The role of foundation with respect to transitive closure in the Zermelo system Z has been investigated by Boffa; our aim is to explore the role of antifoundation. We start by showing the consistency of "Z antifoundation transitive closure" relative to Z (by a technique well known for ZF). Further, we introduce a "weak replacement principle" (deductible from antifoundation and transitive closure) and study the relations among these three statements in Z via interpretations. (...) Finally, we give some adaptations for ZF without infinity. (shrink)

The transitive closure of a binary relation R can be thought of as the best possible approximation of R "from above" by a transitive relation. We consider the question of approximating a relation from below by transitive relations. Our main result is that every thick relation (a relation whose complement contains no infinite chain) on a countable set has a transitive thick subrelation. This allows for a solution to a problem arising from previous work (...) by the author and Alan Taylor. We also exhibit a thick relation on an uncountable set with no transitive thick subrelation. (shrink)

Let R be a binary relation on some domain. Use R∗ for the reflexive transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is reflexive and transitive. Use R+ for the transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is transitive. Use I for the identity relation on the domain. Let n range over natural numbers. Define Rn as follows, by induction: (...) R0 := I Rn+1 := R ◦ R.. (shrink)

Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by a uniform operation of (...) class='Hi'>Transitive Closure, \tau. Given a set a, \tau produces its transitive closure \tau a. We show that the theory ESTE of (Cantini and Crosilla 2010) augmented by \tau is still conservative over Peano Arithmetic. (shrink)

This book is about the way artists generate an endless chain of substitute objects for something they can never quite find. It explores the work involved in art with a focus upon finding, gathering, and assembling charged and auratic objects on the wall beside the work. The author employs the term Das Gegenwerk or the work towards the work. This concept avoids definitive closure and expands the notion of drafting and related practices to include qualitative research methods. The multi-mode (...) transitional practices of Das Gegenwerk are devoid of any demand for a preconceived goal but instead hinge upon the provisional and indeterminate. As such, it is a far cry from the binary logic of the computer and the design cycle but is of interest to an audience engaged with both. Das Gegenwerk hinges on our capacity to respond to the outside rather than the inwardness often attributed to creative agency. A fundamental belief of the book is that by investigating and adapting the practices of expert practitioners, we can gain an understanding of high-level creativity. It is neither a recipe nor a linear or cyclic approach. Rather, artistic creation is an interweave of transitional multi-mode practices where the overriding emphasis is on the handling or habituation of transitional materials in physical place. The author addresses the urgent need to provide a balance between the promise of new technology and our capacity to both respond to and work with what the world bestows. (shrink)

Attributed to Alexander of Aphrodisias -the leading ancient commentator on Aristotle -the Quaestiones exemplify the process through which Aristotle's thought was organized and came to be interpreted as "Aristotelianism." This volume of R.W. Sharples's translation, together with his earlier translation of Quaestiones 1.1-2.15, makes the Quaestiones available in its entirety for the first time in a modern language. The Quaestiones are concerned with problems of physics and metaphysics, psychology and divine providence. Readers interested in Aristotle's psychological views will find the (...) second half of the Quaestiones particularly valuable. Ten of the problems discussed involve issues raised in Aristotle's On the Soul, including the unity of apperception and the transition from first to second actuality in the act of contemplation. An additional twelve problems relate to aspects of physical theory such as infinity, necessity, and potentiality. Quaestio 2.21 concerns divine providence and helps supplement our knowledge of Alexander's position. A study of the Quaestiones also suggests how interpretations of Aristotle were influenced by doctrines of Hellenistic philosophy. Translated first into Arabic and then into Latin, excerpts from the Quaestiones played a significant role in the transmission of ancient Greek philosophy to the medieval world. (shrink)

We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every (...) infinite cardinal κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ ≤ κ+. Moreover, ϱ = κ+ if and only if κ is singular, otherwise ϱ = κ. The statements of the corollary are well known in the presence of the axiom of choice . To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary has been treated independently by T. JECH. (shrink)

• The transitive closure of R is the smallest relation S for which: –R⊆S, – S is transitive. • To express ^r one would need an ‘infinite formula’: {(x, y) | R(x, y) ∨ ∃z(R(x, z) ∧ R(z, y)) ∨∃z, v(R(x, z) ∧ R(z, v) ∧ R(v, y)) ∨∃z, v, w(R(x, z) ∧ R(z, v) ∧ R(v, w) ∧ R(w, y)) ∨ · · ·.

We will prove in Zermelo-Fraenkel set theory without axiom of choice that the transitive hull R* of a relation R is not much “bigger” than R itself. As a measure for the size of a relation we introduce the notion of κ+-narrowness using surjective Hartogs numbers rather than the usul injective Hartogs values. The main theorem of this paper states that the transitive hull of a κ+-narrow relation is κ+-narrow. As an immediate corollary we obtain that, for every (...) infinite cardinal κ, the class HCκ of all κ-hereditary sets is a set with von Neumann rank ϱ(HCκ) ≤ κ+. Moreover, ϱ(HCκ) = κ+ if and only if κ is singular, otherwise ϱ(HCκ) = κ. The statements of the corollary are well known in the presence of the axiom of choice (AC). To prove them without AC - as carried through here - is, however, much harder. A special case of the corollary (κ = ω1, i.e., the class HCω1 of all hereditarily countable sets) has been treated independently by T. JECH. (shrink)

We prove that any positive elementary (least fixed point) induction expressing the negation of transitive closure on finite nondirected graphs requires at least two recursion variables.

We establish a general hierarchy theorem for quantifier classes in the infinitary logic L∞ωωon finite structures. In particular, it is shown that no infinitary formula with bounded number of universal quantifiers can express the negation of a transitive closure.This implies the solution of several open problems in finite model theory: On finite structures, positive transitive closure logic is not closed under negation. More generally the hierarchy defined by interleaving negation and transitive closure operators is (...) strict. This proves a conjecture of Immerman.We also separate the expressive power of several extensions of Datalog, giving new insight in the fine structure of stratified Datalog. (shrink)

We introduce a new logical operator CSTC and show that incorporating this operator into first-order logic enables as to capture the complexity class PSPACE. We also show that by varying how the operator is applied we can capture the complexity classes P, NP, the classes of the Polynomial Hierarchy PH, and PSPACE. As such, the operator CSTC can be regarded as a general purpose operator. We also give applications of these characterizations by showing that P and NP coincide with those (...) problems accepted by two new classes of program schemes , by producing some new complete problems for various complexity classes where the reductions are from first principles and do not use known complete problems , and by giving a simple proof that first-order logic incorporated with the least fixed point operator captures P. (shrink)

This paper argues that decision problems and money-pump arguments should not be a deciding factor against accepting non-transitive better than relations. If the reasons to accept normative standpoints that entail a non-transitive better than relation are compelling enough, we ought to revise our decision method rather than the normative standpoints. The paper introduces the most common argument in favor of non-transitive better than relations. It then illustrates that there are different ways to reconceptualize rational choice (...) so that rational choice is possible also when the relevant better than relation is non-transitive. (shrink)

Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal substructural logic. (...) Soundness and completeness are proven each time. (shrink)

We prove completeness for some language-theoretic models of the full Lambek calculus and its various fragments. First we consider syntactic concepts and syntactic concepts over regular languages, which provide a complete semantics for the full Lambek calculus \. We present a new semantics we call automata-theoretic, which combines languages and relations via closure operators which are based on automaton transitions. We establish the completeness of this semantics for the full Lambek calculus via an isomorphism theorem for the syntactic (...) concepts lattice of a language and a construction for the universal automaton recognizing the same language. Finally, we use automata-theoretic semantics to prove completeness of relation models of binary relations and finite relation models for the Lambek calculus without and with empty antecedents and \), thus solving a problem left open by Pentus. (shrink)

The paper contains an axiomatic treatment of the intuitionistic theory of hereditarily finite sets, based on an induction axiom-schema and a finite set of single axioms. The main feature of the principle of induction used (due to Givant and Tarski) is that it incorporates Foundation. On the analogy of what is done in Arithmetic, in the axiomatic system selected the transitive closure of the membership relation is taken as a primitive notion, so as to permit an immediate adaptation (...) of the theory to cases of restricted induction (in particular primitive recursive induction). At the end of the paper several different forms of induction, which play an important role in the development of the theory, are compared. An alternative axiomatization of the theory, which is of intrinsic interest, is also discussed. (shrink)

We present a semi-formal foundational theory of sorts, akin to sets, named librationism because of its way of dealing with paradoxes. Its semantics is related to Herzberger’s semi inductive approach, it is negation complete and free variables (noemata) name sorts. Librationism deals with paradoxes in a novel way related to paraconsistent dialetheic approaches, but we think of it as bialethic and parasistent. Classical logical theorems are retained, and none contradicted. Novel inferential principles make recourse to theoremhood and failure of theoremhood. (...) Identity is introduced à la Leibniz-Russell, and librationism is highly non-extensional. Π 1 1 -comprehension with ordinary Bar-Induction is accounted for (to be lifted). Power sorts are generally paradoxical, and Cantor’s Theorem is blocked as a camouflaged premise is naturally discarded. (shrink)

Any set x is uniquely specified by the graph of the membership relation on the set obtained by adjoining x to the transitive closure of x. Thus any operation on sets can be looked at as an operation on these graphs. We look at the operations of ordinal arithmetic of sets in this light. This turns out to be simplest for a modified ordinal arithmetic based on the Zermelo ordinals, instead of the usual von Neumann ordinals. In this (...) arithmetic, addition of sets corresponds to concatenating graphs, and multiplication corresponds to replacing each edge of a graph by a copy of another graph. Characterizations for the von Neumann case are also given. (shrink)

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k−1)-ary fragment of partial fixed point logic by all (2k−1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic (...) class='Hi'>transitive closure logic, we show that an extension is possible when we close this logic under congruence. (shrink)

Introduction: Wonder and the births of philosophy -- Socrates' small difficulty -- The wound of wonder -- The death and resurrection of Thaumazein -- The Thales dilemma -- Repetition : Martin Heidegger -- Metaphysics small difficulty -- Wonder and the first beginning -- Wonder and the other beginning -- Theaetetus redux : the ghost of the Pseudes Doxa -- Once again to the cave -- Rethinking Thaumazein -- Openness : Emmanuel Levinas -- Passivity and responsibility -- The ethics of the (...) cave -- Infinity and astonishment -- Opening out : from existent to existence -- Closing down : from existence to existent -- Locking up : totality and infinity -- The phantom of the autrement -- Awakening -- Relation : Jean-Luc Nancy -- The problem of Mitsein -- Mitsein as essential inessentiality -- The myth of essentialism -- Unworking -- Interruption -- Repetition -- Decision : Jacques Derrida -- Thaumazein, the irresponsible, and the undecidable -- Hospitality -- Undecidability revisited -- Much madness is divinest sense (or, who comes after the decision?) -- How to avoid the subject (or, that's not my hedgehog!) -- Undecidability, take three : think here of Kierkegaard -- Mysterium tremendum -- Postlude: Possibility. (shrink)

The link between logic and mathematics has long been recognized by theorists from various fields. For instance, the mathematician, Bertrand Russell (1919), described logic and math as intrinsically...

The article analyzes the effectiveness of quantum theories of mental experience in relation to two ontological problems - the problem of the existence of consciousness in the material world and the problem of the interaction of consciousness and body. A critical analysis of the quantum theories of consciousness by Penrose-Hameroff, M. Tegmark, G. Stapp, M. Fischer and M.B. Mensky shows that they fail to fully explain how complex physical systems generate mental experience without violating the principle of causal closure (...) of the physical world and the principle of epistemological completeness of physics. Quantum mechanics provides specific processes that are the physical basis of the psyche, but do not explain the phenomenal aspect of subjective reality. Nevertheless, the Heisenberg uncertainty principle gives an understanding of how the interaction of consciousness and body within the scientific picture of the world can be carried out without violating the law of energy conservation. It is shown that the quantum theories of consciousness currently being developed have a predominantly panprotopsychic character, which faces a problem due to the fact that the protomental property of physical systems must be expressed quantitatively and correspond to the value included in the physical equations. As a result, it is concluded that in order to develop quantum theories of consciousness more effectively, it is necessary to give an emergent character, not jumping from the quantum level to the psychic, but explaining the mechanism of the emergence of systemic properties during the sequential transition between different ontological regions of existence, including physical, chemical, biological, neurophysiological and psychic. (shrink)

The adaptive reuse of industrial heritage, a critical component in addressing radical climate change-related urban transitions, is increasingly pertinent. This paper distinguishes ‘urban transitions’ from ‘urban transformation,’ emphasizing a more gradual, adaptive approach to urban development under the pressures of climate change. It explores the repurposing of industrial buildings and spaces, maintaining their cultural and historical value while meeting current urban needs. Through a mixed-methods approach, the paper analyses how adaptive reuse contributes to sustainable urban development, examines the scale and (...) impact of such projects from local quarters to city-wide implications, and discusses the potential negative consequences, including gentrif ication. The study spans various global regions, including Europe, the United States, Latin America, Canada, and Australia, using case studies to illustrate the effectiveness of adaptive reuse in promoting sustainability, revitalizing urban areas, and preserving cultural heritage. The paper questions the viability of traditional long-term sustainable urban development strategies in the face of rapid environmental and societal changes, suggesting a potential need for paradigm shifts in urban planning. (shrink)

In the third Logical Investigation Husserl presents an integrated theory of wholes and parts based on the notions of dependency, foundation ( Fundierung ), and aprioricity. Careful examination of the literature reveals misconceptions regarding the meaning and scope of the central axis of this theory, especially with respect to its proper context within the development of Husserl's thought. The present paper will establish this context and in the process correct a number of these misconceptions. The presentation of mereology in the (...) Logical Investigations will be shown to originate largely from Husserl's implicit self-criticism of his prior views on the unity of a whole presented in his first work, Philosophy of Arithmetic. (shrink)

Ordinal addition and multiplication can be extended in a natural way to all sets. I survey the structure of the sets under these operations. In particular, the natural partial ordering associated with addition of sets is shown to be a tree. This allows us to prove that any set has a unique representation as a sum of additively irreducible sets, and that the non-empty elements of any model of set theory can be partitioned into infinitely many submodels, each isomorphic to (...) the original model. Also any model of set theory has an isomorphic extension in which the empty set of the original model is non-empty. Among other results, the relations between the arithmetical operations and the transitive closure and the adductive hierarchy are elucidated. (shrink)

Dag Prawitz (1971) put forward the idea that an admissible reduction process does not affect the identity of proofs represented by derivations in natural deduction. The idea relies on his conjecture that two derivations represent the same proof if and only if they are equivalent in the sense that they are reflexive, transitive and symmetric closure of the immediate reducibility relation. Schroeder-Heister and Tranchini (2017) accept Prawitz’s conjecture and propose the triviality test as the criterion for admissible reductions. (...) In the present paper, we will consider two main troubles of the triviality test. The first is the obscurity of a method of evaluating admissible reductions. The second is the circularity problem that the triviality test already assumes the set of admissible reduction procedures. For the solution of the problems, we will propose the spoiler test which immunes the problems of the triviality test and has the role of the criterion for admissible reductions. At last, we shall cover a plausible problem of the spoiler test that can be caused by Crabbé’s case. (shrink)

Alexander the Great’s conquests ushered in the Hellenistic era throughout the ancient Mediterranean and Middle East. In this period, the Seleucids, one of most successful of the Successor dynasties, ruled over most of the Middle East at the height of their power. Yet two rising powers in the ancient world, Rome and Parthia, played a crucial role in the decline and eventual fall of the Seleucids. In a prior article, I argued that geopolitical developments around the Eastern Mediterranean in the (...) middle third century BCE were indirectly responsible for the emergence of the Parthian state in Iran. Disastrous military conflicts at home and abroad in the west caused a sudden decline of Seleucid power in the 240s–230s, triggering what political scientists call a power-transition crisis. This article utilizes similar approaches to historical analysis and International Relations theory to contend that, after a period of recovery, a further sudden decline of Seleucid power in the 160s–130s triggered another power-transition crisis that brought an end to Seleucid hegemony over the Middle East permanently. The crisis facilitated the rapid transformation of the Parthian state from a minor kingdom to a major empire, drastically changing the international environment of the ancient world. (shrink)

In this paper, I explore some of the temporal structures of racialized experience – what I call racialized time. I draw on the Martiniquan philosopher and psychiatrist Frantz Fanon, in particular his book ‘Black Skin, White Masks,’ in order to ask how racism can be understood as a social pathology which, when internalized or ‘epidermalized,’ may result in aberrations of affect, embodiment and agency that are temporally lived. In this regard, I analyze the racialized experience of coming ‘too late’ to (...) a world predetermined in advance and the distorted relation to possibility – the limitation of playfulness and imaginative variability – that defines this sense of lateness. I argue that the racialization of the past plays a structuring role in such experience. Racialization is not limited to the present, but also colonizes and reconfigures the past, splitting it into a duality of times: one open and civilizational, the other closed, anachronistic and racialized. To understand this colonial construction of the past, I draw on the work of Latin American thinker Aníbal Quijano. (shrink)

The notion of the rational closure of a positive knowledge base K of conditional assertions θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}) was first introduced by Lehmann (1989) and developed by Lehmann and (...) Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice, however, one might expect a knowledge base to consist not just of positive conditional assertions, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} |∼ φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}, but also negative conditional assertions, θi φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} (standing for not if θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document} then normally φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$i$$ \end{document}. Restricting ourselves to a finite language we show that the rational closure still exists for satisfiable knowledge bases containing both positive and negative conditional assertions and has similar properties to those exhibited in Lehmann and Magidor (1992). In particular an algorithm in Lehmann and Magidor (1992) which constructs the rational closure can be adapted to this case and yields, in turn, completeness theorems for the conditional assertions entailed by such a mixed knowledge base. (shrink)

The move to remote learning during COVID-19 has impacted billions of students. While research shows that school closure, and the pandemic more generally, has led to student distress, the possibility that these disruptions can also prompt growth in is a worthwhile question to investigate. The current study examined stress-related growth (SRG) in a sample of students returning to campus after a period of COVID-19 remote learning (n= 404, age = 13–18). The degree to which well-being skills were taught at (...) school (i.e., positive education) before the COVID-19 outbreak and student levels of SRG upon returning to campus was testedviastructural equation modeling. Positive reappraisal, emotional processing, and strengths use in students were examined as mediators. The model provided a good fit [χ2= 5.37,df= 3,p= 0.146, RMSEA = 0.044 (90% CI = 0.00–0.10), SRMR = 0.012, CFI = 99, TLI = 0.99] with 56% of the variance in SRG explained. Positive education explained 15% of the variance in cognitive reappraisal, 7% in emotional processing, and 16% in student strengths use during remote learning. The results are discussed using a positive education paradigm with implications for teaching well-being skills at school to foster growth through adversity and assist in times of crisis. (shrink)

Possibly the most fundamental scientific problem is the origin of time and causality. The inherent difficulty is that all scientific theories of origins and evolution consider the existence of time and causality as given. We tackle this problem by starting from the concept of self-organization, which is seen as the spontaneous emergence of order out of primordial chaos. Self-organization can be explained by the selective retention of invariant or consistent variations, implying a breaking of the initial symmetry exhibited by randomness. (...) In the case of time, we start from a random graph connecting primitive “events”. Selection on the basis of consistency eliminates cyclic parts of the graph, so that transitive closure can transform it into a partial order relation of precedence. Causality is assumed to be carried by causal “agents” which undergo a more traditional variation and selection, giving rise to causal laws that are partly contingent, partly necessary. (shrink)

There is a mistake in the definition of the covering criterion on page 6.

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. The metrological structure (...) of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

The importance of male dominance in the scientific community is no strange to us all. Science, as a source of respected and influential information is a staunchly guarded male domain for millennia. What is specific for our time and place is the nervousness with which female presence is accepted. It is also the time of great changes in the axis of power, and the struggle for control is very aggressive. What is even more so in Serbia and Montenegro one of (...) the pieces of ruins of the late SFRJ, is that the dysfunction of the war and sanctions brought about more inequality than before. And science is a field of professional achievement with slow and uncertain rewards, vast investment of time, effort and funds, for a career that is beneficial more to vanity than to the bank account. Women are seen as frivolous when they devote a huge amount of work and other resources to self-improvement and personal achievement and not to the comfort of the immediate family. Osnazivanje zena i njihovo ravnopravno ucesce u drustvenom, ekonomskom politickom i kulturnom zivotu kao i eliminacija svih oblika porodicne ekonomske, politicke, obrazovne i svake druge rodne diskriminacije i nasilja nad zenama spada u milenijumske ciljeve Ujedinjenih nacija prihvacene od Evropske unije i preporucene vladama svih zemalja u formiranju njihove nacionalne strategije. (shrink)

We study the SIS and SIRI epidemic models discussing different approaches to compute the thresholds that determine the appearance of an epidemic disease. The stochastic SIS model is a well known mathematical model, studied in several contexts. Here, we present recursively derivations of the dynamic equations for all the moments and we derive the stationary states of the state variables using the moment closure method. We observe that the steady states give a good approximation of the quasi-stationary states of (...) the SIS model. We present the relation between the SIS stochastic model and the contact process introducing creation and annihilation operators. For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we present the phase transition lines using the mean field and the pair approximation for the moments. We use a scaling argument that allow us to determine analytically an explicit formula for the phase transition lines in pair approximation. (shrink)

This book is a synthetic historiography of present-day international relations theory, a critical analysis of the continuing diversity and complexity of enduring themes through a sustained focus on the analysis of the empirical evidence accumulated by social scientists. Special attention is given to key historical changes in theoretical approaches over the past half-century with full recognition of the contestation over state-based theory, and the changing fortunes of contemporary approaches. The book suggests that viable theories must transcend current intellectual fashion, (...) and attempts to bring together theory and practice while demonstrating the difficulty of assessing competing theories. It addresses multiple strands of thought and assumes that their development cannot be understood in isolation from each other. (shrink)

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a (...) relation supervenes on its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations. (shrink)

This paper presents an enhanced ontology formalization, combining previous work in Conceptual Structure Theory and Order-Sorted Logic. Most existing ontology formalisms place greater importance on concept types, but in this paper we focus on relation types, which are in essence predicates on concept types. We formalize the notion of ‘predicate of predicates’ as meta-relation type and introduce the new hierarchy of meta-relation types as part of the ontology definition. The new notion of closure of a relation or meta-relation type (...) is presented as a means to complete that relation or meta-relation type by transferring extra arguments and properties from other related types. The end result is an expanded ontology, called the closure of the original ontology, on which automated inference could be more easily performed. Our proposal could be viewed as a novel and improved ontology formalization within Conceptual Structure Theory and a contribution to knowledge representation and formal reasoning (e.g., to build a query-answering system for legal knowledge). (shrink)

The questions of forgiveness and political justice have recently become intertwined with the “transitional justice” project, the aim of which is the coming to terms with past human rights violations. This article demonstrates that “transitional justice” is less concerned with providing justice than with achieving historical closure, moral redemption, and a “new beginning.” It proposes that justice requires a profound reflection of a political nature by introducing and discussing Jean Améry's concept of resentment. Central to Améry's view of resentment (...) is the restoration of the victim's social status and dignity, the validation of the experience of victimhood; his view therefore contrasts with the Nietzschean derogative view of ressentiment. On the basis of Améry's conceptualizations and with reference to Derrida's notions of “hiatus” and “forgiveness as impossibility,” the article problematizes the relation of ethics and politics—which the “transitional justice” project takes as given. It suggests that to theorize on justice, one needs to parenthesize the moral imagery of forgiveness and bring thirdness to the fore as the space where the identities of “victims” and “perpetrators” are established and played out. (shrink)

In La Métaphore Vive, spatial understandings pervade much of Ricoeur’s discussion of metaphor in terms of proximity and distance, tension, substitution, displacement, change of location, image, the ‘open’ structure of words, closure, transparency and opaqueness. Yet this is usually where space is discussed within metaphor, and as a metaphor itself, rather than as a precondition or prior system of relations to language interacting with language. Based on reinterpretation of an aspect of Lévi-Strauss’ structuralist anthropology, diametric and concentric spaces (...) are argued to be such a prior system of relations to language, actively framing metaphor. This article examines the relevance of this prelinguistic spatial discourse to Ricoeur’s framework of metaphor and interrogation of the copula, influenced centrally by Heidegger. Concentric spatial assumed connection and diametric spatial assumed separation offer a framework for understanding, in Ricoeur’s words, the “conflict between identity and difference” in metaphor and early Heidegger’s existential spatiality. (shrink)

An ω-set is a subset of the recursive ordinals whose complement with respect to the recursive ordinals is unbounded and has order type ω. This concept has proved fruitful in the study of sets in relation to metarecursion theory. We prove that the metadegrees of the sets coincide with those of the meta-r.e. ω-sets. We then show that, given any set, a metacomplete set can be found which is weakly metarecursive in it. It then follows that weak relative metarecursiveness is (...) not a transitive relation on the sets, extending a result of G. Driscoll [2, Theorem 3.1]. Coincidentally, we discuss the notions of total and complete regularity. Finally, we solve Post's problem for the transitive closure of weak relative metarecursiveness. We recommend the reader look at pp. 324–328 of the fundamental article [6] of Kreisel and Sacks before proceeding. He will find there a proof of the following very basic fact: a subset of the integers is iff it is metarecursively enumerable (metafinite). (shrink)

This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.