# On the KLM properties of a fuzzy DL with Typicality

arXiv: https://arxiv.org/abs/2106.00390 · HTML: https://mlsanity.com/paper/2106.00390/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 52 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 8 of 8)

- [An ASP approach for reasoning in a concept-aware multipreferential lightweight DL](https://mlsanity.com/paper/2006.04387/) (2020)
- [Weighted defeasible knowledge bases and a multipreference semantics for a deep neural network model](https://mlsanity.com/paper/2012.13421/) (2020)
- [A Polynomial Time Subsumption Algorithm for Nominal Safe ELO_bot under Rational Closure](https://mlsanity.com/paper/1802.08201/) (2018)
- [On Rational Entailment for Propositional Typicality Logic](https://mlsanity.com/paper/1809.10946/) (2018)
- [A conditional, a fuzzy and a probabilistic interpretation of self-organising maps](https://mlsanity.com/paper/2103.06854/) (2021)
- [On a plausible concept-wise multipreference semantics and its relations with self-organising maps](https://mlsanity.com/paper/2008.13278/) (2020)
- [A framework for a modular multi-concept lexicographic closure semantics](https://mlsanity.com/paper/2009.00964/) (2020)
- [The Complexity of Circumscription in DLs](https://mlsanity.com/paper/1401.3476/) (2014)

## Built on by (most cited first, 6 of 6)

- [An ASP approach for reasoning on neural networks under a finitely many-valued semantics for weighted conditional knowledge bases](https://mlsanity.com/paper/2202.01123/) (2022)
- [Weighted Conditional EL{^}bot Knowledge Bases with Integer Weights: an ASP Approach](https://mlsanity.com/paper/2109.08286/) (2021)
- [Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality](https://mlsanity.com/paper/2303.04534/) (2023)
- [From Weighted Conditionals of Multilayer Perceptrons to Gradual Argumentation and Back](https://mlsanity.com/paper/2110.03643/) (2021)
- [A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality](https://mlsanity.com/paper/2305.00304/) (2023)
- [From Common Sense Reasoning to Neural Network Models through Multiple Preferences: an overview](https://mlsanity.com/paper/2107.04870/) (2021)

## 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.