By Topic

Systems, Man and Cybernetics, IEEE Transactions on

Issue 12 • Date Dec 1994

Filter Results

Displaying Results 1 - 11 of 11
  • Conditional events in probability assessment and revision

    Publication Year: 1994 , Page(s): 1741 - 1746
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (592 KB)  

    By resorting to the general interpretation of an event as a proposition, we deal with its natural generalization, the concept of conditional event. No algebraic structure is put on the given family of conditional events. An important feature of our approach is that conditional probability makes sense also when the conditioning event is null. Our attention is centered on de Finetti's approach to probability, whose distinguishing features make it particularly flexible for application to both artificial intelligence and inferential statistics. In particular, the problem of comparing null events by means of conditional events is considered: so the need for the introduction of iterated conditioning naturally arises when we try to compare conditional events of zero conditional probability View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A theory of conditional information with applications

    Publication Year: 1994 , Page(s): 1676 - 1684
    Cited by:  Papers (4)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (892 KB)  

    The development of conditional propositions, deduction between conditionals, and boolean-like operations on conditionals, and their associated probabilities are here unified in terms of boolean relations of the form “b=0” defined on an initially relation-free algebra of boolean polynomials that transcends an initial domain of discourse. The conditional proposition (a|b) is assigned the conditional probability P(a|b), which is different from the probability that (a|b) is a tautology. The resulting algebraic techniques are demonstrated in several examples such as by simplifying a circular rule-based expert system and removing its circularity and by deriving logical and probability formulas for keeping communication lines open View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Toward a comprehensive theory of linguistic and probabilistic evidence: two new approaches to conditional event algebra

    Publication Year: 1994 , Page(s): 1685 - 1698
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1216 KB)  

    This paper first surveys the basic state-of-the art in modeling and combining conditional information, compatible with natural conditional probability evaluations via conditional event algebras. A critical analysis of the situation is given, where current approaches are based upon interpreting conditional events as event intervals. This includes the present problems of modeling conditional random variables, higher order conditionals, and the general incompatibility of these conditional event algebras with the traditional numerically-oriented approach using conditional likelihoods for the independent source case. To address these issues, two new approaches to conditioning are presented here. The first is based upon extending the usual arithmetic division operation to the case of zero denominators and is shown to lead to positive results for the above-mentioned higher order conditioning problem, as well as to a natural way to define fuzzy conditional sets. The second new approach is based upon a joint countable product space representation and not only leads to solutions to all three above problems, but also leads to reasonable definitions of fuzzy conditional sets. One drawback of this approach, however, is the increased computational complexity entailed in its implementation. This issue is also addressed in part. Finally, the techniques are shown to yield a more comprehensive way of dealing with either, or both, linguistic-based evidence and stochastic evidence View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Stone algebras, conditional events, and three valued logic

    Publication Year: 1994 , Page(s): 1699 - 1707
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (684 KB)  

    There are several equivalent ways to represent the set of conditional events, and in some the operations proposed by Goodman and Nguyen (1991) become much simpler, making the development of the theory much easier and much more concise. Such a development is carried out here using a representation whose relation to three-valued logic is analogous to that of Boolean algebras to two-valued logic, and in which the operations are simple and intuitive. There are many ways to extend the operations on events to operations on conditional events, but it is shown that there are only nine ways to extend intersection and nine ways to extend union so that the operations are Boolean polynomials of their arguments and are idempotent and commutative. Further, there is only one way to make such extensions so that the resulting structure is a bounded lattice extension of the space of events. These particular extensions turn out to be the operations proposed by Goodman and Nguyen View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Conditional objects as nonmonotonic consequence relationships

    Publication Year: 1994 , Page(s): 1724 - 1740
    Cited by:  Papers (5)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1684 KB)  

    This paper investigates the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning. Viewed as an inference rule expressing a contextual belief, the conditional object is shown to possess all properties of a well-behaved nonmonotonic consequence relation when a suitable choice of connectives and deduction operation is made. Using previous results from Adams' conditional probabilistic logic, a logic of conditional objects is proposed. Its axioms and inference rules are those of preferential reasoning logic of Lehmann and colleagues. But the semantics relies on a three-valued truth valuation first suggested by De Finetti. It is more elementary and intuitive than the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics. The analysis of a notion of consistency of a set of conditional objects is studied in the light of such a three-valued semantics and higher level counterparts of deduction theorem, modus ponens, resolution and refutation are suggested. Limitations of this logic are discussed View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • A history and introduction to the algebra of conditional events and probability logic

    Publication Year: 1994 , Page(s): 1671 - 1675
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (568 KB)  

    This article is meant to serve as an introduction to the following series of papers on various aspects of conditional event algebra and probability logic. It addresses the history of the problem and gives an overview of the development of the subject and its impact on the investigation of problems within AI View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Updating on conditional information

    Publication Year: 1994 , Page(s): 1708 - 1713
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (628 KB)  

    This paper, concentrating on deductions among conditional expressions, extends some previous ideas of the author as an alternative to the use of conditional event algebra. The approach taken here is through metalanguage-based “high probability relations”. Higher order conditionals are also treated in the same metalevel format, in contrast to the object language format of conditional event algebra. Other comparisons with conditional event algebra are also discussed, and a potentially promising technique is presented for connecting metalanguage probability relations with object language relations View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Probabilistic entailment of conditionals by conditionals

    Publication Year: 1994 , Page(s): 1714 - 1723
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (940 KB)  

    Symbolic logics that embody different theories of natural-language conditionals have been developed. One such logic is that of Ernest Adams. An Adams conditional α>β expresses the idea that the conditional probability Pr(β|α) is close to one; his logic may be used to reason about such ideas. In particular, Adam's logic may be used to reason about imperfect generalizations such as nearly every α is a β, provided that such a statement is taken to mean that the conditional probability that a randomly selected object is a β-given that it is an α-is close to one. In Adams' logic, a finite set of premises {φ11 ,...,φnn} is said to probabilistically entail a finite set of alternative conclusions {η 11,...,ηmm } iff, roughly speaking, whenever the conditional probabilities Pr(ψ11),...,Pr(ψnn) are all close to one, at least one of the conditional probabilities Pr(μ11),..., Pr(μm|η m) will also be close to one. Adams has developed a test for ascertaining whether a set of premises probabilistically entails a set of alternative conclusions. However, his test is computationally intensive. A new, more efficient test is presented in this paper. It also proves that the new test is valid View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Data exploration and conditional probability

    Publication Year: 1994 , Page(s): 1764 - 1766
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (188 KB)  

    It is possible to “read” the data of a 2×2 contingency table by interpreting the various proportions as “conditional probabilities”. If we interpret the probability P as degree of belief in the truth of an event E, then P can be looked on as a substitute of our relevant lack of information concerning the truth or falsity of E. In the same way we consider the conditional probability. A suitable interpretation of the concept of conditional event allows one to look at the so-called “Simpson's paradox”, from a different perspective. We give also a sufficient condition to avoid the paradox View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Conditional events, conditioning, and random sets

    Publication Year: 1994 , Page(s): 1755 - 1763
    Cited by:  Papers (6)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (840 KB)  

    A central problem in the Dempster/Shafer theory of evidence is conditioning. This paper presents a new approach to a solution of this problem by establishing a link between conditional events and discrete random sets. Conditional events are introduced as sets of equivalent events under conditioning. These sets may become targets of a multivalued mapping. Thus, conditional belief functions can be introduced. Both Bayesian and pure random set conditioning rules are derived and discussed. Random set conditioning allows expressing conditional degrees of belief when marginal beliefs are unknown. Finally, an updating rule is introduced that is equivalent to the law of total probability (Jeffrey's rule) if all beliefs are probabilities View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.
  • Coherent numerical and ordinal probabilistic assessments

    Publication Year: 1994 , Page(s): 1747 - 1754
    Cited by:  Papers (3)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (696 KB)  

    Conditions of coherence are given for generalized assessments of probability on arbitrary sets of conditional events, that is assessments including also imprecise values (probability intervals) and ordinal evaluations (comparative probabilities). Such coherence conditions ensure, like the well known de Finetti coherence condition for numerical probabilities, the possibility of extending generalized assessments of probability and preserving coherence. The main results demonstrate that the introduced coherence conditions are necessary and sufficient for the existence of a de Finetti coherent probability, agreeing with the generalized probabilistic assessment View full abstract»

    Full text access may be available. Click article title to sign in or learn about subscription options.