Possibilistic and Probabilistic Logic under Coherence: Default Reasoning and System P

Coletti, Giulianella; Scozzafava, Romano; Vantaggi, Barbara

doi:10.1515/ms-2015-0060

Cited by 35 publications

(27 citation statements)

References 38 publications

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“…Based on Theorem 7, we can now really interpret the biconditional event A||B as the conjunction of the two conditionals pB|Aq and pA|Bq. Moreover, equations (18) and (19) represent what we call two-premise biconditional centering and one-premise biconditional centering respectively, that is tA, Bu |ù p A||B and AB |ù p A||B.…”

Section: Which Is Called Biconditional Introduction Rule With the Mamentioning

confidence: 99%

Probabilistic inferences from conjoined to iterated conditionals

Sanfilippo

Pfeifer

Over

et al. 2018

International Journal of Approximate Reasoning

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There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, Ppif A then Bq, is the conditional probability of B given A, PpB|Aq. We identify a conditional which is such that Ppif A then Bq " PpB|Aq with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals.

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Section: Which Is Called Biconditional Introduction Rule With the Mamentioning

confidence: 99%

Probabilistic inferences from conjoined to iterated conditionals

Sanfilippo

Pfeifer

Over

et al. 2018

International Journal of Approximate Reasoning

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“…When P(Ω 12 ) is a coherent prevision of Ω 12 ≡ { 1 Ω, 2 Ω} it follows that its marginal univariate random quantities, 1 Ω and 2 Ω, represent two separate and finite partitions of incompatible and exhaustive events whose non-negative probabilities sum to 1. Thus, conditions of coherence coincide with non-negativity and finite additivity (de Finetti, 1975), (Coletti, Scozzafava & Vantaggi, 2015), (Coletti, Petturiti & Vantaggi, 2014). We note a very important point: metric properties of the expected value allow us of rewriting some fundamental metric expressions.…”

Section: Metric Properties Of the Expected Value Into A Two-dimensionmentioning

confidence: 90%

An Original and Additional Mathematical Model Characterizing a Bayesian Approach to Decision Theory

Angelini¹

2019

JMR

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We propose an original mathematical model according to a Bayesian approach explaining uncertainty from a point of view connected with vector spaces. A parameter space can be represented by means of random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. We observe that metric properties of the notion of $\alpha$-product mathematically fulfill the ones of a coherent prevision of a bivariate random quantity. We introduce fundamental metric expressions connected with transformed random quantities representing changes of origin. We obtain a posterior probability law by applying the Bayes' theorem into a geometric context connected with a two-dimensional parameter space.

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“…The coherence-based approach to probability and to other uncertain measures has been adopted by many authors (see, e.g., [5,6,9,10,14,15,16,17,18,24,26,30,31,41,42,44]); we therefore recall only selected key features of coherence and its generalizations in this section. An event E is a two-valued logical entity which can be either true or false.…”

Section: Preliminary Notionsmentioning

confidence: 99%

Probabilistic squares and hexagons of opposition under coherence

Pfeifer

Sanfilippo

2017

International Journal of Approximate Reasoning

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Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the set of all coherent assessments. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers.

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Possibilistic and Probabilistic Logic under Coherence: Default Reasoning and System P

Cited by 35 publications

References 38 publications

Probabilistic inferences from conjoined to iterated conditionals

Probabilistic inferences from conjoined to iterated conditionals

An Original and Additional Mathematical Model Characterizing a Bayesian Approach to Decision Theory

Probabilistic squares and hexagons of opposition under coherence

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