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- W4289694538 abstract "Given (1) a set of clauses $T$ in some first-order language $cal L$ and (2) a cost function $c : B_{{cal L}} rightarrow mathbb{R}_{+}$, mapping each ground atom in the Herbrand base $B_{{cal L}}$ to a non-negative real, then the problem of finding a minimal cost Herbrand model is to either find a Herbrand model $cal I$ of $T$ which is guaranteed to minimise the sum of the costs of true ground atoms, or establish that there is no Herbrand model for $T$. A branch-cut-and-price integer programming (IP) approach to solving this problem is presented. Since the number of ground instantiations of clauses and the size of the Herbrand base are both infinite in general, we add the corresponding IP constraints and IP variables `on the fly' via `cutting' and `pricing' respectively. In the special case of a finite Herbrand base we show that adding all IP variables and constraints from the outset can be advantageous, showing that a challenging Markov logic network MAP problem can be solved in this way if encoded appropriately." @default.
- W4289694538 created "2022-08-04" @default.
- W4289694538 creator A5072819898 @default.
- W4289694538 date "2018-08-14" @default.
- W4289694538 modified "2023-09-26" @default.
- W4289694538 title "Finding Minimal Cost Herbrand Models with Branch-Cut-and-Price" @default.
- W4289694538 doi "https://doi.org/10.48550/arxiv.1808.04758" @default.
- W4289694538 hasPublicationYear "2018" @default.
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