Definability for model counting

Lagniez, Jean-Marie; Lonca, Emmanuel; Marquis, Pierre

doi:10.1016/j.artint.2019.103229

Cited by 12 publications

(18 citation statements)

References 22 publications

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“…Finally, though Decision-DNNF does not offer FO in the general case, wherever the forgetting transformation is used for solving the XAI queries considered above, it concerns variables that are defined from unforgotten ones (those of X). In such a case, applying the forgetting algorithm that consists in replacing every decision node labelled by a variable from X by a ∨-node (while keeping the same two children) turns the Decision-DNNF cir-6 In addition, DNNF languages are quite succinct -actually, more than other candidates like OBDD or FBDD (Darwiche and Marquis 2002;Bova et al 2016) -, and there exist compilers targeting those languages when Σ is given at start as a CNF formula (Darwiche 2001;Darwiche 2004;Pipatsrisawat and Darwiche 2010;Muise et al 2012;Lagniez and Marquis 2017) cuit at hand into a d-DNNF circuit (see (Lagniez, Lonca, and Marquis 2020) for details). As a consequence, DPI is tractable when Σ is given as a Decision-DNNF circuit, and IIR and IMO are tractable when Σ is given as a structured Decision-DNNF circuit.…”

Section: Discussionmentioning

confidence: 99%

On Tractable XAI Queries based on Compiled Representations

Audemard

Koriche

Marquis

2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

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One of the key purposes of eXplainable AI (XAI) is to develop techniques for understanding predictions made by Machine Learning (ML) models and for assessing how much reliable they are. Several encoding schemas have recently been pointed out, showing how ML classifiers of various types can be mapped to Boolean circuits exhibiting the same input-output behaviours. Thanks to such mappings, XAI queries about classifiers can be delegated to the corresponding circuits. In this paper, we define new explanation and/or verification queries about classifiers. We show how they can be addressed by combining queries and transformations about the associated Boolean circuits. Taking advantage of previous results from the knowledge compilation map, this allows us to identify a number of XAI queries that are tractable provided that the circuit has been first turned into a compiled representation.

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Section: Discussionmentioning

confidence: 99%

On Tractable XAI Queries based on Compiled Representations

Audemard

Koriche

Marquis

2020

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning

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“…An interesting direction to address this scalability challenge is to investigate whether a component caching-based scheme operating natively over the space of MSSes, i.e., avoiding the reduction to model counting, can lead to a better runtime efficiency. Another line of future work is to evaluate other contemporary projected model counting tools such as nestHDB (Hecher, Thier, and Woltran 2020) or projMC (Lagniez and Marquis 2019), and to employ preprocessing techniques such as (Manthey 2012) or (Lagniez, Lonca, and Marquis 2020). Finally, we plan to examine an extension of our MSS counting approach to other constraint domains where MSSes find an application, e.g., F can be a set of LTL (Barnat et al 2016;Bendík 2017) or SMT (Guthmann, Strichman, and Trostanetski 2016) formulas.…”

Section: Discussionmentioning

confidence: 99%

Counting Maximal Satisfiable Subsets

Bendík

Meel

2021

AAAI

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Given an unsatisfiable set of constraints F, a maximal satisfiable subset (MSS) is a maximal subset of constraints C ⊆ F such that C is satisfiable. Over the past two decades, the steady improvement in runtime performance of algorithms for finding MSS has led to an increased adoption of MSS-based techniques in wide variety of domains. Motivated by the progress in finding an MSS, the past decade has witnessed a surge of interest in design of algorithmic techniques to enumerate all the MSSes, which has subsequently led to discovery of new applications utilizing enumeration of MSSes. The development of techniques for finding and enumeration of MSSes mirrors a similar phenomenon of finding and enumeration of SAT solutions in the early 2000s, which subsequently motivated design of algorithmic techniques for model counting. In a similar spirit, we undertake study to investigate the feasibility of MSS counting techniques. In particular, the focus point of our investigation is to answer whether one can design efficient MSS counting techniques that do not rely on explicit MSS enumeration. The primary contribution of this work is an affirmative answer to the above question. Our tool, CountMSS, uses a novel architecture of a wrapper W and a remainder R such that the desired MSS count can be expressed as |W| − |R|. CountMSS relies on the advances in projected model counting to efficiently compute |W| and |R|. Our empirical evaluation demonstrates that CountMSS is able to scale to instances clearly beyond the reach of enumeration-based techniques.

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“…Finally, since the performances of D4 over many CNF instances are typically boosted when those instances have been first preprocessed using pmc (Lagniez and Marquis 2017b) (or B+E (Lagniez, Lonca, and Marquis 2020) when D4 is used as a model counter), it would be useful to develop and evaluate certification techniques for such preprocessors. This would permit to take advantage of them upstream to CD4, while maintaining the certification requirement.…”

Section: Discussionmentioning

confidence: 99%

Certifying Top-Down Decision-DNNF Compilers

Capelli

Lagniez

Marquis

2021

AAAI

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Certifying the output of tools solving complex problems so as to ensure the correctness of the results they provide is of tremendous importance. Despite being widespread for SAT-solvers, this level of exigence has not yet percolated for tools solving more complex tasks, such as model counting or knowledge compilation. In this paper, the focus is laid on a general family of top-down Decision-DNNF compilers. We explain how those compilers can be tweaked so as to output certifiable Decision-DNNF circuits, which are mainly standard Decision-DNNF circuits decorated by annotations serving as certificates. We describe a polynomial-time checker for testing whether a given CNF formula is equivalent or not to a given certifiable Decision-DNNF circuit. Finally, leveraging a modified version of the compiler d4 for generating certifiable Decision-DNNF circuits and an implementation of the checker, we present the results of an empirical evaluation that has been conducted for assessing how large are in practice certifiable Decision-DNNF circuits, and how much time is needed to compute and to check such circuits.

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Definability for model counting

Cited by 12 publications

References 22 publications

On Tractable XAI Queries based on Compiled Representations

On Tractable XAI Queries based on Compiled Representations

Counting Maximal Satisfiable Subsets

Certifying Top-Down Decision-DNNF Compilers

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