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80
A Complete ManyValued Logic With ProductConjunction
, 1996
"... this paper we investigate some logics whose set of truth values is the real interval [0; 1] and we concentrate our attention to logics having a conjunction whose truth function t(x; y) is a tnorm, and having a corresponding residuated implication (or, as Pavelka [14] observes, the conjunction and t ..."
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Cited by 36 (8 self)
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this paper we investigate some logics whose set of truth values is the real interval [0; 1] and we concentrate our attention to logics having a conjunction whose truth function t(x; y) is a tnorm, and having a corresponding residuated implication (or, as Pavelka [14] observes, the conjunction and the implication form an adjoint couple); i.e., if i(x; y) is the truth function of the implication then
Common Sense and Maximum Entropy
 Synthese
, 2000
"... This paper concerns the question of how to draw inferences common sensically from uncertain knowledge. Since the early work of Shore and Johnson, [10], Paris and Vencovsk a, [6], and Csiszár, [1], it has been known that the Maximum Entropy Inference Process is the only inference process which obeys ..."
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Cited by 24 (3 self)
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This paper concerns the question of how to draw inferences common sensically from uncertain knowledge. Since the early work of Shore and Johnson, [10], Paris and Vencovsk a, [6], and Csiszár, [1], it has been known that the Maximum Entropy Inference Process is the only inference process which obeys certain common sense principles of uncertain reasoning. In this paper we consider the present status of this result and argue that within the rather narrow context in which we work this complete and consistent mode of uncertain reasoning is actually characterised by the observance of just a single common sense principle (or slogan).
HighLevel Primitives for Recursive Maximum Likelihood Estimation
 IEEE Trans. Automatic Control
, 1995
"... This paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms. ..."
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Cited by 17 (4 self)
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This paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood (ML) estimation algorithms.
Approaches to measuring inconsistent information
 Inconsistency Tolerance. Volume 3300 of Lecture Notes in Computer Science
, 2005
"... Abstract. Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the ba ..."
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Cited by 16 (9 self)
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Abstract. Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii’s work [48] for defining the quantity of information of a formula (or knowledgebase) in propositional logic. But this definition is not suitable when the knowledgebase is inconsistent. In this case, it has no classical model, so we have no “event ” to count. This is a shortcoming since in practical applications (e.g. databases) it often happens that the knowledgebase is not consistent. And it is definitely not true that all inconsistent knowledgebases contain the same (null) amount of information, as given by the “classical information theory”. As explored for several years in the paraconsistent logic community, two inconsistent knowledgebases can lead to very different conclusions, showing that they do not convey the same information. There has been some
Combining probabilistic logic programming with the power of maximum entropy
 ARTIF. INTELL
, 2004
"... This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic progra ..."
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Cited by 12 (3 self)
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This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the informationtheoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic programming under maximum entropy. The first one is based on the usual notion of entailment under maximum entropy, and is defined for the very general case of probabilistic logic programs over Boolean events. The second one is based on a new notion of entailment under maximum entropy, where the principle of maximum entropy is coupled with the closed world assumption (CWA) from classical logic programming. It is only defined for the more restricted case of probabilistic logic programs over conjunctive events. We then analyze the nonmonotonic behavior of both approaches along benchmark examples and along general properties for default reasoning from conditional knowledge bases. It turns out that both approaches have very nice nonmonotonic features. In particular, they realize some inheritance of probabilistic knowledge along subclass relationships, without suffering from the problem of inheritance blocking and from the drowning problem. They both also satisfy the property of rational monotonicity and several irrelevance properties. We finally present algorithms for both approaches, which are based on generalizations of techniques from probabilistic
Constructing a Logic of Plausible Inference: a Guide To Cox's Theorem
 International Journal of Approximate Reasoning
, 2003
"... Cox's Theorem provides a theoretical basis for using probability theory as a general logic of plausible inference. The theorem states that any system for plausible reasoning that satisfies certain qualitative requirements intended to ensure consistency with classical deductive logic and corresp ..."
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Cited by 11 (0 self)
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Cox's Theorem provides a theoretical basis for using probability theory as a general logic of plausible inference. The theorem states that any system for plausible reasoning that satisfies certain qualitative requirements intended to ensure consistency with classical deductive logic and correspondence with commonsense reasoning is isomorphic to probability theory. However, the requirements used to obtain this result have been the subject of much debate. We review Cox's Theorem, discussing its requirements, the intuition and reasoning behind these, and the most important objections, and finish with an abbreviated proof of the theorem.
In Defence of the Maximum Entropy Inference Process
, 1997
"... This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the Maximum Entropy Inference Process, ME, is the only inference process respecting 'common sense'. This result was criticised on the grounds that the probabilis ..."
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Cited by 11 (3 self)
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This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the Maximum Entropy Inference Process, ME, is the only inference process respecting 'common sense'. This result was criticised on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identied with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependant. In a nal section we however provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. Introduction and Notation In [1] we gave a justication of the Maximum Entropy Inference Process, ME, by characterising it as the unique probabilistic inference process satisfying a certain collection of common sense principles. In the years following that publication a number of criticisms of these principl...
A New Criterion for Comparing Fuzzy Logics for Uncertain Reasoning
, 1996
"... A new criterion is introduced for judging the suitability of various `fuzzy logics' for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated. Introductio ..."
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Cited by 9 (1 self)
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A new criterion is introduced for judging the suitability of various `fuzzy logics' for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated. Introduction It is a rather widespread assumption in uncertain reasoning, and one that we shall make for the purpose of this paper, that a piece of uncertain knowledge can be adequately captured by attaching a real number (signifying the degree of uncertainty) on some scale to some unequivocal statement or conditional, and that an intelligent agent's knowledge base consists of a large, but nevertheless nite, set K of such expressions. Whether or not this is the correct picture for animate intelligent agents such as ourselves is, perhaps, questionable, but it is certainly the case that many expert systems (which one might feel should be included under the vague title of `intelligent agent') have, by design...
A Semantics for Fuzzy Logic
 Soft Computing
, 1997
"... We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is us ..."
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Cited by 7 (0 self)
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We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Introduction In the literature the expression `Fuzzy Logic' is used in two separate ways (at least). One is where `truth values' are intended to stand for measures of belief (or condence, or certainty of some sort) and the expression `Fuzzy Logic' is taken as a synonym for the assumption that belief values are truth functional. That is, if w() denotes an agent's belief value (on the usual scale [0; 1]) for 2 SL, where SL is the set of sentences from a nite propositional language L built up using the connectives :; ^; _ (we shall consider implication later), then w satises w(:) = F: (w()); w( ^ ) = F^ (w(); w()); w( _ ) = F_ (w(); w()); (1) for some xed functions F: : [0; 1] ! [0; 1] and F^ ; F_ : [0; 1] 2 ! [0; 1]; where ; 2 SL. Two p...
The philosophical significance of Cox’s theorem
 International Journal of Approximate Reasoning
, 2004
"... Cox’s theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of par ..."
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Cited by 5 (2 self)
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Cox’s theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox’s theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox’s theorem.