1. University of Patras and CTI, Patras Multi-inference with Multi- neurules I. Hatzilygeroudis J. Prentzas 2 nd Panhellenic Conference on Artificial Intelligence, 11-12 April, 2002, Thessaloniki

2. Introductory observations Connectionist expert systems is an effort to integrate symbolic representation and neural networks (e.g. MACIE, Gallant 1988 & 1993, Ghalwash 1998) A disadvantage is the lack of naturalness in representation, inference and explanation Another disadvantage is the absolute reliance on empirical data Reason: they give pre-eminence to the connectionist framework both in representation and inference

3. Neurules Introduced by Hatzilygeroudis and Prentzas, 2000 & 2001 Give pre-eminence to the symbolic framework in representation Give pre-eminence to neurocomputing in the inference process

4. Neurules: the model C i : {1, 0, 0.5} {true, false, unknown} D : {1, -1} {success, failure}... D (sf 1 ) (sf 2 ) (sf n ) (sf 0 ) C 1 C 2 C n 1 f(x) x Neurule Adaline Unit

5. Neurules: the syntax (sf 0 ) if C 1 (sf 1 ), C 2 (sf 2 ), …, C n (sf n ) then D 1,D 2 C i : conditions (‘fever is high’) D i : conclusions (‘disease is inflammation’) sf 0 : bias factor sf i : significance factors variable predicate value

6. Neurules: disadvantages Create Neurule bases with multiple representations of the same piece of knowledge (due to the non-separability problem) The associated inference mechanism is rather connectionism oriented, thus reducing naturalness

7. Multi-neurules: the model... D C 1 C 2 C n ( CF 2 ) m ( CF 1 ) m (CF 0 ) m ( CF n ) m Multi-neurule Multi-adaline Unit i= 1, n (sf-tuples)

8. Multi-neurules: the syntax if C 1, C 2, … C n then D RF i = (sf 1i, sf 2i, …, sf ni ) i = 1, m (sf-sets) (sf 01, sf 02, …, sf 0m ) (sf 11, sf 12, …, sf 1m ) (sf 21, sf 22, …, sf 2m ) (sf n1, sf n2, …, sf nm ) RF 1 RF 2 RF m … size: m

9. An example NR5: (-2.2) if Treatment is Biramibio (-2.6), Treatment is Placibin (1.8) then Treatment is Posiboost NR6: (-2.2) if Treatment is Placibin (-1.8), Treatment is Biramibio (1.0) then Treatment is Posiboost NR5: (-2.2, -2.2) if Treatment is Placibin (-1.8, 1.8), Treatment is Biramibio (1.0, -2.6) then Treatment is Posiboost

10. Neurules evaluation (1) Known sum (weighted sum of evaluated conditions E) Remaining sum (largest possible weighted sum of unevaluated conditions U) Firing potential fp = A multi-neurule of size m has m different kn- sums, rem-sums and fps, one for each RF i. kn-sum rem-sum

11. Evaluated conditions: their value (true or false) has been known. If |kn-sum| > rem-sum (fp >1) or rem-sum=0 for a neurule: D = Neurules evaluation (2) 1 if kn-sum  0  fired D in WM -1 if kn-sum < 0  blocked  D in WM

12. Inference processes Connectionism-oriented process –The choice of the next neurule to be considered is based on fp. –Firing or blocking of a neurule results in updates of the fps of the affected neurules. Symbolism-oriented process –It is based on a backward chaining strategy and textual order.

13. Experimental results KB Connectionism oriented process Symbolism oriented process ASKEDEVALSASKEDEVALS ANIMALS (20 inferences) 162 (8.1),364 (18.2)142 (7.1)251 (12.5) LENSES (24 inferences) 79 (3.3)602 (25.1)85 (3.5)258 (10.8) ZOO (101 inferences) 1052 (10.4)8906 (88.2)1013 (10)1963 (19.4) MEDICAL (134 inferences) 670 (5)25031 (186.8)670 (5)11828 (88.3)

14. Multi-neurules result in more concise representation, at a possible expense of some naturalness The symbolism-oriented inference process, apart from being more natural, is also more efficient than the connectionism-oriented one Conclusions