Complex systems are difficult to manage, operate and maintain. This is why we see teams of highly specialised engineers in industries such as aerospace, nuclear and subsurface. Condition based monitoring is also employed to maximise the efficiency of extensive maintenance programmes instead of using periodic maintenance. A level of automation is often required in such complex engineering platforms in order to effectively and safely manage them. Advances in Artificial Intelligence related technologies have offered greater levels of automation but this potentially (...) pivots the weight of decision making away from the operator to the machine. Implementing AI or complex algorithms into a platform can mean that the Operators’ control over the system is diminished or removed altogether. For example, in the Boeing 737 Air Max Disaster, AI had been added to a platform and removed the operators’ control of the system. This meant that the operator could not then move outside the extremely reserved, algorithm defined, “envelope” of operation. This paper analyses the challenges of AI driven condition based monitoring where there is a potential to see similar consequences to those seen in control engineering. As the future of society becomes more about algorithm driven technology, it is prudent to ask, not only whether we should implement AI into complex systems, but how this can be achieved ethically and safely in order to reduce risk to life. (shrink)

Many of the reasons offered for outsourcing security involve costs and benefits – a consequentialist way of reasoning. Thus, I will explore a consequentialist argument against the use of private security contractors (PSCs) in counterinsurgencies. Discussing the benefits and costs of employing PSCs in these kinds of operations will demonstrate that the hiring of PSCs in many cases (perhaps in most) is consequentially unsound. More precisely, the overall negative consequences of hiring PSCs during counterinsurgencies should preclude their use unless in (...) extreme emergencies. Defenders of the use of PSCs readily point to their financial benefits and expected increase in efficiency as the starting point for their argumentation. On my account, if the benefits really do outweigh the foreseeable and expected costs, then hiring PSCs may, in that case, be a morally viable option. However, I contend that, unless we institute broad contractual control and oversight reform, unless we truly understand the costs and benefits, we should have a standing, prima facie prohibition against employing PSCs in counterinsurgencies. (shrink)

The current armed conflict in Afghanistan (briefly, the Afghan conflict) is viewed through the lens of a just war theory. In particular, the question stated by the title is explored by means of a generalized just cause principle. For brevity, empirical, practical, and legal issues about the Afghan conflict are mostly set aside. Hence a definite answer to the question is not proposed. Instead, the main aim is to clarify the question. Specifically, the question is amplified, by distinguishing putative just (...) causes of countering terrorism, countering an insurgency, and countering extreme violations of basic human rights. Apparently, however, U.S. government officials (e.g., President Barack Obama) and U.S. military commanders (e.g., General Stanley McChrystal) have mixed goals or motives concerning current U.S.military operations in Afghanistan. Nonetheless, from the standpoint of a just war theory, it is instructive to analytically distinguish these putative just causes, and to consider them separately. Additionally, it is instructive to consider how they might be combined. Consequently, a fourth putative just cause is considered: countering violent spoilers of peacebuilding. (This paper was completed on March 31, 2010.). (shrink)

. Dzik [2] gives a direct proof of the axiom of choice from the generalized Lindenbaum extension theorem LET. The converse is part of every decent logical education. Inspection of Dzik’s proof shows that its premise let attributes a very special version of the Lindenbaum extension property to a very special class of deductive systems, here called Dzik systems. The problem therefore arises of giving a direct proof, not using the axiom of choice, of the conditional . A partial solution (...) is provided. (shrink)

The actual introduction of a non-reflexive and non-idempotent q -consequence gave birth to the concept of logical three-valuedness based on the idea of noncomplementary categories of rejection and acceptance. A q -consequence may not have bivalent description, the property claimed by Suszko’s Thesis on logical two-valuedness, ( ST ), of structural logics, i.e. structural consequence operations. Recall that ( ST ) shifts logical values over the set of matrix values and it refers to the division of matrix (...) universe into two subsets of designated and undesignated elements using their characteristic functions as logical valuations, cf. [4] The extension of the idea operates with three-valued function, with the third value ascribed to those elements of the matrix which are neither rejected nor accepted. Accordingly, the logical three-valuedness departs naturally from the division of the matrix universe into three subsets and the ( ST ) counterpart says that any inference based on a structural q -consequence may have a bivalent or a three-valued description. After a short presentation of the three-valued inferential framework, we discuss a solution for further exploration of the idea leading to logical n -valuedness for n > 3. Apparently, the first step in that direction is easy and it consists of a division of the matrix universe into more than three subsets. The next move, i.e. a definition of a matrix consequence-like relation being neither a consequence nor a q -consequence, seems extremely difficult. Therefore, here we consider only finite linear matrices with one-argument functions “labelling” respective matrix subsets. By means of these functions it is possible to represent a q-consequence as a “partial” Tarski’s consequence and, ultimately, to define a logically more-valued consequence-like relation. We believe, that the present partial proposal deserves an attention by itself but also that it may lead to a general approach to logically many-valued inference. (shrink)

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)

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.

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)

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)

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.

. 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)

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.

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)

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 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.

The “extreme consequence” is a very common pattern in advertising messages that presents an odd, even negative, situation resulting from the use of the advertised product as a good reason to buy it. By analyzing selected advertisements employing this pattern using the conceptual integration theory and the Argumentum Model of Topics, we aim to understand how “extreme consequence” works at the rhetorical and argumentative levels. The analyses allow us to detect the typical, generic, cognitive, and argumentative structure underlying (...) the pattern and to identify the rhetorical and argumentative role played by its main components, namely exaggeration and cause-effect relation. (shrink)

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 (...) operations. (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)

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)

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.

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)

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)

This chapter explores the consequence of taking Rawls' concerns about the strains of commitment to their logical extreme. If there is no external enforcement at all, so that all agreements must be self-policing, it is shown that deals reached in the original position will generate an egalitarian outcome, as Rawls would wish. The conclusions are broadly consistent with the class of laboratory results that psychologists refer to as “modern equity theory”. The concept of an empathy equilibrium is used to (...) predict the standard of interpersonal comparison needed to operate an egalitarian norm that will evolve in the medium run. The manner in which this standard should be expected to respond to need, effort, ability, and status is then explored. (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.

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.

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 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.

In lieu of an abstract, here is a brief excerpt of the content:On Reviewing: A Response to Mary Ann StankiewiczRalph A. Smith, Professor EmeritusI very much appreciate the positive comments made by Mary Ann Stankiewicz in her review published in Studies in Art Education of my Readings in Discipline-Based Art Education: A Literature of Educational Reform.1 I was gratified to read that she believes the volume is a comprehensive and valuable guide that all art educators should own as a reference (...) source for the intellectual history of American art education in the late-twentieth century. Stankiewicz further notes my steadfastness in holding to a vision ofaesthetic education that is firmly rooted in the humanities and my forthrightness in acknowledging that a different choice of selections might well convey a somewhat different picture of Discipline-Based Art Education (DBAE). Between encomia, however, Stankiewicz raises questions about my editorial politics (that is, opportunities editors have to make selections they think are important) and my views about art education.The format of Stankiewicz's review was patterned after an essay in the volume by Frances Schoonmaker who discusses the professional preparation of teachers in terms of autobiography, school contexts, and scholarship. Accordingly, Stankiewicz recalls in some detail her own extensive participation in the Getty's educational venture in art education. And instead of referring to the Introduction's discussion of historical antecedents of DBAE she provides her own account of events that were contemporaneous with Getty's period of operation and refers to some currents of contemporary thinking. In other words, she does not give the kind of space to the book's contents that reviewers usually do.2 This prompted me to recall some material from the book's Introduction, which is followed by a sketch of the DBAE literature project that furnished the impetus for the volume and rejoinders to some of Stankiewicz's concerns.DBAE RememberedThe Getty Center for Education in the Arts (later renamed the Getty Education Institute for the Arts and eventually discontinued) flourished mainly in the 1980s and 1990s and proceeded under the banner of DBAE. The Getty's notion of DBAE supported a major trend that had been growing in the field since the mid-1950s. In this respect the Getty initiative was neither novel nor revolutionary. Yet by correcting an error of certain reform movements, namely those whose tendency was to bypass professionals in the field, it did constitute a significant venture. Getty officers perceived the field to be [End Page 93] moving in the direction of strengthening the content of art education with additional content that was believed requisite for an intelligent and sensitive engagement with works of art. In effect the Getty position argued that a well-developed sense of art is composed not just of the rudiments of artistic creation art but also those of a number of other relevant disciplines, for example the interrelated disciplines of art making, art history, art criticism, and aesthetics (usually understood as the philosophy of art). It was acknowledged that these were not the only disciplines relevant to art education, but they were considered to be basic. Nor was it believed that these disciplines should be taught as separate subjects; rather, they were meant to suggest content and useful modes of inquiry. As Stankiewicz notes, DBAE endorsed both the substantive and procedural dimensions of the cognitive revolution that was occurring in thinking about mind and learning. Indeed, mind building emerged as one of the major themes in the theory underlying the Getty approach.3Not surprisingly, the Getty approach had its critics. As pointed out in my "Afterthoughts,"the Getty initiative was contemporaneous with the increasing politicization of cultural and educational life.4 The critical literature produced in this climate — subscribing variously to postmodernism, multiculturalism, feminism, cultural studies, social reconstructionism, and deconstruction — was often by turns extreme, dense, and intimidating. It further tended to be skeptical of Western cultural values and traditions. I think it is fair to say that many in the field of art education were ill prepared to digest these writings or to be alert to some of their potential negative consequences. I mention just a few of these.For example, although developing an appreciation for hitherto unfamiliar cultures is... (shrink)

In contemporary academic, political, and media discourse, terrorism is typically portrayed as an existential threat to lives and states, a threat driven by religious extremists who seek the destruction of Western civilization and who are immune to reason and negotiation. In many countries, including the US, the UK, and Australia, this existential threat narrative of terrorism has been used to justify sweeping counterterrorism legislation, as well as military operations and even the use of tactics such as torture and indefinite detention. (...) In this chapter I outline the components of the existential threat narrative, and explain how critical terrorism scholars have critiqued this narrative on two main grounds: that it is based on false empirical claims about the nature, scale, and motivations of modern non-state terrorism, and that counterterrorism policies and practices based on this narrative have had extremely destructive consequences for individuals, communities, and states—in some cases, causing far more destruction than terrorism itself. In the final section I offer some suggestions for the direction of future terrorism research in light of these critiques of the existential threat narrative. (shrink)

Origin of life models based on “energized assemblages of building blocks” are untenable in principle. This is fundamentally a consequence of the fact that any living system is in a physical state that is extremely far from equilibrium, a condition it must itself build and sustain. This in turn requires that it carries out all of its molecular transformations–obligatorily those that convert, and thereby create, disequilibria–using case‐specific mechanochemical macromolecular machines. Mass‐action solution chemistry is quite unable to do this. We (...) argue in Part 2 of this series that this inherent dependence of life on disequilibria‐converting macromolecular machines is also an obligatory requirement for life at its emergence. Therefore, life must have been launched by the operation of abiotic macromolecular machines driven by abiotic, but specifically “life‐like”, disequilibria, coopted from mineral precipitates that are chemically and physically active. Models grounded in “chemistry‐in‐a‐bag” ideas, however energized, should not be considered. (shrink)

In this paper we discuss two hybrid languages, ℒ and ℒ, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using A and ↓ to bind special state variables.This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea of (...) canonical models with the classical idea of witnessed maximal consistent sets. The languages ℒ and ℒ provide us with two extreme examples of the issues involved. In the case of ℒ, we can combine these ideas relatively straightforwardly with the aid of analogs of the Barcan axioms coupled with a modal theory of labeling. In the case of ℒ, on the other hand, although we can still formulate a theory of labeling, the Barcan analogs are not valid. We show how to overcome this difficulty by using COV*, an infinite collection of additional rules of proof which has been used in a number of investigations of extended modal logic. (shrink)