us when (...) the lattice of all structural strengthenings of a given strongly finite consequence operation is finite, and subsequently we give some applications of them. (shrink)

In the present paper, we study some properties of matrices for non-structural consequence operators. These matrices were introduced in a former work (see [3]). In sections 1. and 2., general definitions and theorems are recalled; in section 3. a correspondence is studied, among our matrices and Wójcicki's ones for structural operators. In section 4. a theorem is given about operators, induced by submatrices or epimorphic images, or quotient matrices of a given one.Such matrices are used to characterize lattices of (...) non-structural consequence operators, by constructing lattices, antiisomorphic to them (see section 5.). In the last section, a sufficient condition is given for a non-structural operator to be finite. (shrink)

In this paper we investigate the relation between the axiomatization of a given logical consequence operation and axiom systems defining the class of algebras related to that consequence operation. We show examples which prove that, in general there are no natural relation between both ways of axiomatization.

Using ideas from Murskii [3], Tokarz [4] and Wroski [7] we construct some strongly finite consequence operation having 2%0 standard strengthenings. In this way we give the affirmative answer to the following question, stated in Tokarz [4]: are there strongly finite logics with the degree of maximality greater than 0?

Tarski presented his definition of consequence operator to explain the most important notions which any logical consequence concept must contemplate. A Tarski space is a pair constituted by a nonempty set and a consequence operator. This structure characterizes an almost topological space. This paper presents an algebraic view of the Tarski spaces and introduces a modal propositional logic which has as a model exactly the closed sets of a Tarski space.

Tarski presented his definition of consequence operator to explain the most important notions which any logical consequence concept must contemplate. A Tarski space is a pair constituted by a nonempty set and a consequence operator. This structure characterizes an almost topological space. This paper presents an algebraic view of the Tarski spaces and introduces a modal propositional logic which has as a model exactly the closed sets of a Tarski space. • DOI:10.5007/1808-1711.2010v14n1p47.

Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.