mlsanityData to 7 Oct 2026

On the KLM properties of a fuzzy DL with Typicality

arXiv 2106.00390 ↗First posted 1 Jun 2021cs.AIcited by 6

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Abstract (arXiv)

The paper investigates the properties of a fuzzy logic of typicality. The extension of fuzzy logic with a typicality operator was proposed in recent work to define a fuzzy multipreference semantics for Multilayer Perceptrons, by regarding the deep neural network as a conditional knowledge base. In this paper, we study its properties. First, a monotonic extension of a fuzzy ALC with typicality is considered (called ALC^FT) and a reformulation the KLM properties of a preferential consequence relation for this logic is devised. Most of the properties are satisfied, depending on the reformulation and on the fuzzy combination functions considered. We then strengthen ALC^FT with a closure construction by introducing a notion of faithful model of a weighted knowledge base, which generalizes the notion of coherent model of a conditional knowledge base previously introduced, and we study its properties.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 8 of its 52 references that are in the map. First posted on arXiv 1 Jun 2021.

Builds on

8 of 52 references.

References · 8

  1. 2020An ASP approach for reasoning in a concept-aware multipreferential lightweight DLcited by 12
  2. 2020Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network modelcited by 11
  3. 2018A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closurecited by 8
  4. 2018On Rational Entailment for Propositional Typicality Logiccited by 7
  5. 2021A conditional, a fuzzy and a probabilistic interpretation of self-organising mapscited by 6
  6. 2020On a plausible concept-wise multipreference semantics and its relations with self-organising mapscited by 5
  7. 2020A framework for a modular multi-concept lexicographic closure semanticscited by 5
  8. 2014The Complexity of Circumscription in DLscited by 3

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Cited by year

Citing papers per year: 2021: 3; 2022: 1; 2023: 2.

6 papers.

  1. 2022An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge basescited by 4
  2. 2021Weighted Conditional EL{^}bot Knowledge Bases with Integer Weights: an ASP Approachcited by 2
  3. 2023Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicalitycited by 2
  4. 2021From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Backcited by 1
  5. 2023A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicalitycited by 1
  6. 2021From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overviewcited by 0