How to Enrich Description Logics with Fuzziness

Size: px

Start display at page:

Download "How to Enrich Description Logics with Fuzziness"

Hester Cunningham
5 years ago
Views:

1 How to Enrich Description Logics with Fuzziness Martin Unold Christophe Cruz SAI Computing Conference London Martin Unold

2 Outline Description Logics (DL) in Artificial Intelligence (AI) Description Logics +Fuzziness Some Applications SAI Computing Conference London Martin Unold 2

3 DL in AI Description Logics in the field of Artificial Intelligence SAI Computing Conference London Martin Unold 3

4 Approaches in Artificial Intelligence Symbolic Complexity Structure Logic Abstraction Resolution Generalization Modules Numeric Noise Probabilities Values Graphical Expectation Optimization Regularization SAI Computing Conference London Martin Unold 4

5 (Crisp) Description Logic (DL) Logical formalisms to store and manage knowledge DL consists of Individuals Concepts Roles SAI Computing Conference London Martin Unold 5

6 Example DL with cities Individuals London, Paris, Berlin Concepts Town, City, Capital Roles NorthOf, NearBy, BiggerThan SAI Computing Conference London Martin Unold 6

7 Knowledge Base (KB) KB consists of Axioms Assertional Axioms An individual belongs to a certain concept Two individuals are connected by a role Terminological Axioms General Relation between Concepts and Roles SAI Computing Conference London Martin Unold 7

8 Example: Assertional Axioms London a Capital London northof Paris SAI Computing Conference London Martin Unold 8

9 Example: Terminological Axiom NorthOf is a Transitive Property SAI Computing Conference London Martin Unold 9

10 Example: Terminological Axiom NorthOf is a Transitive Property A northof B. B northof C. A northof C. SAI Computing Conference London Martin Unold 10

11 DL FL Description Logic extended to a Fuzzy Logic SAI Computing Conference London Martin Unold 11

12 Vagueness vs Uncertainty Vagueness Information is formulated in an inexact way. There is space for interpretation. Uncertainty It is unknown, if an information is correct. The information is either true or false. SAI Computing Conference London Martin Unold 12

13 Typical Axioms Vagueness Peter is tall. The tomato is ripe. Uncertainty P =NP. Tomorrow is doomsday. SAI Computing Conference London Martin Unold 13

14 Wheather forecast: 20% Rain tomorrow Vagueness Tomorrow it will rain rather light (with 20% intensity) Unsicherheit In 1 of 5 cases, it will rain tomorrow. In 4 of 5 cases, it will not rain tomorrow. SAI Computing Conference London Martin Unold 14

15 Wheather forecast: 90% Rain tomorrow Vagueness Tomorrow will rise a heavy thunderstorm. (with 90% intensity) Unsicherheit In 1 of 10 cases, it will not rain tomorrow. In 9 of 10 cases, it will rain tomorrow. SAI Computing Conference London Martin Unold 15

16 A is north of B (70%) Vagueness Where is A? Uncertainty Where is A? 30% B B 70% 30% SAI Computing Conference London Martin Unold 16

17 Implications for inference Transitive Property A northof B p. B northof C q. A northof C?. SAI Computing Conference London Martin Unold 17

18 Uncertainty (1) A northof B p. (2) B northof C q. (3) A northof C?. (1) and (2) true (3) true (probability: p*q) (1) and (2) false (3) false (probability: (1-p)*(1-q)) Unknown in the other cases SAI Computing Conference London Martin Unold 18

19 Uncertainty (1) A northof B p. (2) B northof C q. (3) A northof C [p*q,1-(1-p)*(1-q)]. SAI Computing Conference London Martin Unold 19

20 Vagueness (1) A northof B p. (2) B northof C q. (3) A northof C?. There is no correct way to calculate the value for (3) Only heuristic approaches SAI Computing Conference London Martin Unold 20

21 Vagueness Examples Product-Logic p*q Goedel-Logic min(p,q) Lukasiewicz-Logic max(p+q-1,0) SAI Computing Conference London Martin Unold 21

22 Applications Toponym Resolution Extension of SKOS ontology SAI Computing Conference London Martin Unold 22

23 Toponym Resolution X northof Paris 70%. London closeto X 90%. X a Town 80%. Goal: Where is X? SAI Computing Conference London Martin Unold 23

24 Toponym Resolution 24 SAI Computing Conference London Martin Unold 24

25 higeomes.org 25 SAI Computing Conference London Martin Unold 25

26 SKOS Roles Broader Narrower Match SAI Computing Conference London Martin Unold 26

27 i3mainz SAI Computing Conference London Martin Unold 27

28 Thank You For Your Attention SAI Computing Conference London Martin Unold 28

Application of Soft Computing Techniques in Water Resources Engineering

International Journal of Dynamics of Fluids. ISSN 0973-1784 Volume 13, Number 2 (2017), pp. 197-202 Research India Publications http://www.ripublication.com Application of Soft Computing Techniques in