This book is devoted to the presentation of the new quantum mechanical formalism based on the probability representation of quantum states. In the 20s and 30s it became evident that some properties in quantum mechanics can be assigned only to the quantum mechanical system, but not necessarily to its constituents. This led Einstein, Podolsky and Rosen (EPR) to their remarkable 1935 paper where they concluded that quantum mechanics is not a complete theory of nature (EPR paradox). In order to (...) avoid the contradiction which arises from instantaneous action at a distance mentioned above we introduce an extension of the canonical relativity by using measure algebra of physical events in Minkowski space-time. The canonical QM formalism is extended by additional new postulate of EPRB nonlocality for continuous and discrete observables, chapter I. The postulate of EPRB nonlocality is supported by new quantum mechanical formalism based on the probability representation of quantum states. Chapter II is devoted to the new quantum mechanical formalism based on the probability representation of quantum states. Chapter III is devoted to the Einstein's 1927 gedanken experiment resolution. Chapter IV is devoted to the EPR paradox resolution. Chapter V is devoted to the EPR-B paradox resolution. Chapter VI is devoted to the Schrödinger's cat (measured spin) paradox resolution. Chapter VII is devoted to the Bell inequalities revisited. Remind that the canonical arguments which were presented by many authors, namely, that violations of Bell type inequalities signal us that the classical Kolmogorovian model of probability is inapplicable to quantum phenomena. We claimed that the canonical assumption, under which Bell type inequalities were derived, is not supported by real physical nature of the EPRB experiments. The fundamental physical nature violations of the canonical Bell type inequalities explained by Postulate of EPR-Nonlocality and Heisenberg noise-disturbance uncertainty relations. (shrink)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the (...) introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common (...) cause is a shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

Research in multi-agent systems typically assumes a regulative model of social practice. This model starts with agents who are already capable of acting autonomously to further their individual ends. A social practice, according to this view, is a way of achieving coordination between multiple agents by restricting the set of actions available. For example, in a world containing cars but no driving regulations, agents are free to drive on either side of the road. To prevent collisions, we introduce (...) driving regulations, insisting that everyone drives on the left hand side of the road. We accept this limitation on our freedom because it lowers the probability of a collision. -/- This paper describes AI systems that are based on the constitutive view of social practice. According to this alternative view, there are certain actions that are only available to the agent because he is participating in a practice of a certain sort. For example, you can swing a peculiarly shaped piece of wood without participating in any particular practice - but this action will only constitute a strike if you are participating in a game of baseball. I can raise my hand whenever I like, but this only counts as voting for the motion within the institution of voting. But not all the examples are from frivolous, optional or institutional activities. Sellars and Brandom argue that even the fundamental act of assertion is only possible within the context of a particular social practice: the Game of Giving and Asking for Reasons. -/- The constitutive view, which is familiar to philosophers, is relatively unknown within the AI community. -/- The central aim of this paper is to show how the constitutive view of practice can be put to use in AI applications. (shrink)

Model of intelligence and new methods to assess IQ. MA thesis in 1998 (Comenius University). Art exhibitions "From Animation" London 2013, "Fading Memory" Weißenohe 2015, TAIF Tokyo 2017. Conferences in Santorini, Daejon 2016, Geneva 2017.

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements (...) about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into probabilities for individual patients. In the first step, a risk measure in a study population is generalized or extrapolated (...) to a target population. In the second step, the risk measure is particularized or transformed to yield probabilistic information relevant to a patient from the target population. Hence, we call the approach the Risk Generalization-Particularization (Risk GP) Model. There are serious problems at both stages, especially with the extent to which the required assumptions will hold and the extent to which we have evidence for the assumptions. Given that there are other models of prediction that use different assumptions, we should not inflexibly commit ourselves to one standard model. Instead, model pluralism should be standard in medical prediction. (shrink)

In this note, we consider a Merton model for default risk, where the firm’s value is driven by a Brownian motion and a compound Poisson process.

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should (...) be properly formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool. (shrink)

Although the cognition is significant in strategic reasoning, its role has been weakly analyzed, because only the average intelligence is usually considered. For example, prisoner's dilemma in game theory, would have different outcomes for persons with different intelligence. I show how various levels of intelligence influence the quality of reasoning, decision, or the probability of psychosis. I explain my original methodology developed for my MA thesis in clinical psychology in 1998, and grant research in 1999, demonstrating the bias of (...) the classic IQ method, and how the intelligence limits thinking. Based on that I defined Personality Model, providing insight into understanding of psychosis (schizophrenia, bi-polar), which has not been explained yet by psychology or psychiatry. In addition, it enables to analyze and assess non-linear problems, utilizable in computer programming, visualization (animation) or other fields including Baduk game. I've already applied some principles in complex information system www.each.co.uk, and video-animations exhibited in London, Germany, Tokyo. I need to mention my experience in chess composition between 1994 and 2000, winning a few international prizes and inventing a special class of fairy rules redefining the mate. The chess composition principles or patterns show the way to organize logical series to higher advanced mechanisms (like calculus), applicable to other fields. One of such principles is a logical aesthetic innovation: new strategy, defined by Italian composers. Finally I show how the simple redefinition of the classic utility concept links economics and psychology to explain irrational / destructive behavior. All presented results (from the research) can be repeated. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic knowledge or her semantics (...) for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

A reasoned argument or tarka is essential for a wholesome vāda that aims at establishing the truth. A strong tarka constitutes of a number of elements including an anumāna based on a valid hetu. Several scholars, such as Dharmakīrti, Vasubandhu and Dignāga, have worked on theories for the establishment of a valid hetu to distinguish it from an invalid one. This paper aims to interpret Dignāga’s hetu-cakra, called the wheel of grounds, from a modern philosophical perspective by deconstructing it into (...) a simple probabilistic mathematical model. The objective is to understand how and why a vāda based on a probabilistically weaker hetu can degrade into a Jalpa or vitaṇḍā. To do so, the paper maps the concept of ‘Bounded Rationality’ onto the hetu-cakra. Bounded Rationality, an idea coined by the management thinker Herbert Simon, is often employed in understanding decision-making processes of rational agents. In the context of this paper, the concept would state that the prativādin and ālocaka (debater) may not hold unbounded information to back their pratijñā (proposition). The paper argues that within the probabilistically deconstructed hetu-cakra model, most people argue in the ‘Zone of Bounded Rationality’, and thus, the probability of a debate degrading into Jalpa or vitaṇḍā is high. -/- . (shrink)

With the fast pace of AI development, the problem of preventing its global catastrophic risks arises. However, no satisfactory solution has been found. From several possibilities, the confinement of AI in a box is considered as a low-quality possible solution for AI safety. However, some treacherous AIs can be stopped by effective confinement if it is used as an additional measure. Here, we proposed an idealized model of the best possible confinement by aggregating all known ideas in the field (...) of AI boxing. We model the confinement based on the principles used in the safety engineering of nuclear power plants. We show that AI confinement should be implemented in several levels of defense. These levels include 1) AI design in fail-safe manner 2) limiting its capabilities, preventing self-improving and circuit breakers on treacherous turn 3) isolation from the outside world and, lastly, as the final hope 4) outside measures oriented on stopping AI in the wild. We demonstrate that the substantial number (more than 50 ideas listed in the article) of mutually independent measures could provide a relatively high probability of the containment of a human-level AI but may be not sufficient to preserve runaway of superintelligent AI. Thus, these measures will work only if they are used to prevent superintelligent AI creation, but not for containing superintelligence. We suggest that there could be a safe operation threshold, on which AI is useful, but is not able to hack containment system from the inside, the same way as a safe level of chain reaction inside nuclear power plants is maintained. However, overall, a failure of the confinement is inevitable, so we need to use the full AGI limited number of times (AI-ticks). (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the (...) class='Hi'>probability calculus. The previous attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had (...) B as their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to (...) be non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of. (shrink)

Purpose: This article aims to highlight key indicators of residents' quality of life in a specific contemporary building in Kruja, Albania. -/- Design/Method/Approach: A questionnaire with 30 questions was prepared for the inhabitance, and the Binary or Tobit probabilistic models were taken into consideration as part of the methodology, to conclude. The study will further analyze the implications of the inhabitants and their behavior in a specific contemporary building in the city of Kruja. It was examined the statistical significance of (...) each variable (questions) in the models elaborated with EViews 8 software. The stable models that are associated with the “Log-likelihood” statistics were statistically significant at a significance level of p < 5%, or with 95% confidence, based on the model tests. -/- Findings: The study concluded that the most statistically significant quality of life indicators part of the questionnaire is related to the typology of the apartments, methods of cooling during summer, present living conditions, apartment improvement, apartment orientation, and time spent in the living room. Furthermore, the study reveals that most of the quality-of-life indicators (part of the questionnaire) are not statistically important, so they will not be considered part of the models created in the article. The study reveals that increasing the living space and improving orientation is crucial to enhance the satisfaction of apartment inhabitants. When apartment sizes increase and orientation is improved, residents are more likely to opt for fans over air conditioners to reduce electricity costs and avoid installing additional cooling facilities during summer. They believe that better living conditions require larger apartments, additional water supply, increased electrical costs, and more time spent in the living room. The inhabitants also emphasize the importance of reducing moisture levels, decreasing window opening frequency, and increasing time spent with family. Interestingly, a one-degree improvement in summer cooling methods (e.g., switching from air blowers to air conditioning) corresponds to a one-degree improvement in winter heating methods (e.g., switching from gas to electricity), leading to a heightened need for clean electric heating. Overall, the study emphasizes the importance of meeting the physical and spatial needs of the residents to enhance their overall satisfaction and quality of life. Urban policies significantly impact housing affordability, quality, transport systems, environmental sustainability, and social equity, affecting overall living standards and economic growth. Cities must create well-designed policies that consider residents' needs and study findings to ensure sustainable development and citizen welfare. -/- Theoretical Implications: Gujarati’s (Basic Economics) theory was developed in the article. -/- Practical Implications: This study will serve as an indicator to analyze the further improvements that might occur in the specific building (not just in the city of Kruja), considering the main quality of life indicators. -/- Originality/Value: The article will serve as a base for further analysis of resident’s behavior and their social impact in the community in order to be aware of their needs for further developments in the construction field. -/- Research Limitations/Future Research: The findings depend profoundly on the type of building the residents are living in. The research stream that can be inspired by the research is strongly related to mathematical regression models, statistics, and probability. -/- Paper Type: Empirical . (shrink)

Abstract. In this article is presented a model of the change of the probability of the global catastrophic risks in the world with exponentially evolving technologies. Increasingly cheaper technologies become accessible to a larger number of agents. Also, the technologies become more capable to cause a global catastrophe. Examples of such dangerous technologies are artificial viruses constructed by the means of synthetic biology, non-aligned AI and, to less extent, nanotech and nuclear proliferation. The model shows at least (...) double exponential growth of the probability of the global catastrophe which means that the accumulated probability of the catastrophe will grow from negligible to overwhelming at the period of a few doubling times of the technological capabilities. For biotech and AI, such doubling time roughly corresponds to the doubling period of Moore’s law and its analogues in other technologies and is around 2 years. Thus the global catastrophe in the exponential technologies world will most likely happen during a “dangerous decade”. Such a dangerous decade could start as early as in the 2020s. We also found that the double exponential growth in the model makes the model less sensitive to its initial conditions, like the number of dangerous agents or initial probabilities constants. The model also shows that smaller catastrophes could happen earlier than larger ones, and such a smaller catastrophe may be able to stop the technological growth before larger ones become possible, thus global risks will be self-limiting. However, if the growth of the number of dangerous agents will be very quick, the multiple smaller catastrophes could happen simultaneously and will be equal to a global catastrophe. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees (...) of belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it (...) requires us to have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief for action, where those (...) consequences are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations. (shrink)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be (...) borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

This capstone project aimed to develop an offline computer-based assessment (CBA) tool that uses a computer instead of a traditional paper test in evaluating student learning. This addresses the difficulties faced by teachers in administering quarterly assessments. Incorporating technology into student assessment can increase student interest because of the immediate feedback generated automatically and can help teachers improve their work performance. This capstone project employed a developmental approach and utilized a modified ADDIE (Analysis, Design, and Development) model to design (...) the tool using Microsoft PowerPoint and Excel. Ten experts in mathematics, ICT, and assessment validated the face and content validity of the developed CBA tool. Based on the panel’s evaluation, the developed offline CBA tool in Statistics and Probability has passed all the assigned criteria, such as functionality, usability, efficiency, technicality, and accessibility. Overall, the developed CBA tool is suitable for use to address assessment-related issues. (shrink)

Descartes’ first book, 1618’s Compendium of Music, focuses on biomechanical reactions in the human body but also claims that the purpose of art is to arouse emotions. By the end of the 1630s, however, he had given up on precisely predicting how that arousal may occur. This article contends, though, that Descartes’ abandonment of that project is a result of using an inappropriate psychological model for such predictions. An appropriate model is developed in his last book, 1649’s The (...) Passions of the Soul. Especially by attending to generosity and desire, the probability of predicting aesthetic judgments is at least increased. In increasing it, Descartes’ abandonment need not be total. (shrink)

In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely (...) thought to undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

A theory of cognitive systems individuation is presented and defended. The approach has some affinity with Leonard Talmy's Overlapping Systems Model of Cognitive Organization, and the paper's first section explores aspects of Talmy's view that are shared by the view developed herein. According to the view on offer -- the conditional probability of co-contribution account (CPC) -- a cognitive system is a collection of mechanisms that contribute, in overlapping subsets, to a wide variety of forms of intelligent behavior. (...) Central to this approach is the idea of an integrated system. A formal characterization of integration is laid out in the form of a conditional-probabilitybased measure of the clustering of causal contributors to the production of intelligent behavior. I relate the view to the debate over extended and embodied cognition and respond to objections that have been raised in print by Andy Clark, Colin Klein, and Felipe de Brigard. (shrink)

In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the (...) density matrices induced by the experiments or `measurements' is the Lüders mixture operation as in QM. And finally by moving the machinery into the n-dimensional vector space over ℤ₂, different basis sets become different outcome sets. That `non-commutative' extension of finite probability theory yields the pedagogical model of quantum mechanics over ℤ₂ that can model many characteristic non-classical results of QM. (shrink)

The city of Kruja (Albania)contains three types of dwellings that date back to different periods of time: the historic ones, the socialist ones, the modern ones. This paper has to deal only with the historic building's typology. The questionnaire that is applied will be considered for the development of mathematical regression based on specific data for this category. Variation between the relevant variables of the questionnaire is fairly or inverse-linked with a certain percentage of influence. The aim of this study (...) is to have better insights into the important role of building occupancy, people's lifestyle, economic level, and the quality of life of the residents in the inner medieval citadel, the physics characteristics, and the energy efficiency of the historical dwellings. The variables such as the number of residents, quality of life, the surface of the dwellings, heating instruments and time spent in the dwelling, current living conditions, monthly bills, level of satisfaction, restoration, and building improvements, interact with each other with probabilities with different positive or negative percentages. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work (...) in neuroscience and behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

The title of this presentation encompasses three issues: (1) an enigmatic theme (the play of signs and signs of play); (2) a model of doing something, such as unraveling a puzzle; and (3) a methodology dealing with a probable case. Considering that the order of analysis runs in the opposite direction to the order of experience, my first task is to reverse the title. Then, its three parts become: (1) an eidetic and empirical conjunction that implies a taste for (...) evidence; (2) a rigorous model of analysis that implies a relationship between ontology (what I know) and epistemology (how I know); and (3) a case that brings an enigmatic theme. My title, based in the theme of our 42nd Annual Meeting, provided an experience peculiar to a non-native English speaker: how to interpret and use the word “play”. I really felt like I was a living exemplar of one of Professor Lanigan’s favorite examples: what dictionaries and encyclopedias say or do not say. Lanigan said that “dictionaries tell you how to use the words (forms, ideas) but not what word to use” and “encyclopedias tell you what facts to use (structure, experience), but not how to use them” (1992: 208–209). That was my situation with the word “play”. Webster’s dictionary gave me around fifty different meanings for the word “play”. Which one should I choose? I am sure that I made the best choice, as I will demonstrate throughout this presentation, organized around these three ideas that in an inverse order would be theory, method, and case. (shrink)

The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities. This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property, the system instantaneously transforms to one of the eigen states and thus we get only (...) a single value as outcome of the measurement. Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation. In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real world and will identify the root cause behind the stochastic nature of events. Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement. In the process of development of model, we will explain Schrodinger cat paradox and will show how Born’s rule for probability becomes a natural consequence of measurement process. (shrink)

Should we understand implicit attitudes on the model of belief? I argue that implicit attitudes are (probably) members of a different psychological kind altogether, because they seem to be insensitive to the logical form of an agent’s thoughts and perceptions. A state is sensitive to logical form only if it is sensitive to the logical constituents of the content of other states (e.g., operators like negation and conditional). I explain sensitivity to logical form and argue that it is a (...) necessary condition for belief. I appeal to two areas of research that seem to show that implicit attitudes fail spectacularly to satisfy this condition—although persistent gaps in the empirical literature leave matters inconclusive. I sketch an alternative account, according to which implicit attitudes are sensitive merely to spatiotemporal relations in thought and perception, i.e., the spatial and temporal orders in which people think, see, or hear things. (shrink)

I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.

Since the release of OpenAI's ChatGPT, the world has entered a race to develop more capable and powerful AI, including artificial general intelligence (AGI). The development is constrained by the dependency of AI on the model, quality, and quantity of training data, making the AI training process highly costly in terms of resources and environmental consequences. Thus, improving the effectiveness and efficiency of the AI training process is essential, especially when the Earth is approaching the climate tipping points and (...) planetary boundaries. It is evident that AI can function better when trained to mimic certain human mental processes. Based on insights from quantum mechanics and the informational entropy-based notion of value, we suggest AI developers can enhance the AI training processes' effectiveness and efficiency by creating and implementing parameter systems that are capable of effectively assigning probabilities to informational quanta. Such systems can help reduce entropy within the system, which lowers the energy required for data storage and processing while decreasing the likelihood of information loss during training. Successfully applying the concept of information entropy-based value in AI development will be crucial for advancing generative AI and achieving AGI in a sustainable manner. (shrink)

This paper generalises an argument for probabilism due to Lindley [9]. I extend the argument to a number of non-classical logical settings whose truth-values, seen here as ideal aims for belief, are in the set $\{0,1\}$, and where logical consequence $\models $ is given the “no-drop” characterization. First I will show that, in each of these settings, an agent’s credence can only avoid accuracy-domination if its canonical transform is a (possibly non-classical) probability function. In other words, if an agent (...) values accuracy as the fundamental epistemic virtue, it is a necessary requirement for rationality that her credence have some probabilistic structure. Then I show that for a certain class of reasonable measures of inaccuracy, having such a probabilistic structure is sufficient to avoid accuracy-domination in these non-classical settings. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson (...) is speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

Although probabilistic statements are ubiquitous, probability is still poorly understood. This shows itself, for example, in the mere stipulation of policies like expected utility maximisation and in disagreements about the correct interpretation of probability. In this work, we provide an account of probabilistic predictions that explains when, how, and why they can be useful for decision-making. We demonstrate that a calibration criterion on finite sets of predictions allows one to anticipate the distribution of utilities that a given policy (...) will yield. Based on this, we specify assumptions under which expected utility maximisation is a sensible decision criterion. We also introduce the notion of prediction methods, highlighting the dependence on schemes of abstraction, and argue that all probabilities are outputs of such prediction methods. This helps explain how the calibration criterion can be satisfied and shows that also supposedly objective probabilities are model-dependent. We compare our account of probability with conventional interpretations and show that it recovers key intuitions behind the latter. We, thus, provide a general account of what probabilities are and how they can enable successful decision-making under uncertainty. (shrink)

This study was a Persian-English comparative translation investigation on the selected poems of Forough- Farrokhzad, an influential contemporary Iranian poet. Two English translations were analyzed: one by a native Persian speaker, Sholeh Wolpé, an Iranian poet and translator, and the other by a non-native Persian speaker, Jascha Kessler, an American poet, writer and translator. The translations were reviewed according to Vinay and Darbelnet’s(1995) model which identifies two general translation strategies: direct and oblique, resembling literal versus free classifications, respectively, along (...) with their supplementary proce- dures in order to investigate the frequency of the application of each procedure by the two translators. After situating every line of the poems in the related categories, the number of times each procedure was em- ployed was examined. The findings indicated that both translators used the oblique strategy more than the direct one. The non-native translator, however, used the oblique strategy considerably more frequently com- pared to the native translator. Finally, new procedures called complementary procedures were proposed by the researchers to be added to Vinay and Darbelnet’s (1995) model in order to fill the gaps in the application of strategies and procedures to the poems of Forough Farrokhzad and probably other poems. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There are two parts. The notion of an "event" is reinterpreted from being an epistemological state of indefiniteness to being an objective state of indefiniteness. And the mathematical framework of finite probability theory is recast as the quantum probability calculus for QM/sets. (...) The point is not to clarify finite probability theory but to elucidate quantum mechanics itself by seeing some of its quantum features in a classical setting. (shrink)

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, (...) data will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree (...) in the context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

Shepard’s (1987) universal law of generalisation (ULG) illustrates that an invariant gradient of generalisation across species and across stimuli conditions can be obtained by mapping the probability of a generalisation response onto the representations of similarity between individual stimuli. Tenenbaum and Griffiths (2001) Bayesian account of generalisation expands ULG towards generalisation from multiple examples. Though the Bayesian model starts from Shepard’s account it refrains from any commitment to the notion of psychological similarity to explain categorisation. This chapter presents (...) the conceptual spaces theory (Gärdenfors 2000, 2014) as a mediator between Shepard’s and Tenenbaum & Griffiths’ conflicting views on the role of psychological similarity for a successful model of categorisation. It suggests that the conceptual spaces theory can help to improve the Bayesian model while finding an explanatory role for psychological similarity. (shrink)

We evaluate classical probability in relation to the random generation of a Shakespearean sonnet by a typing monkey and the random generation of universes in a World Ensemble based on various multiverse models involving eternal inflation. We calculate that it would take a monkey roughly 10^942 years to type a Shakespearean sonnet, which pushes the scenario into a World Ensemble. The evaluation of a World Ensemble based on various models of eternal inflation suggests that there is no middle ground (...) between eternal Poincare-Zermelo recurrence and a 0 probability in regards to the natural generation of the initial conditions of the universe. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure (...) that interacts directly with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage (...) is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price. (shrink)

A historical review and philosophical look at the introduction of “negative probability” as well as “complex probability” is suggested. The generalization of “probability” is forced by mathematical models in physical or technical disciplines. Initially, they are involved only as an auxiliary tool to complement mathematical models to the completeness to corresponding operations. Rewards, they acquire ontological status, especially in quantum mechanics and its formulation as a natural information theory as “quantum information” after the experimental confirmation the phenomena (...) of “entanglement”. Philosophical interpretations appear. A generalization of them is suggested: ontologically, they correspond to a relevant generalization to the relation of a part and its whole where the whole is a subset of the part rather than vice versa. The structure of “vector space” is involved necessarily in order to differ the part “by itself” from it in relation to the whole as a projection within it. That difference is reflected in the new dimension of vector space both mathematically and conceptually. Then, “negative or complex probability” are interpreted as a quantity corresponding the generalized case where the part can be “bigger” than the whole, and it is represented only partly in general within the whole. (shrink)

In his recent book Warranted Christian Belief (2000), Alvin Plantinga argues that the defender of naturalistic evolution is faced with adefeater for his position: as products of naturalistic evolution, we have no way of knowing if our cognitive faculties are in fact reliably aimed at the truth. This defeater is successfully avoided by the theist in that, given theism, we can be reasonably secure that out cognitive faculties are indeed reliable. I argue that Plantinga’s argument is ultimately based on a (...) faulty comparison, that he is comparing naturalistic evolution generally to one particular model of theism. In light of this analysis, the two models either stand or fall together with respect to the defeater that Plantinga offers. (shrink)