=Paper=
{{Paper
|id=Vol-3799/abstract2GDE24
|storemode=property
|title=Extended abstract: ππΆπ΄ππ - A forgetting technique
for XAI based on goal-directed constraint ASP models
|pdfUrl=https://ceur-ws.org/Vol-3799/abstract2GDE24.pdf
|volume=Vol-3799
|authors=Luciana Fidilio-Allende,JoaquΓn Arias
|dblpUrl=https://dblp.org/rec/conf/iclp/Fidilio-Allende24
}}
==Extended abstract: ππΆπ΄ππ - A forgetting technique
for XAI based on goal-directed constraint ASP models==
https://ceur-ws.org/Vol-3799/abstract2GDE24.pdf
Extended abstract: ππΆπ΄ππ - A forgetting technique
for XAI based on goal-directed constraint ASP models
Luciana Fidilio-Allende, Joaquin Arias
CETINIA, Universidad Rey Juan Carlos, MΓ³stoles, Spain
Abstract
This paper is an extended abstract of: L. Fidilio-Allende, J. Arias, ππΆπ΄ππ : A forgetting technique for XAI based
on goal-directed constraint ASP models, in: XXIII Jornadas sobre ProgramaciΓ³n y Lenguajes (PROLE), 2024. URL:
https://hdl.handle.net/11705/PROLE/2024/13. [1].
Keywords
Privacy, Value Awareness, XAI, ASP, s(CASP), Forgetting
The automation of all sorts of processes through Artificial Intelligence (AI) systems has made
significant progress. More recently, whether through self-regulation and soft law such as guidelines
or through legal regulation (e.g., the General Data Protection Regulation (GDPR) or the Regulation
on AI, both by the EU), it has become apparent that this development needs to be accompanied by
measures that safeguard the fundamental rights and safety of people affected by AI systems. In this
sense, Explainable Artificial Intelligence (XAI) [2] is of foremost importance to design trustworthy
systems. Proposals such as s(LAW) [3], which are based on Answer Set Programming, have shown
their ability to model values and explain the reasons for their decisions, thanks to their rule-based
models. But these explanations could lead to the disclosure of sensitive information, such as details
about victims of gender-based violence. This could violate the right to privacy and confidentiality, or
even cause legal issues, among other concerns. Although explanations can be adjusted to prevent leaks,
e.g., using the s(CASP) framework to control which elements are shown and/or hidden [4], adapting
the models requires the application of techniques such as forgetting (variable elimination) to avoid
revealing sensitive information during an audit. However, current forgetting techniques are mostly
only applied in propositional ASP programs, and they have limitations dealing with even loops.
In this work, we present ππΆπ΄ππ , a new forgetting technique that supports the presence of non-
stratified negations in Constraint Answer Set Programs. ππΆπ΄ππ is based on the dual rules of s(CASP), a
goal-directed CASP reasoner, and therefore, we believe that it can be applied to generic CASP programs
without grounding. We have validated our proposal by solving flagship examples from the literature,
and we plan to use this technique in the context of school places allocation while preserving the privacy
of victims of gender-based violence.
Table 1
Comparison of the more relevant forgetting operators vs. ππΆπ΄ππ
(UP) (SP) Loops Commutative Predicates Constraints
πππ [5] Yes No Yes No No No
πππ [6] Yes Maybe No No No No
*
πππ [7] Yes Maybe Yes Yes No No
ππ΄πΆ [8] Yes Yes Yes Yes No No
ππΆπ΄ππ Yes Yes Yes Yes Maybe Maybe
4th Workshop on Goal-directed Execution of Answer Set Programs (GDEβ24), October 12, 2024
$ luciana.fidilio@urjc.es (L. Fidilio-Allende); joaquin.arias@urjc.es (J. Arias)
0009-0004-7779-8265 (L. Fidilio-Allende); 0000-0003-4148-311X (J. Arias)
Β© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Figure 1: Sketch of the implementation of the predicate f_casp/4
1 f_casp (Flag, [Pred|Preds], P_0, P_Forgetting) :-
2 add_fact (Pred, P_0, P_11),
3 add_missing (Pred, P_11, P_12),
4 add_even_loop (Pred, P_12, P_13), % Step 1
5 gen_dual (Pred, P_13, Dual_Pred),
6 add_dual (P_13, Dual_Pred, P_2), % Step 2
7 forget_pred (Pred, P_2, P_31),
8 restore_even_loop (P_31, P_32), % Step 3
9 f_casp (Flag, Preds, P_32, P_Forgetting). % Repeat 1,2,3
10 f_casp (0, [], P_Forgetting, P_Forgetting). % Skip Step 4
11 f_casp (1, [], P_Forgetting, P_Scasp) :-
12 scasp_even_loop(P_Forgetting, P_Scasp). % Step 4
In Table 1, we compare fCASP with other relevant operators such as those described in [9]
and [10], evaluating its preliminary performance and properties. Through validation using literature
examples, we believe that ππΆπ΄ππ can generate programs with the same answer sets, even when
additional facts (when complying with UP) or propositional rules (when complying with SP) are added
to both programs, avoiding the removed or auxiliary predicates. Additionally, we have tested the
operator with programs involving even loops, and it can generate equivalent programs regardless of
the order in which predicates are removed, that is, it is commutative. In the future, there is potential to
extend it to programs with variables and constraints, thanks to the use of s(CASP) dual rules.
The preliminary design of the algorithm involves three steps repeated iteratively for each predicate
marked to be forgotten, plus a final optional step.
Figure 1 shows an implementation sketch of the operatorβs steps:
β’ The first step (lines 2 β 4) involves adding auxiliary predicates (neg_x) and clauses when the
predicate to be forgotten is part of an even loop, is a fact, or is a missing predicate.
β’ The second step (lines 5 and 6) is generating the dual rule of the predicate to forget, being the dual
rule the negated version of all the predicateβs clauses.
β’ The third step (lines 7 and 8) is forgetting the predicate, replacing its appearances with the content
of its clauses and its negation with the content of its dual rule.
β’ The final step (line 12) is transforming the double negations (not not) into even loops, as s(CASP)
does not explicitly support them. This step is optional.
We have performed an evaluation of fCASP using examples from the literature.
In the first example, we forget predicates in even loops. To conserve the symmetry in answer sets [11],
(preserving the predicates not forgotten in the answer sets even when adding additional rules), it is
necessary to add additional predicates (neg_x) as strong persistence (SP) cannot be achieved (in some
cases) without them [12, 8]. Below we can see the result of forgetting p and q, and the answer sets of
both the original program and the generated one. As they have the same answer sets (ignoring the
forgotten and auxiliary predicates), the programs are equivalent.
π1 = Example 3 from [12] ππΆπ΄ππ (π1 , {π, π})
{a, p}, {b, q} {a, neg_2}, {b, neg_1}
1 a :- p. 1 a :- not not neg_2.
2 b :- q. 2 b :- not not neg_1.
3 p :- not q. 3 neg_1 :- not not neg_1.
4 q :- not p. 4 neg_2 :- not neg_1.
In the second example, we forget predicates present in double negations. This case cannot be resolved
without the use of additional predicates. As we can see on the next example, both the original program
and the one generated with ππΆπ΄ππ forgetting p are equivalent.
π2 = Example 4 from [11] ππΆπ΄ππ (π2 , {π})
{p, q}, {r} {q}, {r, neg_1}
1 p :- not not p. 1 q :- not neg_1.
2 q :- p. 2 r :- not not neg_1.
3 r :- not p. 3 neg_1 :- not not neg_1.
In the third example we forget multiple predicates regardless of the order.
π3 = Example 1 from [7] ππΆπ΄ππ (π3 , {π, π}) and ππΆπ΄ππ (π2 , {π, π})
{p}, {q} {}, {neg_1}
1 a :- p, q. 1 a :- not neg_1, not not neg_1.
2 q :- not p. 2 neg_1 :- not not neg_1.
3 p :- not not p.
In the final example, we compare the performance of ππΆπ΄ππ with ππ΄πΆ , the operator that is closer to
the desired properties. As we can see, ππ΄πΆ may generate a program that outputs redundant answers,
while the one generated with ππΆπ΄ππ preserves the original count.
π4 = Example 5 from [8] ππ΄πΆ (π4 , {π}). ππΆπ΄ππ (π4 , {π}).
{c} {c}, {c, πΏπ } {c, neg_1}
1 q :- not not q, b. 1 a :- b, πΏπ. 1 a :- not neg_1, b.
2 a :- q. 2 c :- not πΏπ. 2 c :- not not neg_1.
3 c :- not q. 3 c :- not b. 3 c :- not b.
4 πΏπ :- not not πΏπ. 4 neg_1 :- not not neg_1.
5 neg_1 :- not b.
To evaluate the practicality of ππΆπ΄ππ , we have defined two (real) use cases in which we use the
operator to remove private and confidential information.
In the first use case, we model the Spanish Organic Law 2/2004, May 3, Articles 116 and 117 and
the Spanish Constitution Articles 27 and 149.1.30. This legislation establishes the criteria used for
assigning public school places in the Comunidad de Madrid, Spain, when the number of applications for
a given center is greater than the offer. After applying ππΆπ΄ππ , we can successfully remove the studentsβ
medical, socio-economical and gender-based violence related private information while conserving the
original model decisions and explainability, complying with the need for transparency required by the
applicable regulations such as the recent European AI Act.
In the second use case [13], we propose an automated decision-making system for energy assignment
in agricultural cooperatives. In this case, the energy is assigned based on how fairly the workers are
paid, pondering their salary and productivity, which are considered confidential and, in some cases,
private. After applying forgetting, we can preserve the confidentiality of the stakeholders without
affecting the decisions and justifications of the model, crucial to make these answers trustworthy.
In conclusion, we have presented a new forgetting operator, ππΆπ΄ππ , designed to work with goal-
directed Answer Set Programs and support dual rules and double negations while being commutative.
As potential lines of work for the future, we have identified the extension of the algorithm to support
variables and constraints, formally determining and proving ππΆπ΄ππ βs properties, and applying the
operator to real use cases.
References
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//hdl.handle.net/11705/PROLE/2024/13.
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