@inproceedings{10.1007/978-3-031-08421-8_10,
    Abstract = {Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called domain liftable. In this paper, we reconstruct the closed-form formula for polynomial-time First Order Model Counting (FOMC) in the universally quantified fragment of FO{\$}{\$}^2{\$}{\$}2, earlier proposed by Beame et al.. We then expand this closed-form to incorporate cardinality constraints and existential quantifiers. Our approach requires a constant time (w.r.t the previous linear time result) for handling equality and allows us to handle cardinality constraints in a completely combinatorial fashion. Finally, we show that the obtained closed-form motivates a natural definition of a family of weight functions strictly larger than symmetric weight functions.},
    Address = {Cham},
    Author = {Malhotra, Sagar and Serafini, Luciano},
    BookTitle = {AIxIA 2021 -- Advances in Artificial Intelligence},
    Editor = {Bandini, Stefania and Gasparini, Francesca and Mascardi, Viviana and Palmonari, Matteo and Vizzari, Giuseppe},
    File = {transcript\_en.pdf},
    ISBN = {978-3-031-08421-8},
    Pages = {137--152},
    Publisher = {Springer International Publishing},
    Title = {A Combinatorial Approach to Weighted Model Counting in the Two-Variable Fragment with Cardinality Constraints},
    Year = {2022},
    date-added = {2023-07-06 07:30:02 +0200},
    date-modified = {2023-07-06 07:30:02 +0200},
    doi = {10.1007/978-3-031-08421-8_10}
}

@inproceedings{10.1007/978-3-031-08421-8_10, Abstract = {Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order logic theory on a given finite domain. First-Order Logic theories that admit polynomial-time WFOMC w.r.t domain cardinality are called domain liftable. In this paper, we reconstruct the closed-form formula for polynomial-time First Order Model Counting (FOMC) in the universally quantified fragment of FO{\$}{\$}^2{\$}{\$}2, earlier proposed by Beame et al.. We then expand this closed-form to incorporate cardinality constraints and existential quantifiers. Our approach requires a constant time (w.r.t the previous linear time result) for handling equality and allows us to handle cardinality constraints in a completely combinatorial fashion. Finally, we show that the obtained closed-form motivates a natural definition of a family of weight functions strictly larger than symmetric weight functions.}, Address = {Cham}, Author = {Malhotra, Sagar and Serafini, Luciano}, BookTitle = {AIxIA 2021 -- Advances in Artificial Intelligence}, Editor = {Bandini, Stefania and Gasparini, Francesca and Mascardi, Viviana and Palmonari, Matteo and Vizzari, Giuseppe}, File = {transcript_en.pdf}, ISBN = {978-3-031-08421-8}, Pages = {137--152}, Publisher = {Springer International Publishing}, Title = {A Combinatorial Approach to Weighted Model Counting in the Two-Variable Fragment with Cardinality Constraints}, Year = {2022}, date-added = {2023-07-06 07:30:02 +0200}, date-modified = {2023-07-06 07:30:02 +0200}, doi = {10.1007/978-3-031-08421-8_10} }