scholarly journals Probabilistic justification logic

2020 ◽  
Vol 30 (1) ◽  
pp. 257-280
Author(s):  
Ioannis Kokkinis ◽  
Zoran Ognjanović ◽  
Thomas Studer
Keyword(s):  
Rational Belief ◽  
Satisfiability Problem ◽  
Uncertain Reasoning ◽  
Justification Logic ◽  
Lottery Paradox ◽  
Degrees Of Belief ◽  
Strong Completeness ◽  
Probabilistic Justification ◽  
Insight Into

Abstract We present a probabilistic justification logic, $\mathsf{PPJ}$, as a framework for uncertain reasoning about rational belief, degrees of belief and justifications. We establish soundness and strong completeness for $\mathsf{PPJ}$ with respect to the class of so-called measurable Kripke-like models and show that the satisfiability problem is decidable. We discuss how $\mathsf{PPJ}$ provides insight into the well-known lottery paradox.

Rational belief

1983 ◽  
Vol 6 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Henry E. Kyburg
Keyword(s):  
Inductive Logic ◽  
Bayes Theorem ◽  
Rational Belief ◽  
Degrees Of Belief ◽  
Probability Calculus ◽  
Probabilistic Rule ◽  
New Evidence ◽  
Normative Content ◽  
Interval Valued ◽  
Made In

AbstractThere is a tension between normative and descriptive elements in the theory of rational belief. This tension has been reflected in work in psychology and decision theory as well as in philosophy. Canons of rationality should be tailored to what is humanly feasible. But rationality has normative content as well as descriptive content.A number of issues related to both deductive and inductive logic can be raised. Are there full beliefs – statements that are categorically accepted? Should statements be accepted when they become overwhelmingly probable? What is the structure imposed on these beliefs by rationality? Are they consistent? Are they deductively closed? What parameters, if any, does rational acceptance depend on? How can accepted statements come to be rejected on new evidenceShould degrees of belief satisfy the probability calculus? Does conformity to the probability calculus exhaust the rational constraints that can be imposed on partial beliefs? With the acquisition of new evidence, should beliefs change in accord with Bayes' theorem? Are decisions made in accord with the principle of maximizing expected utility? Should they be?A systematic set of answers to these questions is developed on the basis of a probabilistic rule of acceptance and a conception of interval-valued logical probability according to which probabilities are based on known frequencies. This leads to limited deductive closure, a demand for only limited consistency, and the rejection of Bayes' theorem as universally applicable to changes of belief. It also becomes possible, given new evidence, to reject previously accepted statements.

scholarly journals First steps towards probabilistic justification logic

2015 ◽  
Vol 23 (4) ◽  
pp. 662-687 ◽  
Author(s):  
Ioannis Kokkinis ◽  
Petar Maksimović ◽  
Zoran Ognjanović ◽  
Thomas Studer
Keyword(s):  
Justification Logic ◽  
Probabilistic Justification

Attributing Knowledge

2020 ◽  
Author(s):  
Jody Azzouni
Keyword(s):  
Rational Belief ◽  
Cognitive Ethology ◽  
Lottery Paradox ◽  
Preface Paradox ◽  
Rational Agents ◽  
Correct Application ◽  
Mechanical Devices ◽  
The Preface Paradox ◽  
The Lottery Paradox ◽  
Knowledge Closure

The word “know” is revealed as vague, applicable to fallible agents, factive, and criterion-transcendent. It is invariant in its meaning across contexts and invariant relative to different agents. Only purely epistemic properties affect its correct application—not the interests of agents or those who attribute the word to agents. These properties enable “know” to be applied correctly—as it routinely is—to cognitive agents ranging from sophisticated human knowers, who engage in substantial metacognition, to various animals, who know much less and do much less, if any, metacognition, to nonconscious mechanical devices such as drones, robots, and the like. These properties of the word “know” suffice to explain the usage phenomena that contextualists and subject-sensitive invariantists invoke to place pressure on an understanding of the word that treats its application as involving no interests of agents, or others. It is also shown that the factivity and the fallibilist-compatibility of the word “know” explain Moorean paradoxes, the preface paradox, and the lottery paradox. A fallibility-sensitive failure of knowledge closure is given along with a similar failure of rational-belief closure. The latter explains why rational agents can nevertheless believe A and B, where A and B contradict each other. A substantial discussion of various kinds of metacognition is given—as well as a discussion of the metacognition literature in cognitive ethology. An appendix offers a new resolution of the hangman paradox, one that turns neither on a failure of knowledge closure nor on a failure of KK.

Rational Belief

2021 ◽  
pp. 171-196
Author(s):  
Daniel Whiting
Keyword(s):  
Rational Belief ◽  
Epistemic Rationality ◽  
Lottery Paradox ◽  
First Order ◽  
Modal Theory ◽  
Safety Condition ◽  
Closure Principles ◽  
Order Commitment ◽  
The Lottery Paradox

This chapter generalizes the modal theory of subjective reasons to the epistemic domain and combines it with the first-order commitment that truth is the sole right-maker for belief. The result is a modal account of epistemic rationality, according to which there is a safety condition on rational belief distinct from but mirroring the more familiar safety condition on knowledge. The chapter shows that the account delivers plausible closure principles on rational belief and offers a straightforward resolution of the lottery paradox. It also explores the implications of the view for whether it is rational to believe necessary propositions, preface propositions, and Moorean propositions.

Probability theory and epistemology

2018 ◽  
Author(s):  
Barry Loewer
Keyword(s):  
Probability Theory ◽  
Rational Belief ◽  
Bayesian Epistemology ◽  
Dutch Book ◽  
Degrees Of Belief ◽  
Rational Person ◽  
Degree Of Belief ◽  
New Evidence ◽  
Probabilistic Epistemology ◽  
Instrumental Goal

The primary uses of probability in epistemology are to measure degrees of belief and to formulate conditions for rational belief and rational change of belief. The degree of belief a person has in a proposition A is a measure of their willingness to act on A to obtain satisfaction of their preferences. According to probabilistic epistemology, sometimes called ‘Bayesian epistemology’, an ideally rational person’s degrees of belief satisfy the axioms of probability. For example, their degrees of belief in A and -A must sum to 1. The most important condition on changing degrees of belief given new evidence is called ‘conditionalization’. According to this, upon acquiring evidence E a rational person will change their degree of belief assigned to A to the conditional probability of A given E. Roughly, this rule says that the change should be minimal while accommodating the new evidence. There are arguments, ‘Dutch book arguments’, that are claimed to demonstrate that failure to satisfy these conditions makes a person who acts on their degrees of belief liable to perform actions that necessarily frustrate their preferences. Radical Bayesian epistemologists claim that rationality is completely characterized by these conditions. A more moderate view is that Bayesian conditions should be supplemented by other conditions specifying rational degrees of belief. Support for Bayesian epistemology comes from the fact that various aspects of scientific method can be grounded in satisfaction of Bayesian conditions. Further, it can be shown that there is a close connection between having true belief as an instrumental goal and satisfaction of the Bayesian conditions. Some critics of Bayesian epistemology reject the probabilistic conditions on rationality as unrealistic. They say that people do not have precise degrees of belief and even if they did it would not be possible in general to satisfy the conditions. Some go further and reject the conditions themselves. Others claim that the conditions are much too weak to capture rationality and that in fact almost any reasoning can be characterized so as to satisfy them. The extent to which Bayesian epistemology contributes to traditional epistemological concerns of characterizing knowledge and methods for obtaining knowledge is controversial.

Calibration problems in hydrogen luminosities

1966 ◽  
Vol 24 ◽  
pp. 322-330
Author(s):  
A. Beer
Keyword(s):  
Galactic Structure ◽  
B Stars ◽  
Insight Into

The investigations which I should like to summarize in this paper concern recent photo-electric luminosity determinations of O and B stars. Their final aim has been the derivation of new stellar distances, and some insight into certain patterns of galactic structure.

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