TY - GEN
T1 - On the KLM Properties of a Fuzzy DL with Typicality
AU - Giordano, Laura
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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 ALCFT ) 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 ALCFT 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.
AB - 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 ALCFT ) 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 ALCFT 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.
KW - Description logics
KW - Fuzzy logics
KW - Knowledge representation
KW - Preferential semantics
UR - https://www.scopus.com/pages/publications/85115855722
U2 - 10.1007/978-3-030-86772-0_40
DO - 10.1007/978-3-030-86772-0_40
M3 - Conference contribution
AN - SCOPUS:85115855722
SN - 9783030867713
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 557
EP - 571
BT - Symbolic and Quantitative Approaches to Reasoning with Uncertainty - 16th European Conference, ECSQARU 2021, Proceedings
A2 - Vejnarová, Jirina
A2 - Wilson, Nic
PB - Springer Science and Business Media Deutschland GmbH
T2 - 16th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2021
Y2 - 21 September 2021 through 24 September 2021
ER -