Jumping to explanations versus jumping to conclusions

Pino-Pérez, Ramón; Uzcátegui, Carlos

doi:10.1016/s0004-3702(99)00038-7

Cited by 25 publications

(56 citation statements)

References 14 publications

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“…In [9] and [10] similar ideas are developed, but with different motivations. In some situations, it might be relevant to find the most pertinent worlds that are models of a proposition B.…”

Section: Discussionmentioning

confidence: 99%

Logics for approximate and strong entailments

Esteva¹,

Godo²,

Rodríguez³

et al. 2012

Fuzzy Sets and Systems

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We consider two kinds of similarity-based reasoning and formalise them in a logical setting. In one case, we are led by the principle that conclusions can be drawn even if they are only approximately correct. This leads to a graded approximate entailment, which is weaker than classical entailment. In the other case, we follow the principle that conclusions must remain correct even if the assumptions are slightly changed. This leads to a notion of a graded strong entailment, which is stronger than classical entailment. We develop two logical calculi based on the notions of approximate and of strong entailment, respectively.

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“…In [9] and [10] similar ideas are developed, but with different motivations. In some situations, it might be relevant to find the most pertinent worlds that are models of a proposition B.…”

Section: Discussionmentioning

confidence: 99%

Logics for approximate and strong entailments

Esteva¹,

Godo²,

Rodríguez³

et al. 2012

Fuzzy Sets and Systems

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“…In this section, we consider the rationality postulates introduced by Pino-Perez and Uzcategui in [4]. It has been shown in [5] that all of them hold in the crisp case for ⊲ ℓc , while for ⊲ ℓne most of them hold and for a few of them only weaker forms are satisfied.…”

Section: Rationality Postulatesmentioning

confidence: 99%

“…[1] or [2,3] for fuzzy abduction), we focus on the search for minimal and consistent explanations of an observation, relying on the axiomatic approach proposed in [4]. Explicit explanatory relations satisfying the rationality axioms identified in [4] have been proposed in [5,6], based on operators from the mathematical morphology framework, in particular erosions. We extend this work by considering fuzzy sets of models, and mathematical morphology operators on them.…”

Section: Introductionmentioning

confidence: 99%

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A fuzzy extension of explanatory relations based on mathematical morphology

Atif¹,

Bloch²,

Distel³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In this paper, we build upon previous work defining explanatory relations based on mathematical morphology operators on logical formulas in propositional logics. We propose to extend such relations to the case where the set of models of a formula is fuzzy, as a first step towards morphological fuzzy abduction. The membership degrees may represent degrees of satisfaction of the formula, preferences, vague information for instance related to a partially observed situation, imprecise knowledge, etc. The proposed explanatory relations are based on successive fuzzy erosions of the set of models, conditionally to a theory, while the maximum membership degree in the results remains higher than a threshold. Two explanatory relations are proposed, one based on the erosion of the conjunction of the theory and the formula to be explained, and the other based on the erosion of the theory, while remaining consistent with the formula at least to some degree. Extensions of the rationality postulates introduced by Pino-Perez and Uzcategui are proposed. As in the classical crisp case, we show that the second explanatory relation exhibits stronger properties than the first one.

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“…Despite the absent of a general definition of explanation, there have been several attempts to develop a logical account of explanatory reasoning [1][2][3][4][5]7,[10][11][12]20,22,23]. Some of these attempts have followed the so-called KLM methodology developed by Kraus, Lehmann and Magidor and many others for the study of consequence relations (see [16,18,19] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Representation theorems for explanatory reasoning based on cumulative models

Diaz

Uzcátegui

2008

Journal of Applied Logic

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We show several representation theorems for explanatory reasoning based on cumulative models. An explanatory process is given by a binary relation £ between formulas in a propositional language where the intended meaning of α £ γ is "γ is a preferred explanation of α". To each cumulative model E (a variation of those studied by Kraus, Lehmann and Magidor) is associated an explanatory relation £ E . We show results of the following type: An explanatory relation £ satisfies certain logical postulates iff it coincides with £ E for some cumulative model E of the appropriate type.

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Jumping to explanations versus jumping to conclusions

Cited by 25 publications

References 14 publications

Logics for approximate and strong entailments

Logics for approximate and strong entailments

A fuzzy extension of explanatory relations based on mathematical morphology

Representation theorems for explanatory reasoning based on cumulative models

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