A Semantics for Hyperintensional Belief Revision Based on Information Bases

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided.

Tracking probabilistic truths: a logic for statistical learning

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds (or more generally, truth in all the worlds that are plausible enough). We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: (1) learning observable evidence obtained by repeated sampling from the unknown distribution; and (2) learning higher-order information about the distribution. The first changes only the plausibility map (via a ‘plausibilistic’ version of Bayes’ Rule), but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions (safe belief and statistical knowledge), as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense (statistical) knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning.

Somebody Knows

Several different notions of group knowledge have been extensively studied in the epistemic and doxastic logic literature, including common knowledge, general knowledge (everybody-knows) and distributed knowledge. In this paper we study a natural notion of group knowledge between general and distributed knowledge: somebody-knows. While something is general knowledge if and only if it is known by everyone, this notion holds if and only if it is known by someone. This is stronger than distributed knowledge, which is the knowledge that follows from the total knowledge in the group. We introduce a modality for somebody-knows in the style of standard group knowledge modalities, and study its properties. Unlike the other mentioned group knowledge modalities, somebody-knows is not a normal modality; in particular it lacks the conjunctive closure property. We provide an equivalent neighbourhood semantics for the language with a single somebody-knows modality, together with a completeness result: the somebody-knows modalities are completely characterised by the modal logic EMN extended with a particular weak conjunctive closure axiom. We also show that the satisfiability problem for this logic is PSPACE-complete. The neighbourhood semantics and the completeness and complexity results also carry over to logics for so-called local reasoning (Fagin et al. 1995) with bounded ``frames of mind'', correcting an existing completeness result in the literature (Allen 2005).

Bayesian Model for Covid-19 to Achieve Immunity by Parsimony of Exponential Functions Minimizing the Inoculum

A ribonucleoside analog MK-4482/EIDD-2801 blocks SARS-CoV-2 transmission in ferrets and might be able to diminish transmission until vaccineinduced or naturally acquired protective herd immunity is reached [1]. As skinner pointed out, behavioral problems have to be solved through behavioral engineering [2]. Cybernetics has full application in the present condition. As in alcohol consumption, smoking, drugs, gun crimes, wars, and sexually acquired diseases, the teleological Aristotelian causes are not tobacco, drugs, and any other issue, but the aberrant behavior. The situation is not trivial and involves non-classic logic and other mathematical logics [3,4]. The neural topography corresponds to the nucleus accumbens. The latter is the battlefield, and the subject’s obsession is the rise of the neurotransmitter dopamine [3,4]. In general, people are very demanding from their governments; nevertheless, at the same time, they are deeply tolerant with their aberrant behavior promoting the dissemination of the SARSCoV-2 [4,5]. This paper examines how to deal with this problem from a scientific perspective, considering probability methods and classical and doxastic logic, using the Parsimony Principle aiming to reach immunity by minimizing the inoculum.

Application of the Parsimony Principle of Exponential Functions to the Production of COVID-19 Immunity, According to Bayesian Theorem and Cybernetics, to Tame Anti-scientific Doxastic Logic and the Pandemic

The purpose of this work is to provide evidence to the scientific community that there is solid scientific knowledge available to tame the pandemic, which is mainly a behavioral problem that requires cybernetics through behavioral engineering. Scientifically it is clear that the problem of the pandemic originates in human behavior and misinformation. Behavioral problems are addressed by cybernetics through behavioral engineering. Aristotelian causes of the pandemic are aberrant behavior. This is the field of battle and the obsession of the subject is the rise of the neurotransmitter dopamine. The question is not what is the probability that a patient with COVID-19 has a certain symptom or sign? Rather it is to calculate the probability that a patient with a certain sign or symptom has COVID-19. Without grasping the differential equations modeled by Kermack and McKendrick, it is impossible to have an idea of what is happening in the pandemic. Our straightforward theoretical approach is to use the wild unmodified SARS-CoV-2 to produce immunity by the simple expedient of diminishing the amount of the inoculum to the minimum minimorum. The problem with allowing people, deliberately attempting herd immunity, is that it has the dire effect that a high percentage will necessarily die. It is a matter of competence between two exponential functions. On one hand the exponential reproduction of the virus, and on the other hand, the exponential production of antibodies and activation of T cells. The aim is to diminish the amount of the inoculum to the minimum minimorum capable of infecting the minimum susceptible cell subpopulation. In this manner, herd immunity could be reached, which would allow a parsimonical response in the viral exponential growth that would not overwhelm the exponential immune response. It is expected that susceptible subjects could be infected in a variolation modality through the universal use of masks, maximizing the distance, rather than in a noregulated exposure of a putative low-risk segment of the population. In the logic of the decision, we must distinguish a desideratum from what is physically, economically, legally, and politically implementable. It is a matter of policy-making supported by science and law instead of doxastic logic based on misinformation and bigotry. It is a matter of policy enforcement by cybernetics, by behavior engineering, not of a recommendation. The guidelines, if they are to be implemented, depend on the application of cybernetics, and behavioral engineering. The apodictic inference from fallacies, in a doxastic and desiderative logic, is the origin of disinformation. Keywords: COVID-19 Inoculum; Bayes Theorem; Cybernetics; Variolation; Herd immunity

Quantified Temporal Alethic Boulesic Doxastic Logic

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of $$T \times W$$ T × W models, and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper.

Rational requirements for suspended judgment

How does rationality bind the agnostic, that is, the one who suspends judgment about whether a given proposition is true? In this paper I explore two alternative ways of establishing what the rational requirements of agnosticism are: the Lockean–Bayesian framework and the doxastic logic framework. Each of these proposals faces strong objections. Fortunately, however, there is a rich kernel of requirements of agnosticism that are vindicated by both of them. One can then endorse the requirements that belong to that kernel without thereby committing oneself to the problematic implications that stem from either of the aforementioned proposals.

A three-valued doxastic logic based on Kleene’s and Bochvar’s ideas

W tym artykule zaproponuję konstrukcję trójwartościowej logiki przekonań, którą nazywam: LSB3_1 (skrót od: logika trójwartościowa dla typu silnej wiary). Podam również i udowodnię kompletność LSB3_1 w odniesieniu do danej semantyki. LSB3_1 opiera się na preformalnych założeniach i intuicjach, które przedstawiono w sekcji 1. Sekcja 2 zawiera składnię i podział instrukcji LSB3_1 na wewnętrzne i zewnętrzne. Rozdział 3 przedstawia semantykę LSB3_1, a także szereg tautologii i formuł nietautologicznych w LSB3_1 wraz z ich intuicyjną interpretacją. System aksjomatyczny dla LSB3_1 i jego porównanie z silną logiką Kleene'a są przedstawione w sekcji 4. Twierdzenie o kompletności dla LSB3_1 jest przedstawione w rozdziale 5. Zdefiniuję termin koniunkcyjna forma normalna i przedstawię lematy, które prowadzą do udowodnienia redukcji języka LSB3_1 wzory przed udowodnieniem twierdzenia o zupełności.