scholarly journals A logic with higher order conditional probabilities

2007 ◽  
pp. 141-154 ◽  
Author(s):  
Zoran Ognjanovic ◽  
Nebojsa Ikodinovic
Keyword(s):  
Conditional Probability ◽  
Probability Space ◽  
Possible Worlds ◽  
Axiomatic System ◽  
Probability Logic ◽  
Conditional Probabilities ◽  
Unconditional Probability ◽  
Possible World ◽  
Intended Meaning ◽  
Probability Operators

We investigate probability logic with the conditional probability operators This logic, denoted LCP, allows making statements such as: P?s?, CP?s(? | ?) CP?0(? | ?) with the intended meaning "the probability of ? is at least s" "the conditional probability of ? given ? is at least s", "the conditional probability of ? given ? at most 0". A possible-world approach is proposed to give semantics to such formulas. Every world of a given set of worlds is equipped with a probability space and conditional probability is derived in the usual way: P(? | ?) = P(?^?)/P(?), P(?) > 0, by the (unconditional) probability measure that is defined on an algebra of subsets of possible worlds. Infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. Decidability of the presented logic is proved.

scholarly journals A first-order conditional probability logic with iterations

2013 ◽  
Vol 93 (107) ◽  
pp. 19-27 ◽  
Author(s):  
Milos Milosevic ◽  
Zoran Ognjanovic
Keyword(s):  
Conditional Probability ◽  
Completeness Theorem ◽  
Axiomatic System ◽  
Probability Logic ◽  
Intended Meaning ◽  
First Order

We investigate a first-order conditional probability logic with equality, which is, up to our knowledge, the first treatise of such logic. The logic, denoted LFPOIC=, allows making statements such as: CP?s(?, ?), and CP?s(?, ?), with the intended meaning that the conditional probability of ? given ? is at least (at most) s. The corresponding syntax, semantic, and axiomatic system are introduced, and Extended completeness theorem is proven.

scholarly journals Completeness theorem for a logic with imprecise and conditional probabilities

2005 ◽  
Vol 78 (92) ◽  
pp. 35-49 ◽  
Author(s):  
Zoran Ognjanovic ◽  
Zoran Markovic ◽  
Miodrag Raskovic
Keyword(s):  
Probability Space ◽  
Probabilistic Models ◽  
Completeness Theorem ◽  
Probability Logic ◽  
Conditional Probabilities ◽  
Possible World

We present a prepositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripke-like probabilistic models is defined to give semantics to probabilistic formulas. Every possible world of such a model is equipped with a probability space. The corresponding probabilities may have nonstandard values. The proposition "the probability is close to r" means that there is an infinitesimal ?, such that the probability is equal to r ? ? (or r + ?). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.

Conditional Probability

2017 ◽  
Author(s):  
Kenny Easwaran
Keyword(s):  
Conditional Probability ◽  
Conditional Probabilities ◽  
Unconditional Probability

Conditional probability has been put to many uses in philosophy, and several proposals have been made regarding its relation to unconditional probability, especially in cases involving infinitely many alternatives that may have probability 0. This chapter briefly summarizes some of the literature connecting conditional probabilities to probabilities of conditionals and to Humphreys' Paradox for chances, and then investigates in greater depth the issues around probability 0. Approaches due to Popper, Rényi, and Kolmogorov are considered. Some of the limitations and alternative formulations of each are discussed, in particular the issues arising around the property of “conglomerability” and the idea that conditional probabilities may depend on a conditioning algebra rather than just an event.

scholarly journals A logic with conditional probability operators

2010 ◽  
Vol 87 (101) ◽  
pp. 85-96 ◽  
Author(s):  
Dragan Doder ◽  
Bojan Marinkovic ◽  
Petar Maksimovic ◽  
Aleksandar Perovic
Keyword(s):  
Conditional Probability ◽  
Decision Procedure ◽  
Conditional Probabilities ◽  
Linear Combinations ◽  
Complete Axiomatization ◽  
Probability Operators

We present a sound and strongly complete axiomatization of a reasoning about linear combinations of conditional probabilities, including comparative statements. The developed logic is decidable, with a PSPACE containment for the decision procedure.

The dependence of the majority voting decision-making probabilities on a multi-expert binary system experts number

2020 ◽  
pp. 7-14
Author(s):  
E. D. Avedyan ◽  
Le Thi Trang Linh
Keyword(s):  
Decision Making ◽  
Binary System ◽  
Conditional Probability ◽  
Majority Voting ◽  
Correct Solution ◽  
Conditional Probabilities ◽  
Analytical Results ◽  
Independent Expert ◽  
Mutually Independent

The article presents the analytical results of the decision-making by the majority voting algorithm (MVA). Particular attention is paid to the case of an even number of experts. The conditional probabilities of the MVA for two hypotheses are given for an even number of experts and their properties are investigated depending on the conditional probability of decision-making by independent experts of equal qualifications and on their number. An approach to calculating the probabilities of the correct solution of the MVA with unequal values of the conditional probabilities of accepting hypotheses of each statistically mutually independent expert is proposed. The findings are illustrated by numerical and graphical calculations.

A first-order conditional probability logic

2011 ◽  
Vol 20 (1) ◽  
pp. 235-253 ◽  
Author(s):  
M. Milosevic ◽  
Z. Ognjanovic
Keyword(s):  
Conditional Probability ◽  
Probability Logic ◽  
First Order

scholarly journals Mínimo e máximo em estruturas nominais – uma análise semântica

2019 ◽  
pp. 250-264
Author(s):  
Rui Marques
Keyword(s):  
Possible Worlds ◽  
Modal Operator ◽  
Possible World

This paper is concerned with the semantics of the portuguese phrases with the form o mínimo/máximo N (‘the minimum N’) and o mínimo/máximo de N (‘the minimum/maximum of N’). Some nouns may occur in both of these constructions, while others might occur in only one of them, and still other nouns might occur only if accompanied by a modal operator. The proposal is made that these facts can be straightforwardly explained by the hypothesis that the first and the second of these syntactic constructions have, respectively, an extensional and an intensional meaning, together with the fact that some nouns have the same denotation in any possible world, while others denote different sets of entities in different possible worlds.

scholarly journals Nonexistence, Vague Existence, Merely Possible Existence

Disputatio ◽  
2012 ◽  
Vol 4 (33) ◽  
pp. 427-443
Author(s):  
Iris Einheuser
Keyword(s):  
Possible Worlds ◽  
Target Object ◽  
Possible World ◽  
Plausible Assumption ◽  
De Re ◽  
Modal Semantics ◽  
Vague Existence

Abstract This paper explores a new non-deflationary approach to the puzzle of nonexistence and its cousins. On this approach, we can, under a plausible assumption, express true de re propositions about certain objects that don’t exist, exist indeterminately or exist merely possibly. The defense involves two steps: First, to argue that if we can actually designate what individuates a nonexistent target object with respect to possible worlds in which that object does exist, then we can express a de re proposition about “it”. Second, to adapt the concept of outer truth with respect to a possible world – a concept familiar from actualist modal semantics – for use in representing the actual world.

Analysing Modality

2020 ◽  
pp. 22-73
Author(s):  
Alastair Wilson
Keyword(s):  
Actual World ◽  
Possible Worlds ◽  
Modal Realism ◽  
Possible World ◽  
Metaphysical Modality ◽  
Novel Theory ◽  
Reductive Theory

This chapter presents and defends the basic tenets of quantum modal realism. The first of these principles, Individualism, states that Everett worlds are metaphysically possible worlds. The converse of this principle, Generality, states that metaphysically possible worlds are Everett worlds. Combining Individualism and Generality yields Alignment, a conjecture about the nature of possible worlds that is closely analogous to Lewisian modal realism. Like Lewisian modal realism, Alignment entails that each possible world is a real concrete individual of the same basic kind as the actual world. These similarities render EQM suitable for grounding a novel theory of the nature of metaphysical modality with some unique properties. Also like Lewisian modal realism, quantum modal realism is a reductive theory: it accounts for modality in fundamentally non-modal terms. But quantum modal realism also has unique epistemological advantages over Lewisian modal realism and other extant realist approaches to modality.

Counterfactual conditionals

2018 ◽  
Author(s):  
Frank Doring
Keyword(s):  
Possible Worlds ◽  
Laws Of Nature ◽  
Possible World ◽  
Counterfactual Conditional ◽  
Counterfactual Conditionals

‘If bats were deaf, they would hunt during the day.’ What you have just read is called a ‘counterfactual’ conditional; it is an ‘If…then…’ statement the components of which are ‘counter to fact’, in this case counter to the fact that bats hear well and sleep during the day. Among the analyses proposed for such statements, two have been especially prominent. According to the first, a counterfactual asserts that there is a sound argument from the antecedent (‘bats are deaf’) to the consequent (‘bats hunt during the day’). The argument uses certain implicit background conditions and laws of nature as additional premises. A variant of this analysis says that a counterfactual is itself a condensed version of such an argument. The analysis is called ‘metalinguistic’ because of its reference to linguistic items such as premises and arguments. The second analysis refers instead to possible worlds. (One may think of possible worlds as ways things might have gone.) This analysis says that the example is true just in case bats hunt during the day in the closest possible world(s) where they are deaf

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