In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost (...) from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about. (shrink)

The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...) is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF. (shrink)

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has only recently started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics (...) to artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

Serious thinking about the computational aspects of situation theory is just starting. There have been some recent proposals in this direction (viz. PROSIT and ASTL), with varying degrees of divergence from the ontology of the theory. We believe that a programming environment incorporating bona fide situation-theoretic constructs is needed and describe our very recent BABY-SIT implementation. A detailed critical account of PROSIT and ASTL is also offered in order to compare our system with these pioneering and influential frameworks.

While situation theory and situation semantics provide an appropriate framework for a realistic model-theoretic treatment of natural language, serious thinking on their 'computational' aspects has just started. Existing proposals mainly offer a Prolog- or Lisp-like programming environment with varying degrees of divergence from the ontology of situation theory. In this paper, we introduce a computational medium (called BABY-SIT) based on situations. The primary motivation underlying BABY-SIT is to facilitate the development and testing of programs in domains ranging from linguistics to (...) artificial intelligence in a unified framework built upon situation-theoretic constructs. (shrink)

We describe a novel approach to the analysis of pronominal anaphora in Turkish. A computational medium which is based on situation theory is used as our implementation tool. The task of resolving pronominal anaphora is demonstrated in this environment which employs situation-theoretic constructs for processing.

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.

Sobre la base de una línea interpretativa propiciada por la misma doctrina de Plotino, este trabajo pretende estudiar el problema que conlleva el fin último del alma humana en vista de su ascenso hacia el Uno-Bien. En varios pasajes de su obra, el filósofo sostiene que, conociendo el propio sí-mismo, se puede tomar contacto con un principio supremo, anterior incluso a la potencia intelectiva, en virtud de cuya visión es dable gozar de un amor sin medida. El remate en la (...) unificación no depende en última instancia del acierto racional, sino de concordar en el mismo centro con aquello de semejante al Uno-Bien que hay en el alma. Estas distinciones abonarían la posibilidad de una unión mística dentro del sistema plotiniano. Sin embargo, desde el punto de vista epistemológico, el estatuto místico es controvertido y plantea una serie dificultades teóricas que es necesario dilucidar. Para el análisis de los tópicos mentados se desarrolla una lectura a la vez hermenéutica y crítica tanto de las fuentes como de la bibliografía erudita. (shrink)

The filtration method is often used to prove the finite model property of modal logics. We adapt this technique to the generalized Veltman semantics for interpretability logics. In order to preserve the defining properties of generalized Veltman models, we use bisimulations to define adequate filtrations. We give an alternative proof of the finite model property of interpretability logic with respect to Veltman models, and we prove the finite model property of the systems and with respect to generalized Veltman models.

This paper starts by investigating Ackermann's interpretation of finite set theory in the natural numbers. We give a formal version of this interpretation from Peano arithmetic (PA) to Zermelo-Fraenkel set theory with the infinity axiom negated (ZF−inf) and provide an inverse interpretation going the other way. In particular, we emphasize the precise axiomatization of our set theory that is required and point out the necessity of the axiom of transitive containment or (equivalently) the axiom scheme of ∈-induction. This clarifies the (...) nature of the equivalence of PA and ZF−inf and corrects some errors in the literature. We also survey the restrictions of the Ackermann interpretation and its inverse to subsystems of PA and ZF−inf, where full induction, replacement, or separation is not assumed. The paper concludes with a discussion on the problems one faces when the totality of exponentiation fails, or when the existence of unordered pairs or power sets is not guaranteed. (shrink)

A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained (...) types of modal definability on the level of Kripke models, we give characterization theorems in the usual form, in terms of algebraic closure conditions. As some consequences of these, various preservation results are presented. Also, some characterizations are strengthened by replacing closure under ultraproducts with closure under ultrapowers. (shrink)

We can formalize judgments as logical formulas. Judgment aggregation deals with judgments of several agents, which need to be aggregated to a collective judgment. There are several logical formalizations of judgment aggregation. This paper focuses on a modal formalization which nicely expresses classical properties of judgment aggregation rules and famous results of social choice theory, like Arrow’s impossibility theorem. A natural deduction system for modal logic of judgment aggregation is presented in this paper. The system is sound and complete. As (...) an example of derivation, a formal proof of Arrow’s impossibility theorem is given. (shrink)

This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.

A 4-valued framework is proposed to distinguish intuitionistically valid formulas within classical validities.

We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable (...) under any valuation (the so‐called existential validity). Continuing previous work in which model theoretic characterization for this type of definability of elementary classes was proved, we give an analogous general result without the assumption of the first‐order definability. Furthermore, we outline relationships between sets of existentially valid formulas corresponding to several well‐known modal logics. (shrink)

_Health Education: Critical perspectives_ provides a socio-cultural and critical approach to health education. The book draws together international experts in the fields of health and education who deconstruct contemporary discourses and practices, and re-imagine a health education that both connects with young people and offers a way forward in addressing issues of health and wellbeing. Chapters within specifically link academic work on neoliberalism, healthism, risk and the body to wider discourses of health and health education. They challenge current practices and (...) call for a re-thinking of current health programs in education settings. A unique feature of this book is the analyses of health education from both political and applied levels across a range of international contexts. The book is divided into three sections: the social and political contexts informing health education how individual health issues articulate in education in complex ways alternative ways to think about health and health education pedagogy. The overall theme of the book offers a perspective that the current approach to health education – promoting a fear of ill health, self-surveillance and individual responsibility – can become a form of health fascism, and we need to be cognisant of this potential and its consequences for young people. The book will be of key interest to academics and researchers exploring the political context of health education. (shrink)

In an earlier paper the first author initiated the study of generic cuts of a model of Peano arithmetic relative to a notion of an indicator in the model. This paper extends that work. We generalise the idea of an indicator to a related neighbourhood system; this allows the theory to be extended to one that includes the case of elementary cuts. Most results transfer to this more general context, and in particular we obtain the idea of a generic cut (...) relative to a neighbourhood system, which is studied in more detail. The main new result on generic cuts presented here is a description of truth in the structure , where I is a generic cut of a model M of Peano arithmetic. The special case of elementary generic cuts provides a partial answer to a question of Kossak [R. Kossak, Four problems concerning recursively saturated models of arithmetic, Notre Dame Journal of Formal Logic 36 519–530]. (shrink)

The current study aimed to investigate the extent to which familial history of reading and math difficulties have an impact on children’s academic outcomes within a 3-year longitudinal study, which evaluated their core reading and math skills after first and second grades, as well as performance on complex academic tasks after second and third grades. At baseline, parents were asked to complete the Adult Reading History Questionnaire and its adaption, Adult Math History Questionnaire, to index familial history of reading and (...) math difficulties, respectively. Preliminary findings established the psychometric properties of the AMHQ, suggesting that it is a reliable and valid scale. Correlation analyses indicated that the ARHQ was negatively associated with children’s reading skills, whereas the AMHQ was negatively related to math outcomes. Path results revealed that the ARHQ predicted children’s performance on complex reading tasks indirectly via their core reading skills, and the AMHQ was linked to complex math outcomes indirectly via core math abilities. The ARHQ was also found to be negatively correlated with measures of children’s math performance, with path findings suggesting that these relations were indirectly explained by differences in their core reading skills. These results suggest that assessing familial risk for academic difficulties may be crucial to understanding comorbid etiological and developmental associations between reading and math differences. (shrink)

A phenomenon is that which appears. In his phenomenology, Jean-Luc Marion shows how a phenomenon that appears in and out of itself evades the metaphysical demand of grounding. Classical philosophy has acknowledged phenomena only in so far as they can be sanctioned by the concepts of the intellect. This holds good also of Husserl’s constitutive ego. Now, Marion distinguishes between such intuitively “poor phenomena” and the “saturated phenomena” that exceed the intentional consciousness; they are given not by the consciousness but (...) to the consciousness in an excess of intuition. This “gift of appearance” is Marion’s main concern, in the visible in general, and in painting in particular. But whereas idols only reflect our own desire to see and to be seen, icons surprise us by the gaze the saint directs on us. A picture is the scene of a possible revelation; and the revelation is nothing but the phenomenon taken in its fullest meaning: intuitive saturation at its maximum. A crucial question, nonetheless, remains: What is the relation between revelation as a phenomenological possibility, and Revelation as a theological dogma of the utmost importance? (shrink)

In recent years there has been an increasing interest in museum studies in exhibitions on what is termed Difficult Matters —such as rape and mass murder—and how such exhibitions may evoke ethical change. This raises the question about the conditions on which such exhibitions can lead to an ethical change. By developing a conceptual framework this article contributes to museum studies on Difficult Matters demonstrating how vulnerability can work as a key concept in a relational pedagogical understanding of the conditions (...) for ethical change. Inspired by feminist ethics the article suggests that there is an “ambivalent potentiality” of the concept of vulnerability and forwards a double perspective on vulnerability as condition: vulnerability is inherent to the human condition and always situational. From this point of departure vulnerability is fleshed out as a key concept in museum pedagogy via pedagogical thinkers inspired by the philosopher Emmanuel Lévinas’ ethics. Concepts like heteronomy, incarnation, Face and Saying/Said are introduced to define vulnerability and the relation between exhibition and visitor is defined as a teaching–learning relation conditioned by vulnerability. Vulnerability is defined as openness to an encounter with the Other as being different, which is conditional of an ethical transformation of existing perceptions of self, others and the world. Finally, inspired by feminist philosophy a norm critical is introduced. It is argued that displaying Difficult Matters in order to evoke an ethical transformation museum professionals need consider critically the norms of vulnerability at play in particular situations. On this basis, the concept of vulnerability can serve as a lever for discussions on the pedagogy of exhibitions on Difficult Matters and the ethical responsibility of museum professionals in public museums in this regard. (shrink)

Formalizing commonsense knowledge for reasoning about time has long been a central issue in AI. It has been recognized that the existing formalisms do not provide satisfactory solutions to some fundamental problems, viz. the frame problem. Moreover, it has turned out that the inferences drawn do not always coincide with those one had intended when one wrote the axioms. These issues call for a well-defined formalism and useful computational utilities for reasoning about time and change. Yoav Shoham of Stanford University (...) introduced in his 1986 Yale doctoral thesis an appealing temporal nonmonotonic logic and identified a class of theories, causal theories, which have computationally simple model-theoretic properties. This paper is a study towards building upon Shoham's work on causal theories. We concentrate on improving computational aspects of causal theories while preserving their model-theoretic properties. (shrink)

Planlama --- bir amaca ulaşmak üzere bir aksiyonlar bütünü tasarlamak --- yapay zekadaki en temel problemlerden biridir. Bu yazıda, robotikte planlama konusuna mantıkçı (logicist) yaklaşım ele alınmaktadır. [Planning --- devising a plan of action to reach a given goal --- is a fundamental problem in AI. This paper reviews the logicist approach to planning in robotics.].

We extend causal theories and study actions in domains involving multiple agents. Causal theories, invented by Yoav Shoham, are based on a temporal nonmonotonic logic and have computationally tractable aspects. Since Shoham's formalism does not provide an adequate mechanism for representing simultaneous actions and specifying their consequences, we introduce the notion of counteractions while preserving the efficiency and model-theoretic properties of causal theories.

After a review of situation theory and previous attempts at 'computational' situation theory, we present a new programming environment, BABY-SIT, which is based on situation theory. We then demonstrate how problems requiring formal temporal reasoning can be solved in this framework. Specifically, the Yale Shooting Problem, which is commonly regarded as a canonical problem for nonmonotonic temporal reasoning, is implemented in BABY-SIT using Yoav Shoham's causal theories.

Situation theory has been developed over the last decade and various versions of the theory have been applied to a number of linguistic issues. However, not much work has been done in regard to its computational aspects. In this paper, we review the existing approaches towards 'computational situation theory' with considerable emphasis on our own research.

Recently, there have been some attempts towards developing programming languages based on situation theory. These languages employ situation-theoretic constructs with varying degrees of divergence from the ontology of the theory. In this paper, we review three of these programming languages.

Over the past six decades, Antarctic Treaty Consultative Parties have developed legal agreements to protect various aspects of the Antarctic environment. Strong anthropocentrism (e.g., unsustainable harvesting of marine living resources) is generally rejected, and stewardship (e.g., minimizing risks of contamination) is accepted while protection of nonanthropocentric values (e.g., wilderness and intrinsic values) is evoked when it furthers human interests. As one of the world’s remaining large wildernesses, Antarctica is under threat from the continuous expansion of the human footprint and is (...) in need of attention from the wider society, including the environmental ethics community. The interdependence of all life on this planet means that problems in Antarctica are not as far away and trivial as it may seem. Furthermore, Antarctica’s extreme position at the edge of civilization challenges humans as moral agents to think about where our moral duties and rights begin and end on this planet, and elsewhere in the universe. Considerations of wilderness and intrinsic values, equity, and abiotic ethics are some of the issues that environmental ethics can contribute toward the protection of the Antarctic wilderness. (shrink)

Australia’s punitive policy towards people seeking asylum deliberately causes severe psychological harm and meets recognised definitions of torture. Consequently, there is a tension between doctors’ obligation not to be complicit in torture and doctors’ obligation to provide best possible care to their patients, including those seeking asylum. In this paper, we explore the nature of complicity and discuss the arguments for and against a proposed call for doctors to boycott working in immigration detention. We conclude that a degree of complicity (...) is unavoidable when working in immigration detention, but that it may be ethically justifiable. We identify ways to minimise the harms associated with complicity and argue that it is ethical to continue working in immigration detention as long as due care and attention is paid to minimising the harms of complicity. (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...

We prove that any proof of a [Formula: see text] sentence in the theory [Formula: see text] can be translated into a proof in [Formula: see text] at the cost of a polynomial increase in size. In fact, the proof in [Formula: see text] can be obtained by a polynomial-time algorithm. On the other hand, [Formula: see text] has nonelementary speedup over the weaker base theory [Formula: see text] for proofs of [Formula: see text] sentences. We also show that for (...) [Formula: see text], proofs of [Formula: see text] sentences in [Formula: see text] can be translated into proofs in [Formula: see text] at a polynomial cost in size. Moreover, the [Formula: see text]-conservativity of [Formula: see text] over [Formula: see text] can be proved in [Formula: see text], a fragment of bounded arithmetic corresponding to polynomial-time computation. For [Formula: see text], this answers a question of Clote, Hájek and Paris. (shrink)