Normal Forms of Conditional Knowledge Bases Respecting Entailments and Renamings

Beierle, Christoph; Haldimann, Jonas

doi:10.1007/978-3-030-39951-1_2

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…We Among all belief bases that are observationally equivalent with respect to an inductive inference operator and a set of queries we want to select a unique representative. For this, we employ an ordering on the set of belief bases over NFC (Σ) as it is developed in (Beierle and Haldimann 2020a). This ordering uses signature renamings, where a function ρ : Σ → Σ is a renaming if ρ is a bijection.…”

Section: Observational Equivalence and Observational Normal Formmentioning

confidence: 99%

“…While recently, normal forms of conditional belief bases, containing conditionals of the form "If A then usually B", have gained some attention (e.g. (Beierle 2019;Beierle and Kutsch 2019a;2019b;Beierle and Haldimann 2020a;2020b;Beierle, Haldimann, and Kutsch 2021)), the main focus of research in conditional belief bases has been on different semantics (e.g., Lewis' system of spheres (Lewis 1973), conditional objects evaluated using boolean intervals (Dubois and Prade 1994), possibility distributions (Benferhat, Dubois, and Prade 1999), or ranking functions (Spohn 1988;2012)) and on general inference properties (e.g. (Adams 1965;Kraus, Lehmann, and Magidor 1990;Lehmann and Magidor 1992)).…”

Section: Introductionmentioning

confidence: 99%

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Observational Equivalence of Conditional Belief Bases

Beierle

Haldimann

Schwarzer

2023

FLAIRS

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In nonmonotonic reasoning, a conditional of the form ‘If A then usually B’ is typically accepted if a situation where both A and B hold is deemed to be more plausible, more probable, or less surprising, etc., than a situation where A holds, but B does not hold. In a propositional setting, this leads to a relation on the propositional interpretations, also called worlds, by comparing worlds according to their plausibility. In this paper, we address the question of which kind of relations on the set of worlds can be obtained by completing a conditional belief base via an inductive inference operator. As a key concept for our investigations, we introduce and employ the notion of observational equivalence of belief bases that takes an inductive inference operator and a set of queries into account. This leads to the notion of the observational normal form (ONF) and, by focussing on so-called base conditionals, to the base conditional normal form (BCNF). The acceptance of base conditionals corresponds to the plausibility ordering on possible worlds induced by an inference method. Both normal forms ONF and BCNF are combined with renamings as an additional dimension. We establish the interrelationships among the normal forms and evaluate them empirically with respect to systematically generated belief bases.

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Section: Observational Equivalence and Observational Normal Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observational Equivalence of Conditional Belief Bases

Beierle

Haldimann

Schwarzer

2023

FLAIRS

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“…Conditional knowledge is the knowledge that informants have when strategies, skills, and resources are used, why they are used, what conditions are needed for them to take place, and the best steps if there are several procedures (Beierle, C., & Haldimann, J. 2020).…”

Section: Conditional Knowledgementioning

confidence: 99%

Self-Regulatory Learning Patterns of Disabled Students at UIN Sunan Kalijaga Yogyakarta

Zamakhsari

Masruri

Sutrisno

2020

IJIEP

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This study aims to find the learning patterns of students with visual disabilities through self-regulation. This research approach is qualitative with phenomenological design and descriptive methods. This research study is a self-regulation pattern in students with visual disabilities by observing the interaction between students and the learning environment and social environments to achieve individual and academic goals. The author collected the data through interviews, observations, and documentation. This study concludes that this informants' metacognitive contribution provided positive and supportive directions for learning patterns based on students' self-regulation with visual disabilities UIN Sunan Kalijaga Yogyakarta. The self-regulation of informants in learning formed from this metacognitive knowledge relied on the sense of hearing. The strategy came from listening, taking, and reading notes.

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“…This article is a revised and largely extended version of [19], and it also extends our work presented in [20]. The extensions include in particular the development of a general notion of renaming normal form for arbitrary knowledge bases, the covering of renamings also across different signatures, the provision of algorithms for transforming knowledge bases into any of the normal forms, and the establishment of the formal relationship between normal form transformation on the one hand and the systematic generation of knowledge bases in ρRANF on the other hand.…”

Section: Introductionmentioning

confidence: 99%

Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings

Beierle

Haldimann

2021

Ann Math Artif Intell

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Conditionals are defeasible rules of the form If A then usually B, and they play a central role in many approaches to nonmonotonic reasoning. Normal forms of conditional knowledge bases consisting of a set of such conditionals are useful to create, process, and compare the knowledge represented by them. In this article, we propose several new normal forms for conditional knowledge bases. Compared to the previously introduced antecedent normal form, the reduced antecedent normal form (RANF) represents conditional knowledge with significantly fewer conditionals by taking nonmonotonic entailments licenced by system P into account. The renaming normal form(ρNF) addresses equivalences among conditional knowledge bases induced by renamings of the underlying signature. Combining the concept of renaming normal form with other normal forms yields the renaming antecedent normal form (ρ ANF) and the renaming reduced antecedent normal form (ρ RANF). For all newly introduced normal forms, we show their key properties regarding, existence, uniqueness, model equivalence, and inferential equivalence, and we develop algorithms transforming every conditional knowledge base into an equivalent knowledge base being in the respective normal form. For the most succinct normal form, the ρ RANF, we present an algorithm KBρra systematically generating knowledge bases over a given signature in ρ RANF. We show that the generated knowledge bases are consistent, pairwise not antecedentwise equivalent, and pairwise not equivalent under signature renaming. Furthermore, the algorithm is complete in the sense that, when taking signature renamings and model equivalence into account, every consistent knowledge base is generated. Observing that normalizing the set of all knowledge bases over a signature Σ to ρ RANF yields exactly the same result as KBρra (Σ), highlights the interrelationship between normal form transformations on the one hand and systematically generating knowledge bases in normal form on the other hand.

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Normal Forms of Conditional Knowledge Bases Respecting Entailments and Renamings

Cited by 4 publications

References 14 publications

Observational Equivalence of Conditional Belief Bases

Observational Equivalence of Conditional Belief Bases

Self-Regulatory Learning Patterns of Disabled Students at UIN Sunan Kalijaga Yogyakarta

Normal forms of conditional knowledge bases respecting system P-entailments and signature renamings

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