We investigate two different broad traditions in the abstract valuational model theory for nontransitive and nonreflexive logics. The first of these traditions makes heavy use of the natural Galois connection between sets of valuations and sets of arguments. The other, originating with work by Grzegorz Malinowski on nonreflexive logics, and best systematized in Blasio et al. : 233–262, 2017), lets sets of arguments determine a more restricted set of valuations. After giving a systematic discussion of these two different traditions (...) in the valuational model theory for substructural logics, we turn to looking at the ways in which we might try to compare two sets of valuations determining the same set of arguments. (shrink)

Is there a unique way to de-idealize models? If not, how might the possible ways of reducing the distortion between models and reality differ from each other? Based on an empirical case study conducted in financial markets, this paper discusses how a popular valuation model (the Discounted Cash Flow model) idealizes reality and how the market participants de-idealize it in concrete market situations. In contrast to Cartwright's view that economic models are generally over-constrained, this paper suggests that (...) valuation models are under-constrained. This serves as the reason why the relaxation of simplifying assumptions and concretization do not work as methods of de-idealization. The paper finds that financial market participants de-idealize models using commentary that takes the form of judgment. As a conclusion, a hypothesis is formulated that proposes that the more underdetermined the model is the bigger role narrative and other pragmatic elements play in the process of model application. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and (...) show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

Boolean-valued models for first-order languages generalize two-valued models, in that the value range is allowed to be any complete Boolean algebra instead of just the Boolean algebra 2. Boolean-valued models are interesting in multiple aspects: philosophical, logical, and mathematical. The primary goal of this paper is to extend a number of critical model-theoretic notions and to generalize a number of important model-theoretic results based on these notions to Boolean-valued models. For instance, we will investigate (first-order) Boolean valuations, which (...) are natural generalizations of (first-order) theories, and prove that Boolean-valued models are sound and complete with respect to Boolean valuations. With the help of Boolean valuations, we will also discuss the Löwenheim-Skolem theorems on Boolean-valued models. (shrink)

This paper is intended to draw the main theoretical lines of the notion of value, in order to avoid some flaws in the quantitative surveys on values as well as in some qualitative studies of value judgements. Through a number of redefinitions based on a pragmatic approach, inspired not only by Dewey’s concept of ‘valuation’ but also by the new French pragmatic sociology and by the pragmatist trend in linguistics, it tries to specify the conditions under which sociology can (...) address the notion of ‘value’ while avoiding their reduction to scholarly supports for morals or normative guides for action and evaluation. Meanwhile, it tries to construct a unified concept of value that would work for all the concerned disciplines: not only sociology but also economics, psychology, anthropology, and even philosophy. (shrink)

A central question for psychologists, economists, and philosophers is how human lives should be valued. Whereas egalitarian considerations give rise to models emphasizing that every life should be valued equally, empirical research has demonstrated that valuations of lives depend on a variety of factors that often do not conform to specific normative expectations. Such factors include emotional reactions to the victims and cognitive considerations leading to biased perceptions of lives at risk (e.g., attention, mental imagery, pseudo-inefficacy, and scope neglect). They (...) can lead to a valuation function with decreasing marginal value and sometimes even decreasing absolute value as the number of victims increases. As a result, people spend more money to save an individual while at the same time being insensitive and apathetic to large losses of life, despite endorsing egalitarian norms. In this conceptual paper, we propose a descriptive model highlighting the role of different motivations and the conditions under which cognitions and emotions result in deviations from egalitarian normative valuations of human lives. (shrink)

This paper introduces valuation structures associated with preferential models. Based on KLM valuation structures, we present a canonical approach to obtain injective preferential models for any preferential relation satisfying the property INJ, and give uniform proofs of representation theorems for injective preferential relations appeared in the literature. In particular, we show that, in any propositional language (finite or infinite), a preferential inference relation satisfies INJ if and only if it can be represented by a standard preferential model. (...) This conclusion generalizes the result obtained by Freund. In addition, we prove that, when the language is finite, our framework is sufficient to establish a representation theorem for any injective relation. (shrink)

We prove that every convexly ordered valuation ring has a unique completion as a uniform space, which furthermore is a convexly ordered valuation ring. In addition, we give a model theoretic characterisation of complete convexly ordered valuation rings, and give a necessary and sufficient condition for the completion of a convexly ordered valuation ring to be a real closed ring.

For paediatric medicine to advance, research must be conducted specifically with children. Concern about poor recruitment has led to debate about payments to child research participants. Although concerns about undue influence by such ‘compensation’ have been expressed, it is useful to determine whether children can relate the time and inconvenience associated with participation to the value of payment offered. This study explores children's ability to determine fair remuneration for research participation, and reviews payments to children participating in research. Forty children (...) were interviewed before outpatient visits at two London Hospitals: Great Ormond Street Children's Hospital and the Whittington Hospital District General Hospital. Children were asked to value their involvement in two hypothetical research scenarios – the first an ‘additional blood sample’, the second also involving daily oral oil capsules taken for a fortnight before further venesection. Background knowledge about familiarity with money, and experience with hospitalisation was assessed. The mean valuation of involvement in the second scenario (£13.18) was higher than in the first (£2.84) (p<0.001). This higher valuation persisted when children were categorised into groups ‘aged 12+’ and ‘below 12’. Those undergoing a blood test on the day placed a higher valuation on participation in the second scenario (£10.43, £21.67, p=0.044). These children aged 8–16 demonstrated the capacity to discern a fair valuation for participation in medical research. The monetary sums are influenced by the time and inconvenience involved in the research, and by the extent of recent experience with hospital procedures. The authors review current ethical thinking regarding payments to child research participants and suggest that a fair wage model might be an ethically acceptable way to increase participation of children in research. (shrink)

Contingent valuation of the environment has proven popular amongst environmental economists in recent years and has increased the role of monetary valuation in public policy. However, the underlying economic model of human psychology fails to explain why certain types of stated behaviour are observed. Thus, good scope exists for interdisciplinary research in the area of economics and psychology with regard to environmental valuation. A critical review is presented here of some recent research by social psychologists in (...) the US attempting to explain stated behaviour in contingent valuation. Attitudinal scales have been used to analyse the role of ecocentric, biocentric and altruistic motives for giving. However, the research is shown to draw some potentially misleading conclusions and be unrepresentative of contingent valuation. Two recent economic studies using contingent valuation are then reported and shown to have identified non-economic motives for WTP. The complexity of value formation and expression is found to go far beyond that generally accepted by economic models. Greater consideration of the role played by attitudes and ethical considerations then becomes relevant to the interpretation of results being used in standard cost-benefit analysis and environmental policy. (shrink)

We continue the study of a theory which is a valued analogue of the theory of regular rings studied by Carson, Lipshitz and Saracino, characterize it as the model companion of the theory of Prüfer rings, and prove its decidability. We then link it to the theory of p.p. rings developed by Weispfenning and show that it admits quantifier elimination in a related language.

Philosophical investigation in synthetic biology has focused on the knowledge-seeking questions pursued, the kind of engineering techniques used, and on the ethical impact of the products produced. However, little work has been done to investigate the processes by which these epistemological, metaphysical, and ethical forms of inquiry arise in the course of synthetic biology research. An attempt at this work relying on a particular area of synthetic biology will be the aim of this chapter. I focus on the reengineering of (...) metabolic pathways through the manipulation and construction of small DNA-based devices and systems synthetic biology. Rather than focusing on the engineered products or ethical principles that result, I will investigate the processes by which these arise. As such, the attention will be directed to the activities of practitioners, their manipulation of tools, and the use they make of techniques to construct new metabolic devices. Using a science-in-practice approach, I investigate problems at the intersection of science, philosophy of science, and sociology of science. I consider how practitioners within this area of synthetic biology reconfigure biological understanding and ethical categories through active modelling and manipulation of known functional parts, biological pathways for use in the design of microbial machines to solve problems in medicine, technology, and the environment. We might describe this kind of problem-solving as relying on what Helen Longino referred to as “social cognition” or the type of scientific work done within what Hasok Chang calls “systems of practice”. My aim in this chapter will be to investigate the relationship that holds between systems of practice within metabolic engineering research and social cognition. I will attempt to show how knowledge and normative valuation are generated from this particular network of practitioners. In doing so, I suggest that the social nature of scientific inquiry is ineliminable to both knowledge acquisition and ethical evaluations. (shrink)

The model companion of the theory of fields with valuation and automorphism exists. A counterexample shows that the theory of models of ACFA equipped with valuation is not this model companion.

We present a Kripke model for Girard's Linear Logic (without exponentials) in a conservative fashion where the logical functors beyond the basic lattice operations may be added one by one without recourse to such things as negation. You can either have some logical functors or not as you choose. Commutatively and associatively are isolated in such a way that the base Kripke model is a model for noncommutative, nonassociative Linear Logic. We also extend the logic by adding (...) a coimplication operator, similar to Curry's subtraction operator, which is resituated with Linear Logic's contensor product. And we can add contraction to get nondistributive Relevance Logic. The model rests heavily on Urquhart's representation of nondistributive lattices and also on Dunn's Gaggle Theory. Indeed, the paper may be viewed as an investigation into nondistributive Gaggle Theory restricted to binary operations. The valuations on the Kripke model are three valued: true, false, and indifferent. The lattice representation theorem of Urquhart has the nice feature of yielding Priestley's representation theorem for distributive lattices if the original lattice happens to be distributive. Hence the representation is consistent with Stone's representation of distributive and Boolean lattices, and our semantics is consistent with the Lemmon-Scott representation of modal algebras and the Routley-Meyer semantics for Relevance Logic. (shrink)

The main goal of the article is a further development of the usage of income and comparable approaches to company valuation aimed at defining market capitalization sensitivity to value changing in the conditions of dynamization of internal and external business parameters. The relevance of the researched topic is determined by the importance of establishing the factors influencing the change in company market capitalization based on the synthesis of approaches to company valuation. To obtain the results of the study, (...) the following methods were used: structural and logical analysis – to improve the process approach to company valuation in the context of determining the impact of its change on market capitalization; discounted cash flow method (DCF-model) – to determine the value of the enterprise based on the income approach; comparable companies method – to determine the value of the company on the basis of a market approach; factor analysis method – to assess the impact of changes in value on company market capitalization; generalization and logical analysis – in conclusions building. The results of critical analysis of publications of domestic and foreign scientists on the application of company valuation methods identified the need of improvement the process approach to company valuation in the context of determining the impact of its change on the company market capitalization. To adequately assess company value, the use of a synthesis of income and market approaches is proposed. The implementation of the DCF-model and comparable companies valuation method while valuation of Private Joint-Stock Company “SKF Ukraine” allowed to establish that the greatest impact on the target metric (company market capitalization) has an average industry multiplier EV/EBITDA, terminal growth rate and weighted average cost of capital – 5.9 %, 3.2% and 2.7% respectively. The practical value of the results of the study is determined by the importance of forming a full analytical basis for establishing the attractiveness of the performance of joint-stock companies in the market and consolidating management decisionsin order to increase market capitalization. (shrink)

In his Ph.D. thesis [7], L. van den Dries studied the model theory of fields with finitely many orderings and valuations where all open sets according to the topology defined by an order or a valuation is globally dense according with all other orderings and valuations. Van den Dries proved that the theory of these fields is companionable and that the theory of the companion is decidable .In this paper we study the case where the fields are expanded (...) with finitely many orderings and an independent derivation. We show that the theory of these fields still admits a model companion in the language Lequation image = {+, –, ·, D, <1, …, model companion by CODFm and give a geometric axiomatization of this theory which uses basic notions of algebraic geometry and some generalized open subsets which appear naturally in this context. This axiomatization allows to recover the one given in [4] for the theory CODF of closed ordered differential fields. Most of the technics we use here are already present in [2] and [4].Finally, we prove that it is possible to describe the completions of CODFm and to obtain quantifier elimination in a slightly enriched language. This generalizes van den Dries' results in the “derivation free” case. (shrink)

Daniel Hausman’s book ‘Valuing Health’ is a valuable contribution to our understanding of QALYs and DALYs and to moving health economics to adopting a broader perspective than that taken in conventional cost-effectiveness analysis. Hausman’s attempt at constructing a public value table for health states without having recourse to data from population preferences studies is also a fascinating read. But I have serious concerns about his resulting table. Hausman’s views on which dimensions of health a benevolent liberal state should care about (...) are essentially not different from what has long been emphasized in health economists’ work on valuations of health outcomes. His table would have been helpful as a sketch if it was the first attempt in health economics to quantify numerically the societal value of different types and degrees of health improvement. But research in the field has gone far beyond that. Multi-attribute utility instruments with much more accurate health classification systems than Hausman’s sketch are now at hand. Available also are models of societal valuations of QALYs that are broadly consistent with general population values, incorporate wider concerns than Hausman’s table does and do not have the questionable numerical properties that characterize Hausman’s sketch. (shrink)

The study of corporate social responsibility has been the object of much research in recent decades, although there is a need to continue investigating its benefits as a marketing tool. In the current work we adopt a multi-dimensional perspective of social responsibility, and we carry out market research to determine the perceptions of users of mobile telephone services about economic, legal, ethical and social aspects of their operating companies. With these data we determine the structure and components of the concept (...) of social responsibility. Subsequently, this is related with the overall evaluation of the service and loyalty by means of a model of structural equations, in order to determine the influence of corporate social responsibility on these concepts, and hence its benefits as a commercial tool. (shrink)

Boolean-valued models generalize classical two-valued models by allowing arbitrary complete Boolean algebras as value ranges. The goal of my dissertation is to study Boolean-valued models and explore their philosophical and mathematical applications.In Chapter 1, I build a robust theory of first-order Boolean-valued models that parallels the existing theory of two-valued models. I develop essential model-theoretic notions like “Boolean-valuation,” “diagram,” and “elementary diagram,” and prove a series of theorems on Boolean-valued models, including the (strengthened) Soundness and Completeness Theorem, the (...) Löwenheim–Skolem Theorems, the Elementary Chain Theorem, and many more.Chapter 2 gives an example of a philosophical application of Boolean-valued models. I apply Boolean-valued models to the language of mereology to model indeterminacy in the parthood relation. I argue that Boolean-valued semantics is the best degree-theoretic semantics for the language of mereology. In particular, it trumps the well-known alternative—fuzzy-valued semantics. I also show that, contrary to what many have argued, indeterminacy in parthood entails neither indeterminacy in existence nor indeterminacy in identity, though being compatible with both.Chapter 3 (joint work with Bokai Yao) gives an example of a mathematical application of Boolean-valued models. Scott and Solovay famously used Boolean-valued models on set theory to obtain relative consistency results. In Chapter 3, I investigate two ways of extending the Scott–Solovay construction to set theory with urelements. I argue that the standard way of extending the construction faces a serious problem, and offer a new way that is free from the problem.Abstract prepared by Xinhe Wu.E-mail: [email protected]. (shrink)

We study the model theory of fields k carrying a henselian valuation with real closed residue field. We give a criteria for elementary equivalence and elementary inclusion of such fields involving the value group of a not necessarily definable valuation. This allows us to translate theories of such fields to theories of ordered abelian groups, and we study the properties of this translation. We also characterize the first-order definable convex subgroups of a given ordered abelian group and (...) prove that the definable real valuation rings of k are in correspondence with the definable convex subgroups of the value group of a certain real valuation of k. (shrink)

L. van den Dries proved that the theory of n-valued rings has a model companion. We show here that this result is still true when the valuation rings are required to satisfy given inclusion relations (we restrict ourselves to the case of residual characteristic zero).

This contribution is concerned with a particular model theoretic semantics of the object language of quantum physics. The object language considered here comprises logically connected propositions, sequentially connected propositions and modal propositions. The model theoretic semantics arises from the already established dialogic semantics, if the pragmatic concept of the dialog-game is replaced by a "metaphysical" concept of the game. The game is determined by a game tree, the branches of which constitute a set, the set of "possible worlds" (...) of an individual quantum physical system. The semantic concepts like truth, falsity and valuation are defined with respect to this set. (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

This article uses the case of “social impact bonds” (SIBs) to explore the role of social science methods in new markets in “social investment.” Pioneered in the UK in 2010, SIBs use private capital to fund social programs with governments paying returns for successful outcomes. Central to the SIB model is the question of evaluation and the method to be used in determining program outcomes and investor returns. In the United States, the randomized controlled trial (RCT) has been the (...) dominant method. However, this has not been without controversy. Some SIB practitioners and investors have argued that, while this may be the perfect tool, the need to grow the SIB market demands a more pragmatic approach. Drawing from a three-year study of SIBs, and informed by Science and Technology Studies (STS)-inspired work on valuation and the social life of methods, the article explores RCTs as both a valuation technology central to SIB design and the object of a micropolitics of valuation which has impeded market growth. It is the relationship between, and the politics of, evaluation and valuation that is a key lesson of the SIB experiment and an important insight for future research on “social investment” and other settings where methods are constitutive of financial value. (shrink)

Theories of decision-making and its neural substrates have long assumed the existence of two distinct and competing valuation systems, variously described as goal-directed vs. habitual, or, more recently and based on statistical arguments, as model-free vs. model-based reinforcement-learning. Though both have been shown to control choices, the cognitive abilities associated with these systems are under ongoing investigation. Here we examine the link to cognitive abilities, and find that individual differences in processing speed covary with a shift from (...) model-free to model-based choice control in the presence of above-average working memory function. This suggests shared cognitive and neural processes; provides a bridge between literatures on intelligence and valuation; and may guide the development of process models of different valuation components. Furthermore, it provides a rationale for individual differences in the tendency to deploy valuation systems, which may be important for understanding the manifold neuropsychiatric diseases associated with malfunctions of valuation. (shrink)

We use the Drozd-Warfield structure theorem for finitely presented modules over a serial ring to investigate the model theory of modules over a serial ring, in particular, to give a simple description of pp-formulas and to classify the pure-injective indecomposable modules. We also study the question of whether every pure-injective indecomposable module over a valuation ring is the hull of a uniserial module.

Given a weakly o-minimal structure${\cal M}$and its o-minimal completion$\bar{{\cal M}}$, we first associate to$\bar{{\cal M}}$a canonical language and then prove thatTh$\left$determines$Th\left$. We then investigate the theory of the pair$\left$in the spirit of the theory of dense pairs of o-minimal structures, and prove, among other results, that it is near model complete, and every definable open subset of${\bar{M}^n}$is already definable in$\bar{{\cal M}}$.We give an example of a weakly o-minimal structure interpreting$\bar{{\cal M}}$and show that it is not elementarily equivalent to any (...) reduct of an o-minimal trace. (shrink)

Health care is not merely a matter of individual encounters between patients and physicians or other health care personnel. For patients and those who provide health care come to these encounters already possessed of learned habits of perception and judgment, valuation and action, which define their roles in relation to one another and affect every aspect of their encounter. So the presuppositions of these encounters must be examined if our understanding of patients' autonomy is to be complete. In this (...) paper I sketch three models of what is presupposed in the relationship between the health care professional and the lay patient; and I discuss the ways in which patients' autonomy is preserved and/or compromised under each of the three models. The models discussed are the Guild Model, the Commercial Model, and the Interactive Model. (shrink)

Despite the success of artificial intelligence, we are still far away from AI that model the world as humans do. This study focuses for explaining human behavior from intuitive mental models’ perspectives. We describe how behavior arises in biological systems and how the better understanding of this biological system can lead to advances in the development of human-like AI. Human can build intuitive models from physical, social, and cultural situations. In addition, we follow Bayesian inference to combine intuitive models (...) and new information to make decisions. We should build similar intuitive models and Bayesian algorithms for the new AI. We suggest that the probability calculation in Bayesian sense is sensitive to semantic properties of the objects’ combination formed by observation and prior experience. We call this brain process as computational meaningfulness and it is closer to the Bayesian ideal, when the occurrence of probabilities of these objects are believable. How does the human brain form models of the world and apply these models in its behavior? We outline the answers from three perspectives. First, intuitive models support an individual to use information meaningful ways in a current context. Second, neuroeconomics proposes that the valuation network in the brain has essential role in human decision making. It combines psychological, economical, and neuroscientific approaches to reveal the biological mechanisms by which decisions are made. Then, the brain is an over-parameterized modeling organ and produces optimal behavior in a complex word. Finally, a progress in data analysis techniques in AI has allowed us to decipher how the human brain valuates different options in complex situations. By combining big datasets with machine learning models, it is possible to gain insight from complex neural data beyond what was possible before. We describe these solutions by reviewing the current research from this perspective. In this study, we outline the basic aspects for human-like AI and we discuss on how science can benefit from AI. The better we understand human’s brain mechanisms, the better we can apply this understanding for building new AI. Both development of AI and understanding of human behavior go hand in hand. (shrink)

This paper formulates and axiomatizes utility models for denumerable time streams that make no commitment in regard to discounting future outcomes. The models address decision under certainty and decision under risk. Independence assumptions in both contexts lead to additive or multiplicative utilities over time periods that allow unambiguous comparisons of the relative importance of different periods. The models accommodate all patterns of future valuation. This discount-neutral feature is attained by restricting preference comparisons to outcome streams or probability distributions on (...) outcome streams that differ in at most a finite number of periods. (shrink)

According to Vázquez and Liz (Found Sci 16(4): 383–391, 2011), Points of View (PoV) can be considered in two different ways. On the one hand, they can be explained following the model of propositional attitudes. This model assumes that the internal structure of a PoV is constituted by a subject, a set of contents, and a set of relations between the subject and those contents. On the other hand, we can analyze points of view taking as a (...) class='Hi'>model the notions of location and access. If we choose to follow the second approach, instead of the first one, the internal structure of a PoV is not directly addressed, and the emphasized features of PoV are related to the function that PoV are intended to have. That is, PoV are directly identified by their role and they can solely be understood as ways of accessing the world that bring some kind of perspective about it. Having this in mind, we would like to propose a notation that explains how to understand such access as a sort of models (that can allow the creation of concepts), independently of whether the precise PoV under consideration is impersonal or non-impersonal, its kind of content, and its subjective or objective character. First, we will present an account of some previous approaches to the study of points of view. Then, we will analyze what kind of structure the world is assumed to posses and how the access to it is possible. Third, we will develop a notation that explains PoV as qualitative dimensions by means of which it is possible to valuate objects and states of the world. (shrink)

An exponential $\exp $ on an ordered field $$. The structure $$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp = 1$. This (...) study is mainly motivated by the Transfer Conjecture, which states as follows:Any o-minimal exponential field $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp =1$ is elementarily equivalent to $\mathbb {R}_{\exp }$.Here, $\mathbb {R}_{\exp }$ denotes the real exponential field $$, where $\exp $ denotes the standard exponential $x \mapsto \mathrm {e}^x$ on $\mathbb {R}$. Moreover, elementary equivalence means that any first-order sentence in the language $\mathcal {L}_{\exp } = \{+,-,\cdot,0,1, <,\exp \}$ holds for $$ if and only if it holds for $\mathbb {R}_{\exp }$.The Transfer Conjecture, and thus the study of o-minimal exponential fields, is of particular interest in the light of the decidability of $\mathbb {R}_{\exp }$. To the date, it is not known if $\mathbb {R}_{\exp }$ is decidable, i.e., whether there exists a procedure determining for a given first-order $\mathcal {L}_{\exp }$ -sentence whether it is true or false in $\mathbb {R}_{\exp }$. However, under the assumption of Schanuel’s Conjecture—a famous open conjecture from Transcendental Number Theory—a decision procedure for $\mathbb {R}_{\exp }$ exists. Also a positive answer to the Transfer Conjecture would result in the decidability of $\mathbb {R}_{\exp }$. Thus, we study o-minimal exponential fields with regard to the Transfer Conjecture, Schanuel’s Conjecture, and the decidability question of $\mathbb {R}_{\exp }$.Overall, we shed light on the valuation theoretic invariants of o-minimal exponential fields—the residue field and the value group—with additional induced structure. Moreover, we explore elementary substructures and extensions of o-minimal exponential fields to the maximal ends—the smallest elementary substructures being prime models and the maximal elementary extensions being contained in the surreal numbers. Further, we draw connections to models of Peano Arithmetic, integer parts, density in real closure, definable Henselian valuations, and strongly NIP ordered fields.Parts of this thesis were published in [2–5].Abstract prepared by Lothar Sebastian KrappE-mail: [email protected]: https://d-nb.info/1202012558/34. (shrink)

This thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$. Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$, for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises (...) the following structures: $$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$. We present a setting for the existence of a model-companion $TS$ of $T_S$. As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$, $\mathrm {SCF}_{e,p}$, $\mathrm {Psf}_p$, $\mathrm {ACFA}_p$, $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$, $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$, and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$, simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture : Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.prepared by Christian d’Elbée.E-mail: [email protected]: https://choum.net/~chris/page_perso. (shrink)

It is shown that the intuitionistic propositional calculus is sound and complete with respect to Kripke-style models that are not quasi-ordered. These models, called rudimentary Kripke models, differ from the ordinary intuitionistic Kripke models by making fewer assumptions about the underlying frames, but have the same conditions for valuations. However, since accessibility between points in the frames need not be reflexive, we have to assume, besides the usual intuitionistic heredity, the converse of heredity, which says that if a formula holds (...) in all points accessible to a point x, then it holds in x. Among frames of rudimentary Kripke models, particular attention is paid to those that guarantee that the assumption of heredity and converse heredity for propositional variables implies heredity and converse heredity for all propositional formulae. These frames need to be neither reflexive nor transitive. (shrink)

How do people use information from others to solve complex problems? Prior work has addressed this question by placing people in social learning situations where the problems they were asked to solve required varying degrees of exploration. This past work uncovered important interactions between groups' connectivity and the problem's complexity: the advantage of less connected networks over more connected networks increased as exploration was increasingly required for optimally solving the problem at hand. We propose the Social Interpolation Model (SIM), (...) an agent‐based model to explore the cognitive mechanisms that can underlie exploratory behavior in groups. Through results from simulation experiments, we conclude that “exploration” may not be a single cognitive property, but rather the emergent result of three distinct behavioral and cognitive mechanisms, namely, (a) breadth of generalization, (b) quality of prior expectation, and (c) relative valuation of self‐obtained information. We formalize these mechanisms in the SIM, and explore their effects on group dynamics and success at solving different kinds of problems. Our main finding is that broad generalization and high quality of prior expectation facilitate successful search in environments where exploration is important, and hinder successful search in environments where exploitation alone is sufficient. (shrink)

It is usually accepted in the literature that negation is a contradictory-forming operator and that two statements are contradictories if and only if it is logically impossible for both to be true and logically impossible for both to be false. These two premises have been used by Hartley Slater [Slater, 1995] to argue that paraconsistent negation is not a “real” negation because a sentence and its paraconsistent negation can be true together. In this paper we claim that a counterpart of (...) Slater´s argument can be directed against the negation operator of classical logic. Carnap’s discovery that there are models of classical propositional logic with non-standard or non-normal interpretations of the connectives will be used to build such an argument. One such non-normal valuation which can be added to the set of classically admissible valuations without altering the set of theorems or the set of valid consequences assigns true to every well-formed formula and, therefore, assigns a designated value to every formula and its negation. We ponder the consequences of these arguments for the claims that paraconsistent negations are not genuine negations and that the negation of classical logic is a contradictory-forming operator. (shrink)

Recent work in positive psychology demonstrates the importance of self-transcendence: understanding oneself to be part of something greater than the self, such as a family, community, or tradition of sacred practice. Self-transcendence is positively associated with wellbeing and a sense of meaning and purpose. Philosophers have argued that self-transcendent motivation has a central role in good character, or virtue. Positive psychologists are just now beginning to integrate the aim of developing such motivation in character interventions. In this paper we draw (...) attention to an important but overlooked condition on effectively developing self-transcendent motivation constitutive of virtue: such a process must engage the subject’s will in the right way. If a process does not meet this condition it will fail to produce motivation constitutive of virtue according to leading philosophical accounts of virtue. We identify a suite of strategies for cultivating motivations that do meet this condition but have not been explored in relation to character interventions, namely, reappraisal strategies from the extended process model of emotion regulation (EPM-ER). (shrink)

Seeking consensuses from the public is difficult, this also applies to the heritage sector, particularly in heritage preservation. ‘What, why and how to preserve?’ are the core of debates in the field and the differ- ences between points of views are basically due to the difference in valuation. In order to know everyone’s needs, views and expectations better and for sustainability, involving the community for preservation be- comes fundamental. Education, an experience which does not only provide opportunities for enlightenments (...) and widening horizons, but also introduce various concepts in terms of moral, ethical and social through systematic instructions. Having such great impact to community, promoting heritage education can be an effective approach awakening public consciousness on heritage preservation, and thus, enhancing people’s responsibility towards heritage, for both tangible and intangible, and developing a sustainable future for heritage through public engagement. However, it is necessary to understand the structure or the level of engagement prior setting the goal for heritage education. A model for classifying the level of engagement from performance is proposed for clarification and appraisal. This model is part of the research project of Community Engagement with Heritage in Macau which has an intention to examine its level of community engagement and give suggestions. This essay will first discuss community engagement, then classify the levels of engagement with models and lastly argue heritage education can elevate the level of community engagement which ultimately achieves the aim of heritage preservation. (shrink)

This paper explores the possibilities of the recognition and valuation of care by implementing an unconditional basic income and presents a feminist redefinition of the concept of a UBI. The author proposes the notion of a caring revolutionary transformation as a process of institutionalising the social and economic conditions for recognition of care which is a cornerstone of struggles for women’s emancipation and gender equity. It is a process of practically realisable transformative steps which together with their combined and (...) mutually reinforcing effects enable more radical social changes beyond a mere reform. The author argues that these transformative steps have to address two conditions embedded in the institutionalised structures of late modern capitalist society: the limited understanding of meaningful work as paid employment; and the liberal ideal of the independent and autonomous individual. Whereas a UBI can challenge the first condition, a public model of care questions the second condition by shifting the primary responsibility of care from the family towards a social solidarity. While insufficient when introduced separately, the combination of these two remedies has the potential to radically alter social structures on which gendered inequalities rest. (shrink)

Consumers can have difficulty expressing their buying intentions on an explicit level. The most common explanation for this intention-action gap is that consumers have many cognitive biases that interfere with decision making. The current resource-rational approach to understanding human cognition, however, suggests that brain environment interactions lead consumers to minimize the expenditure of cognitive energy. This means that the consumer seeks as simple of a solution as possible for a problem requiring decision making. In addition, this resource-rational approach to decision (...) making emphasizes the role of the principle of Occam’s Razor, inductive inference, and Bayesian reasoning by illuminating the human-environment relationship. This paper introduces the Consumer Contextual Decision-Making Model (CCDMM). Based on the CCDMM, two hypothetical strategies of consumer decision making will be presented. First, the SIMilarity-Strategy (SIMS) is one in which most of a consumer’s decisions in a real-life context are based on prior beliefs about the role of a commodities specific to real-life situation being encountered. Because beliefs are based on previous experiences, consumers are already aware of the most likely consequences of their actions. At the same time, they do not waste time on developing contingencies for what, based on previous experience, is unlikely to happen. Second, the What-is-Out-there-in-the-World-Strategy (WOWS) is one in which prior beliefs do not work in a real-life situation, requiring consumers to update their beliefs. The principle argument being made is that most experimental consumer research describes decision making based on the WOWS, when participants cannot apply their previous knowledge and situation-based strategy to problems. The article analyses sensory and cognitive biases described by behavioral economists from a CCDMM perspective, followed by a description and explanation of the typical intention-action gap based on the model. Prior to a section dedicated to discussion, the neuroeconomic approach will be described along with the valuation network of the brain, which has evolved to solve problems that the human has previously encountered in an information-rich environment. The principles of brain functions will also be compared to CCDMM. Finally, different approaches and the future direction of consumer research from a contextual point of view will be presented. (shrink)

Few other social technologies and institutions are more consequential to human societies than money. Yet money remains a deeply perplexing phenomenon. On the one hand, it is a pan-human system of valuation, but on the other, it is conventional and variable in its uses. While it is controversial if money instantiates a fully-fledged sign system, it is rife with semiotic capacities. To present an illuminating analysis of money is thus a test case for the Motivation & Sedimentation Model (...) (MSM) of meaning making, with roots in the phenomenology of Husserl and Merleau-Ponty. Using MSM, we analyze two origin accounts of money: the commodity money account evidenced in archaic and classical Greek coinage, and the credit money account exemplified by early findings in Mesopotamia. Both accounts focus on the interactions between the three levels of MSM: the pre-signitive Embodied, the cultural Sedimented, and the interactional Situated levels of meaning and propose different series of “loops” to account for the genesis of money. Despite key differences in the two origins, both imply semiotic processes operating according to motivated, and hence non-arbitrary, conventions developing within institutional formations that ultimately influenc present-day concepts of money. (shrink)

We give foundational results for the model theory of AfinK, the ring of finite adeles over a number field, construed as a restricted product of local fields. In contrast to Weispfenning we work in the language of ring theory, and various sortings interpretable therein. In particular we give a systematic treatment of the product valuation and the valuation monoid. Deeper results are given for the adelic version of Krasner's hyperfields, relating them to the Basarab–Kuhlmann formalism.

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets (...) of all the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

" In Imagination and the Meaningful Brain, psychoanalyst Arnold Modell claims that subjective human experience must be included in any scientific...

Abstract.Since the gene splicing debates of the 1980s, the public has been exposed to an ongoing sequence of genetic and reproductive technologies. Many issue areas have outcomes that lose track of people's inner values or engender opposing religious viewpoints defying final resolution. This essay relocates the discussion of what is an acceptable application from the individual to the societal level, examining technologies that stand to address large numbers of people and thus call for policy resolution, rather than individual fiat, in (...) their application. A major source of guidance is the “Genetic Frontiers” series of professional dialogues and conferences held by the National Conference for Community and Justice from 2002 to 2004. Genetic testing, human gene therapy, genetic engineering of plants and animals, and stem cell technology are examined. While differences in perspective on the beginning of life persist, a stepwise approach to the examination of genetic testing reveals areas of general agreement. Stewardship of life, human co‐creativity with the divine, and social justice help define the bounds of application of genetic engineering and therapy; compassionate care plays a major role in establishing stem cell policy. Active, sustained dialogue is a useful resource for enabling sharing of religious values and crystallization of policies. (shrink)

Aristotle is oftentimes viewed through a strictly philosophical lens as heir to Plato and has having introduced logical rigor where an emphasis on the theory of Forms formerly prevailed. It must be appreciated that Aristotle was the son of a physician, and that his inculcation of the thought of other Greek philosophers addressing health and the natural elements led to an extremely broad set of biologically- and medically-related writings. As this article proposes, Aristotle deepened the fourfold theory of the elements (...) with anatomic and physiologic observations. In books like History of Animals, Parts of Animals, and the lost Anatomai, he actively dissected organisms and recorded his findings. The corpus of medically-related literature Aristotle developed had a direct influence on subsequent Greek thinkers, including Galen, and on Medieval Islamic and modern Western practitioners such as William Harvey. Aristotle's ideas continue to influence modern medical thinkers in Europe and America through both his interpretation by European philosophers gaining the attention of medical humanists, and his writings' enduring impact on medical researchers balancing scientific with more personalistic approaches to medicine. (shrink)