Interpretable DNFs

Cl\'ement Carbonnel; Imane Bousdira; Martin C. Cooper

REVIEW 3 major objections 4 minor 25 references

Interpretable DNFs

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A boolean classifier is interpretable exactly when both it and its negation are short DNF formulas, and nested k-DNFs form a new such family that competes with decision trees.

desk verdict New interpretable model family with a clean bound, but the key expressivity proof is flawed and needs a real repair before the central comparison to decision trees can be trusted. read the letter →

arxiv 2505.21212 v1 pith:S5MF7JHJ submitted 2025-05-27 cs.AI

Martin C. Cooper , Imane Bousdira , Clément Carbonnel This is my paper

classification cs.AI MSC 06E3068Q32

keywords interpretablemachinelearningbooleanclassifiersDNFformulasabductiveexplanationsdecisiontreesnestedk-DNFcertificatecomplexityinducedmatchings

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

A classifier is called interpretable here when every decision has an abductive explanation involving at most $k$ features. For boolean features, the paper shows this is equivalent to both the classifier and its complement being expressible as $k$-DNF formulas, so interpretability reduces to a syntactic question about DNFs. It then introduces nested $k$-DNFs, whose terms are prefixes of rows of a $k\times k$ matrix of literals, and proves these are always $k$-AXp-interpretable. The paper claims every boolean function of $k$ variables can be written as a nested $k$-DNF, and that a simple heuristic learns such formulas with accuracy comparable to depth-$k$ decision trees while typically using fewer terms.

What carries the argument

The load-bearing object is the nested $k$-DNF: a $k\times k$ matrix of literals $L=(\ell_{i,j})$, where each term is $\bigwedge_{i=1}^k \bigwedge_{j=1}^{r_i} \ell_{i,j}$ for integers $r_i\ge0$ with $\sum_i r_i\le k$, so no term exceeds $k$ literals. The interpretability proof runs through the bipartite graph $G_D$ whose vertices are the literals and terms of a DNF $D$; if the largest induced matching in $G_D$ has size at most $k$, then every minimal transversal of $D$ has size at most $k$, so the complement is also a $k$-DNF and every decision has an explanation of size at most $k$. A counting argument (stars and bars) on the possible row sums then compares the family's expressiveness with depth-$k$ decision trees.

What would settle it

Take the parity function on three variables, $x_1\oplus x_2\oplus x_3$, and check whether it can be written as a nested $3$-DNF by allowing arbitrary literals (positive and negative) in a $3\times3$ matrix; if no such matrix exists, Proposition 3 is false for non-monotone functions and nested $k$-DNFs are strictly less expressive than depth-$k$ decision trees.

Watch

Extended reading notes

Core claim

The central discovery is that strong interpretability for boolean classifiers has a clean logical characterization: $\kappa$ is $k$-AXp-interpretable if and only if both $\kappa$ and $\overline{\kappa}$ are $k$-DNF formulas, making the pair of DNFs of small prime implicants the canonical description. On top of this, the paper defines nested $k$-DNFs -- disjunctions whose terms are the prefixes of rows of a single $k\times k$ literal matrix -- and proves that every such formula has bounded-size explanations. It further claims that nested $k$-DNFs capture every boolean function of $k$ variables, that for many feature counts they represent strictly more functions than depth-$k$ decision trees, and that a greedy learning heuristic attains accuracy comparable to those trees on a range of datasets.

Load-bearing premise

The proof that every boolean function of $k$ variables is a nested $k$-DNF builds each term from positive literals only; to cover functions such as XOR, the prefix construction must also work with negated literals, which the paper does not demonstrate.

Editorial extensions

If this is right

Every $k$-AXp-interpretable classifier can be written as a $k$-DNF with at most $k^k$ terms, so all decisions can be explained using at most $2k^k$ distinct explanations.
Nested $k$-DNFs always provide explanations of size at most $k$ for both positive and negative decisions, even when the same function cannot be represented by a decision tree of depth $k$.
For $k\ge4$ and $n\le 2^{2k-1}/k -1$ with $k^2\le n$, nested $k$-DNFs express more boolean functions than depth-$k$ decision trees.
The greedy learning heuristic matches depth-$k$ decision trees on eleven datasets and typically produces models with far fewer rules than the trees have leaves.
Because nested $k$-DNFs are always $k$-AXp-interpretable, the family qualifies as interpretable under the paper's formal definition, opening a route to interpretable models other than decision trees.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

As written, the proof of Proposition 3 constructs terms only from positive literals; a natural test is whether negated literals in the matrix suffice to express non-monotone functions such as parity, which would settle whether nested $k$-DNFs really match depth-$k$ decision trees in expressiveness.
The induced-matching condition suggests a larger unexplored family: any $k$-DNF whose literal-term graph has maximum induced matching at most $k$ is interpretable, so learning could target that broader class instead of the stricter prefix structure.
The reported run-to-run variance in accuracy indicates that exact search for optimal nested $k$-DNFs with small $k$ is a plausible next step; an exact learner would say whether the family's best models beat optimal depth-$k$ decision trees.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, the paper has a genuinely new idea: nested k-DNFs, a syntactic family of k-DNFs whose complements are also k-DNFs, with a sufficient condition based on induced matchings. Theorem 1's bound—every k-AXp-interpretable classifier has a k-DNF with at most k^k terms—looks correct and is sharp; that's a solid contribution on its own. Second, the main expressivity claim (Proposition 3: every boolean function of k variables is a nested k-DNF) is not proven as written. The construction in the proof ignores negated literals entirely, so it cannot handle non-monotone functions like XOR. And even for positive terms it is wrong: the r_i values it assigns sum to k, so the term it builds contains k literals, not the h literals of the target term. The stress-test note is right about this; I checked the algebra. This matters because the paper's motivation—nested k-DNFs as an alternative to depth-k decision trees—rests on that expressivity.

The supporting results are in better shape. Proposition 2's proof is fine. The induced-matching criterion (Lemma 2) is clean. Proposition 4's counting argument has a smaller problem: the stated range k≥4 is not supported; the inequalities only give the conclusion for k around 8 or higher. Not fatal, but it overstates the expressivity comparison.

The experiments are honest but preliminary. The heuristic is simple, the accuracy is comparable to CART rather than better, and there are no error bars or significance tests. The model-size comparison in Table 3 is suggestive but also unaccompanied by variance.

Net: this is a paper worth a serious referee, but the referee will need the authors to repair Proposition 3 or weaken the claim. If the expressivity can be fixed with a different matrix construction, the paper becomes a nice contribution to formal interpretability. If not, the family is still well-defined but the decision-tree comparison loses its backing. I'd send it to review with a clear request to address the proof gap. A reading group could have a useful discussion about what kinds of syntactic families can guarantee small explanations.

Recommendation: peer review, yes, with the Prop 3 issue as the main revision point.

Referee Report

3 major / 4 minor

Summary. This paper defines a k-AXp-interpretable boolean classifier as one for which every decision has an abductive explanation of size at most k, observes (Proposition 1) that this is equivalent to both the classifier and its complement being expressible as k-DNFs, and proves (Theorem 1) that such classifiers have a k-DNF with at most k^k terms. It then introduces nested k-DNFs, a matrix-prefix family of k-DNFs, proves they are k-AXp-interpretable via an induced-matching condition (Proposition 2), and claims that every boolean function of k variables is a nested k-DNF (Proposition 3). The paper also compares the number of nested k-DNFs with depth-k decision trees (Proposition 4) and reports experiments comparing a heuristic learner for nested k-DNFs with CART.

Significance. Proposition 1 and Theorem 1 are clean, self-contained contributions to the theory of interpretable boolean classifiers, and the induced-matching criterion in Proposition 2 is an elegant sufficient condition. The proposed family of nested k-DNFs is novel, and the heuristic is simple and reproducible. However, the paper's central expressivity claim (Proposition 3) is false, so the advertised parity with depth-k decision trees does not hold; this weakens the motivation for the family and for the experimental comparison. The experimental section is also too preliminary to establish competitiveness, as no variance or significance information is reported.

major comments (3)

[Section 5, Proposition 3] The proposition is false, not merely unproved. The proof uses a matrix L containing only positive literals, so it cannot generate terms with negated literals. For k=2, the XOR function (¬x1∧x2)∨(x1∧¬x2) is not expressible as a nested 2-DNF: the first column of the 2×2 literal matrix is fixed, so the same row prefix cannot provide both x1 and ¬x1 (nor both x2 and ¬x2) in different terms. Moreover, the prefix construction is internally inconsistent even for monotone terms: for a term t with h positive literals, the defined r_i sum to k, so the generated conjunction contains k literals; for k=3 and t=x1∧x2 the construction yields x1∧x2∧x3, not t. Consequently, the statement in Section 5 that nested k-DNFs can fit any consistent dataset when k equals the number of variables is unsupported, and the comparison in Figure 1 with depth-k decision trees rests on a false premise.
[Section 5, Proposition 4] The proof only supports k≥8, not k≥4. With the stated bounds log2 NDT ≤ (2^k−1)(2k−1−log2 k)+2^k and log2 Nnested ≥ 2^{2k−1}/k, substituting n = 2^{2k−1}/k gives log2 NDT > log2 Nnested for k=4,5,6,7; the inequality first holds at k=8. Either sharpen the bounds or restrict the statement to k≥8.
[Section 6, Table 2] The claim that nested k-DNFs are 'comparable' to depth-k decision trees is not supported statistically. The table reports only point averages, with no standard deviations, confidence intervals, or paired significance tests; Section 7 itself acknowledges variability across runs. Without these, differences of a few percentage points cannot be interpreted. Please report the variance and run appropriate tests, or temper the conclusion.

minor comments (4)

[Table 2] In the Monks-1, k=6 DNF column, '83,33' uses a comma as decimal separator; use a decimal point for consistency.
[Section 6.3 and Table 2] The two DNF columns are both labelled 'DNF'; the column for the complement experiment should be labelled, for example, 'DNF (complement)' or with an overline on κ.
[Section 6.2/6.3] It is unclear how the five train/test splits are defined for the Monks datasets, whose test sets are fixed; please clarify the protocol.
[Section 3, proof of Theorem 1] In Case 2, the sentence 'this is not possible because at least one term in Dκ contains Q′' is inaccurate when Q′ is itself an implicant; the argument can be repaired by noting that then all terms of S must equal Q′, so |S|=1 and |Dκ|<k^j. Please correct this step for readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's theoretical claims are proven in-text from independent definitions, and the empirical evaluation is separate from the derivation.

full rationale

The paper's central chain is self-contained rather than circular. It defines k-AXp-interpretability by explanation size, proves in Proposition 1 that this is equivalent to both a classifier and its complement being expressible as k-DNFs, and then constructs nested k-DNFs so that their associated bipartite graphs have induced matchings of size at most k. Proposition 2 then applies the independently proven Lemma 2. No parameter is fitted to data in order to establish these results; the learning heuristic in Section 6 is an empirical evaluation, not a source of the theoretical claims. The only overlapping-author citation, [8] in Example 2, provides an illustrative characterization of 2-DNFs whose complements are 2-DNFs, but this example is not load-bearing for the main theorems, which are proved directly. Concerns about Proposition 3 raised by a skeptical reading concern a possible gap in the proof of expressivity, which is a correctness issue, not a circularity issue: the statement is not assumed as an input, and no result is derived from itself. Therefore the paper does not exhibit the self-definitional, fitted-input, or self-citation patterns that would constitute circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 1 invented entities

The central theoretical claims rest on standard combinatorial tools (induction, pigeonhole, stars and bars) and on the paper's definition of interpretability. The nested k-DNF family is a new formal object, not an ungrounded postulate. The empirical comparison uses several hand-designed heuristic parameters that are not fitted in a principled way.

free parameters (4)

k (explanation-size bound) = 2, 3, 4, 5, 6 in experiments
Chosen by the user; controls model complexity and explanation length.
matrix construction limit = limit = min(k-j, ceil(2(n-j)/i - 1))
Hand-designed rule in Algorithm 1 to control literal diversity; not learned from data.
literal score G = G = Ec1 - Ec0
Score used to select the next literal in the matrix; a heuristic choice.
term selection / pruning thresholds = Q < P; cover class-1 with no class-0
Criteria for accepting or pruning terms; chosen by the authors.

assumptions (5)

standard math Induction principle
Used in the proof of Theorem 1.
standard math Pigeonhole principle
Used in Proposition 2 to show no induced matching of size k+1.
standard math Stars-and-bars counting
Used in Proposition 4 to count nested k-DNF terms.
standard math Hypergraph dualisation property
Used in Section 4 to characterize the complement of a DNF via transversals.
domain assumption AXp-based interpretability definition
The paper adopts the criterion that all decisions have short abductive explanations; this is a modeling choice, not a theorem.

invented entities (1)

Nested k-DNFs
purpose: A new family of interpretable boolean classifiers with bounded explanation size.
The family is a formal construction introduced by the authors; its utility is tested within the paper, not by external predictions.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Interpretable DNFs." pith.science (2026). https://pith.science/paper/S5MF7JHJ

@misc{pith2026250521212,
  author       = {Pith},
  title        = {Pith review of: Interpretable DNFs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/S5MF7JHJ}},
  note         = {Machine review of arXiv:2505.21212}
}

abstract

A classifier is considered interpretable if each of its decisions has an explanation which is small enough to be easily understood by a human user. A DNF formula can be seen as a binary classifier $\kappa$ over boolean domains. The size of an explanation of a positive decision taken by a DNF $\kappa$ is bounded by the size of the terms in $\kappa$, since we can explain a positive decision by giving a term of $\kappa$ that evaluates to true. Since both positive and negative decisions must be explained, we consider that interpretable DNFs are those $\kappa$ for which both $\kappa$ and $\overline{\kappa}$ can be expressed as DNFs composed of terms of bounded size. In this paper, we study the family of $k$-DNFs whose complements can also be expressed as $k$-DNFs. We compare two such families, namely depth-$k$ decision trees and nested $k$-DNFs, a novel family of models. Experiments indicate that nested $k$-DNFs are an interesting alternative to decision trees in terms of interpretability and accuracy.

Figures

Figures reproduced from arXiv: 2505.21212 by the authors.

**Figure 1.** The landscape of k-AXp-interpretable classifiers κ be represented as a nested k-DNF formula is a well-defined measure that cannot exceed the number of variables (as is the case for decision trees of depth k). One criterion for comparing families of models M is to estimate the number of distinct functions that can be represented by M. Let NDT (k, n) and Nnested (k, n) be, respectively, the number of functions repre… view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

25 extracted references · 24 canonical work pages

[1]

Axiomatic foundations of explainability

Leila Amgoud and Jonathan Ben-Naim. Axiomatic foundations of explainability. In Luc De Raedt, editor, IJCAI, pages 636–642. ijcai.org, 2022

work page 2022
[2]

Computational Com- plexity: A Modern Approach

Sanjeev Arora and Boaz Barak. Computational Com- plexity: A Modern Approach . Cambridge University Press, USA, 1st edition, 2009

work page 2009
[3]

On the computational intelligibility of boolean classifiers

Gilles Audemard, Steve Bellart, Louenas Bounia, Fr´ed´eric Koriche, Jean-Marie Lagniez, and Pierre Mar- quis. On the computational intelligibility of boolean classifiers. In Meghyn Bienvenu, Gerhard Lakemeyer, and Esra Erdem, editors, KR, pages 74–86, 2021

work page 2021
[4]

Model interpretability through the lens of computational complexity

Pablo Barcel ´o, Mika ¨el Monet, Jorge P ´erez, and Bernardo Subercaseaux. Model interpretability through the lens of computational complexity. In Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin, editors, NeurIPS, 2020

work page 2020
[5]

Hypergraphs: Combinatorics of finite sets

Claude Berge. Hypergraphs: Combinatorics of finite sets. 1989

work page 1989
[6]

The query complexity of certification

Guy Blanc, Caleb Koch, Jane Lange, and Li-Yang Tan. The query complexity of certification. In Stefano Leonardi and Anupam Gupta, editors, STOC ’22: 54th Annual ACM SIGACT Symposium on Theory of Com- puting, pages 623–636. ACM, 2022

work page 2022
[7]

Leo Breiman, J. H. Friedman, Richard A. Olshen, and C. J. Stone. Classification and Regression Trees . Wadsworth, 1984

work page 1984
[8]

Cooper, and Jo ˜ao Marques-Silva

Cl´ement Carbonnel, Martin C. Cooper, and Jo ˜ao Marques-Silva. Tractable explaining of multivariate de- cision trees. In Pierre Marquis, Tran Cao Son, and Gabriele Kern-Isberner, editors, KR, pages 127–135, 2023

work page 2023

Show all 25 references

[9]

Diameter versus cer- tificate complexity of boolean functions

Siddhesh Chaubal and Anna G ´al. Diameter versus cer- tificate complexity of boolean functions. In Filippo Bonchi and Simon J. Puglisi, editors,46th International Symposium on Mathematical Foundations of Computer Science, MFCS , volume 202 of LIPIcs, pages 31:1– 31:22. Schloss...

2021
[10]

Cooper and Leila Amgoud

Martin C. Cooper and Leila Amgoud. Abductive ex- planations of classifiers under constraints: Complexity and properties. In Kobi Gal, Ann Now ´e, Grzegorz J. Nalepa, Roy Fairstein, and Roxana Radulescu, editors, ECAI, volume 372 of Frontiers in Artificial Intelligence and Appl...

2023
[11]

Cooper and Jo ˜ao Marques-Silva

Martin C. Cooper and Jo ˜ao Marques-Silva. Tractabil- ity of explaining classifier decisions. Artif. Intell., 316, 2023

2023
[12]

Blossom: an anytime algorithm for computing optimal decision trees

Emir Demirovic, Emmanuel Hebrard, and Louis Jean. Blossom: an anytime algorithm for computing optimal decision trees. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett, editors, ICML, volume 202, pages 7533–7562. PMLR, 2023

2023
[13]

Bounds on depth of decision trees derived from decision rule systems with discrete attributes

Kerven Durdymyradov and Mikhail Moshkov. Bounds on depth of decision trees derived from decision rule systems with discrete attributes. Ann. Math. Artif. In- tell., 92(3):703–732, 2024

2024
[14]

Cooper, Nicholas Asher, and Jo˜ao Marques-Silva

Xuanxiang Huang, Yacine Izza, Alexey Ignatiev, Mar- tin C. Cooper, Nicholas Asher, and Jo˜ao Marques-Silva. Tractable explanations for d-DNNF classifiers. InAAAI, pages 5719–5728. AAAI Press, 2022

2022
[15]

Stuckey, and Jo˜ao Marques-Silva

Alexey Ignatiev, Yacine Izza, Peter J. Stuckey, and Jo˜ao Marques-Silva. Using MaxSAT for efficient explana- tions of tree ensembles. In AAAI, pages 3776–3785. AAAI Press, 2022

2022
[16]

SAT-based rigorous explanations for decision lists

Alexey Ignatiev and Jo ˜ao Marques-Silva. SAT-based rigorous explanations for decision lists. In Chu-Min Li and Felip Many `a, editors, Theory and Applications of Satisfiability Testing - SAT , volume 12831 of Lecture Notes in Computer Science , pages 251–269. Springer, 2021

2021
[17]

Abduction-based explanations for machine learn- ing models

Alexey Ignatiev, Nina Narodytska, and Jo ˜ao Marques- Silva. Abduction-based explanations for machine learn- ing models. In AAAI, pages 1511–1519. AAAI Press, 2019

2019
[18]

On tackling explanation redundancy in decision trees.J

Yacine Izza, Alexey Ignatiev, and Jo ˜ao Marques-Silva. On tackling explanation redundancy in decision trees.J. Artif. Intell. Res., 75:261–321, 2022

2022
[19]

On explaining ran- dom forests with SAT

Yacine Izza and Jo˜ao Marques-Silva. On explaining ran- dom forests with SAT. In Zhi-Hua Zhou, editor, IJCAI, pages 2584–2591. ijcai.org, 2021

2021
[20]

Logic-based explainability: Past, present & future

Jo˜ao Marques-Silva. Logic-based explainability: Past, present & future. CoRR, abs/2406.11873, 2024

2024 arXiv
[21]

Cooper, Alexey Ignatiev, and Nina Narodytska

Jo˜ao Marques-Silva, Thomas Gerspacher, Martin C. Cooper, Alexey Ignatiev, and Nina Narodytska. Ex- plaining naive Bayes and other linear classifiers with polynomial time and delay. In Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Li...

2020
[22]

Cooper, Alexey Ignatiev, and Nina Narodytska

Jo˜ao Marques-Silva, Thomas Gerspacher, Martin C. Cooper, Alexey Ignatiev, and Nina Narodytska. Expla- nations for monotonic classifiers. In Marina Meila and Tong Zhang, editors, ICML, volume 139, pages 7469–
[23]

Interpretable machine learning - A brief history, state-of-the-art and challenges

Christoph Molnar, Giuseppe Casalicchio, and Bernd Bischl. Interpretable machine learning - A brief history, state-of-the-art and challenges. CoRR, abs/2010.09337, 2020

2010 arXiv
[24]

Stop explaining black box machine learning models for high stakes decisions and use inter- pretable models instead

Cynthia Rudin. Stop explaining black box machine learning models for high stakes decisions and use inter- pretable models instead. Nat. Mach. Intell. , 1(5):206– 215, 2019

2019
[25]

A sym- bolic approach to explaining bayesian network classi- fiers

Andy Shih, Arthur Choi, and Adnan Darwiche. A sym- bolic approach to explaining bayesian network classi- fiers. In J ´erˆome Lang, editor, IJCAI, pages 5103–5111. ijcai.org, 2018

2018

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Axiomatic foundations of explainability

Leila Amgoud and Jonathan Ben-Naim. Axiomatic foundations of explainability. In Luc De Raedt, editor, IJCAI, pages 636–642. ijcai.org, 2022

work page 2022

[2] [2]

Computational Com- plexity: A Modern Approach

Sanjeev Arora and Boaz Barak. Computational Com- plexity: A Modern Approach . Cambridge University Press, USA, 1st edition, 2009

work page 2009

[3] [3]

On the computational intelligibility of boolean classifiers

Gilles Audemard, Steve Bellart, Louenas Bounia, Fr´ed´eric Koriche, Jean-Marie Lagniez, and Pierre Mar- quis. On the computational intelligibility of boolean classifiers. In Meghyn Bienvenu, Gerhard Lakemeyer, and Esra Erdem, editors, KR, pages 74–86, 2021

work page 2021

[4] [4]

Model interpretability through the lens of computational complexity

Pablo Barcel ´o, Mika ¨el Monet, Jorge P ´erez, and Bernardo Subercaseaux. Model interpretability through the lens of computational complexity. In Hugo Larochelle, Marc’Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin, editors, NeurIPS, 2020

work page 2020

[5] [5]

Hypergraphs: Combinatorics of finite sets

Claude Berge. Hypergraphs: Combinatorics of finite sets. 1989

work page 1989

[6] [6]

The query complexity of certification

Guy Blanc, Caleb Koch, Jane Lange, and Li-Yang Tan. The query complexity of certification. In Stefano Leonardi and Anupam Gupta, editors, STOC ’22: 54th Annual ACM SIGACT Symposium on Theory of Com- puting, pages 623–636. ACM, 2022

work page 2022

[7] [7]

Leo Breiman, J. H. Friedman, Richard A. Olshen, and C. J. Stone. Classification and Regression Trees . Wadsworth, 1984

work page 1984

[8] [8]

Cooper, and Jo ˜ao Marques-Silva

Cl´ement Carbonnel, Martin C. Cooper, and Jo ˜ao Marques-Silva. Tractable explaining of multivariate de- cision trees. In Pierre Marquis, Tran Cao Son, and Gabriele Kern-Isberner, editors, KR, pages 127–135, 2023

work page 2023